{"id":1690,"date":"2017-10-27T16:32:41","date_gmt":"2017-10-27T16:32:41","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/nuclear-decay-and-conservation-laws\/"},"modified":"2017-11-08T03:27:50","modified_gmt":"2017-11-08T03:27:50","slug":"nuclear-decay-and-conservation-laws","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/chapter\/nuclear-decay-and-conservation-laws\/","title":{"raw":"Nuclear Decay and Conservation Laws","rendered":"Nuclear Decay and Conservation Laws"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Define and discuss nuclear decay.<\/li>\n<li>State the conservation laws.<\/li>\n<li>Explain parent and daughter nucleus.<\/li>\n<li>Calculate the energy emitted during nuclear decay.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id3035108\">Nuclear <span data-type=\"term\">decay<\/span> has provided an amazing window into the realm of the very small. Nuclear decay gave the first indication of the connection between mass and energy, and it revealed the existence of two of the four basic forces in nature. In this section, we explore the major modes of nuclear decay; and, like those who first explored them, we will discover evidence of previously unknown particles and conservation laws.<\/p>\n<p id=\"import-auto-id2688849\">Some nuclides are stable, apparently living forever. Unstable nuclides decay (that is, they are radioactive), eventually producing a stable nuclide after many decays. We call the original nuclide the <span data-type=\"term\">parent<\/span> and its decay products the <span data-type=\"term\" id=\"import-auto-id2429491\">daughters<\/span>. Some radioactive nuclides decay in a single step to a stable nucleus. For example, [latex]{}^{\\text{60}}\\text{Co}[\/latex] is unstable and decays directly to [latex]{}^{\\text{60}}\\text{Ni}[\/latex], which is stable. Others, such as [latex]{}^{\\text{238}}\\text{U}[\/latex], decay to another unstable nuclide, resulting in a <span data-type=\"term\" id=\"import-auto-id1518523\">decay series<\/span> in which each subsequent nuclide decays until a stable nuclide is finally produced. The decay series that starts from [latex]{}^{\\text{238}}\\text{U}[\/latex] is of particular interest, since it produces the radioactive isotopes [latex]{}^{\\text{226}}\\text{Ra}[\/latex] and [latex]{}^{\\text{210}}\\text{Po}[\/latex], which the Curies first discovered (see <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a>). Radon gas is also produced ([latex]{}^{\\text{222}}\\text{Rn}[\/latex] in the series), an increasingly recognized naturally occurring hazard. Since radon is a noble gas, it emanates from materials, such as soil, containing even trace amounts of [latex]{}^{\\text{238}}\\text{U}[\/latex] and can be inhaled. The decay of radon and its daughters produces internal damage. The [latex]{}^{\\text{238}}\\text{U}[\/latex] decay series ends with [latex]{}^{\\text{206}}\\text{Pb}[\/latex], a stable isotope of lead.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1930472\">\n<div class=\"bc-figcaption figcaption\">The decay series produced by [latex]{}^{\\text{238}}\\text{U}[\/latex], the most common uranium isotope. Nuclides are graphed in the same manner as in the chart of nuclides. The type of decay for each member of the series is shown, as well as the half-lives. Note that some nuclides decay by more than one mode. You can see why radium and polonium are found in uranium ore. A stable isotope of lead is the end product of the series.<\/div>\n<p><span data-type=\"media\" data-alt=\"A graph is shown in which decay of alpha and beta is shown. Also half lives of each isotope are shown. Uranium decays in one mode but some isotopes decay by more than one mode. Finally a stable isotope of lead results.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"A graph is shown in which decay of alpha and beta is shown. Also half lives of each isotope are shown. Uranium decays in one mode but some isotopes decay by more than one mode. Finally a stable isotope of lead results.\" width=\"360\"><\/span><\/p><\/div>\n<p id=\"import-auto-id1916253\">Note that the daughters of [latex]\\alpha [\/latex] decay shown in <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a> always have two fewer protons and two fewer neutrons than the parent. This seems reasonable, since we know that [latex]\\alpha [\/latex] decay is the emission of a [latex]{}^{4}\\text{He}[\/latex] nucleus, which has two protons and two neutrons. The daughters of [latex]\\beta [\/latex] decay have one less neutron and one more proton than their parent. Beta decay is a little more subtle, as we shall see. No [latex]\\gamma [\/latex] decays are shown in the figure, because they do not produce a daughter that differs from the parent.<\/p>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Alpha Decay<\/h1>\n<p id=\"import-auto-id1206958\">In <span data-type=\"term\">alpha decay<\/span>, a [latex]{}^{4}\\text{He}[\/latex] nucleus simply breaks away from the parent nucleus, leaving a daughter with two fewer protons and two fewer neutrons than the parent (see <a href=\"#import-auto-id3078027\" class=\"autogenerated-content\">(Figure)<\/a>). One example of [latex]\\alpha [\/latex] decay is shown in <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a> for [latex]{}^{\\text{238}}\\text{U}[\/latex]. Another nuclide that undergoes [latex]\\alpha [\/latex] decay is [latex]{}^{\\text{239}}\\text{Pu}[\/latex]. The decay equations for these two nuclides are<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}^{\\text{238}}\\text{U}\\to {}^{\\text{234}}{\\text{Th}}_{\\text{92}}^{\\text{234}}+{}^{4}\\text{He}[\/latex]<\/div>\n<p id=\"import-auto-id1403527\">and<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}^{\\text{239}}\\text{Pu}\\to {}^{\\text{235}}\\text{U}+{}^{4}\\text{He}.[\/latex]<\/div>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Alpha decay is the separation of a [latex]{}^{4}\\text{He}[\/latex] nucleus from the parent. The daughter nucleus has two fewer protons and two fewer neutrons than the parent. Alpha decay occurs spontaneously only if the daughter and [latex]{}^{4}\\text{He}[\/latex] nucleus have less total mass than the parent.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1386075\" data-alt=\"The image shows conditions before and after alpha decay. Before alpha decay the nucleus is labeled parent and after decay the nucleus is labeled daughter.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"The image shows conditions before and after alpha decay. Before alpha decay the nucleus is labeled parent and after decay the nucleus is labeled daughter.\" width=\"200\"><\/span><\/p><\/div>\n<p id=\"import-auto-id3007716\">If you examine the periodic table of the elements, you will find that Th has [latex]Z=\\text{90}[\/latex], two fewer than U, which has [latex]Z=\\text{92}[\/latex]. Similarly, in the second <span data-type=\"term\">decay equation<\/span>, we see that U has two fewer protons than Pu, which has [latex]Z=\\text{94}[\/latex]. The general rule for [latex]\\alpha [\/latex] decay is best written in the format [latex]{}_{Z}^{A}{\\text{X}}_{N}[\/latex]. If a certain nuclide is known to [latex]\\alpha [\/latex] decay (generally this information must be looked up in a table of isotopes, such as in <a href=\"\/contents\/666f5335-e742-451e-b7ff-245efeff8bd9@2\">Appendix B<\/a>), its [latex]\\alpha [\/latex]<span data-type=\"term\" id=\"import-auto-id2930041\"> decay equation<\/span> is<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}^{A}{\\text{X}}_{N}\\to {}_{Z-2}^{A-4}{\\text{Y}}_{N-2}+{}_{2}^{4}{\\text{He}}_{2}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\left(\\alpha \\phantom{\\rule{0.25em}{0ex}}\\text{decay}\\right)[\/latex]<\/div>\n<p id=\"import-auto-id1825060\">where Y is the nuclide that has two fewer protons than X, such as Th having two fewer than U. So if you were told that [latex]{}^{\\text{239}}\\text{Pu}[\/latex] [latex]\\alpha [\/latex] decays and were asked to write the complete decay equation, you would first look up which element has two fewer protons (an atomic number two lower) and find that this is uranium. Then since four nucleons have broken away from the original 239, its atomic mass would be 235.<\/p>\n<p id=\"import-auto-id2639290\">It is instructive to examine conservation laws related to [latex]\\alpha [\/latex] decay. You can see from the equation [latex]{}_{Z}^{A}{\\text{X}}_{N}\\to {}_{Z-2}^{A-4}{\\text{Y}}_{N-2}+{}_{2}^{4}{\\text{He}}_{2}[\/latex]  that total charge is conserved. Linear and angular momentum are conserved, too. Although conserved angular momentum is not of great consequence in this type of decay, conservation of linear momentum has interesting consequences. If the nucleus is at rest when it decays, its momentum is zero. In that case, the fragments must fly in opposite directions with equal-magnitude momenta so that total momentum remains zero. This results in the [latex]\\alpha [\/latex]<em data-effect=\"italics\"> particle carrying away most of the energy, as a bullet from a heavy rifle carries away most of the energy of the powder burned to shoot it. Total mass\u2013energy is also conserved: the energy produced in the decay comes from conversion of a fraction of the original mass. As discussed in <a href=\"\/contents\/05208266-2374-4008-9060-7ddddbe877f2@2\">Atomic Physics<\/a>, the general relationship is<\/em><\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]E\\phantom{\\rule{0.15em}{0ex}}=\\left(\\Delta m\\right){c}^{2}.[\/latex]<\/div>\n<p id=\"import-auto-id3181645\">Here, [latex]E[\/latex] is the <span data-type=\"term\" id=\"import-auto-id3403043\">nuclear reaction energy<\/span> (the reaction can be nuclear decay or any other reaction), and [latex]\\Delta m[\/latex] is the difference in mass between initial and final products. When the final products have less total mass, [latex]\\Delta m[\/latex] is positive, and the reaction releases energy (is exothermic). When the products have greater total mass, the reaction is endothermic ([latex]\\Delta m[\/latex] is negative) and must be induced with an energy input. For [latex]\\alpha [\/latex] decay to be spontaneous, the decay products must have smaller mass than the parent.<\/p>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1816061\">\n<div data-type=\"title\" class=\"title\">Alpha Decay Energy Found from Nuclear Masses<\/div>\n<p id=\"import-auto-id1547918\">Find the energy emitted in the [latex]\\alpha [\/latex] decay of [latex]{}^{\\text{239}}\\text{Pu}[\/latex].<\/p>\n<p id=\"import-auto-id3013051\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id2661877\">Nuclear reaction energy, such as released in <em data-effect=\"italics\">\u03b1<\/em> decay, can be found using the equation [latex]E=\\left(\\Delta m\\right){c}^{2}[\/latex]. We must first find [latex]\\Delta m[\/latex], the difference in mass between the parent nucleus and the products of the decay. This is easily done using masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a>.<\/p>\n<p id=\"import-auto-id2662636\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id3095513\">The decay equation was given earlier for [latex]{}^{\\text{239}}\\text{Pu}[\/latex] ; it is<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}^{\\text{239}}\\text{Pu}\\to {}^{\\text{235}}\\text{U}+{}^{4}\\text{He}.[\/latex]<\/div>\n<p id=\"import-auto-id2684784\">Thus the pertinent masses are those of [latex]{}^{\\text{239}}\\text{Pu}[\/latex], [latex]{}^{\\text{235}}\\text{U}[\/latex], and the [latex]\\alpha [\/latex] particle or [latex]{}^{4}\\text{He}[\/latex], all of which are listed in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a>. The initial mass was [latex]m{\\left(}^{\\text{239}}\\text{Pu}\\right)=\\text{239}\\text{.}\\text{052157 u}[\/latex]. The final mass is the sum [latex]m{\\left(}^{\\text{235}}\\text{U}\\right)\\text{+}m{\\left(}^{4}\\text{He}\\right)\\text{= 235}\\text{.}\\text{043924 u + 4.002602 u = 239.046526 u}[\/latex]. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\begin{array}{lll}\\Delta m&amp; =&amp; m{\\left(}^{\\text{239}}\\text{Pu}\\right)-\\left[m{\\left(}^{\\text{235}}\\text{U}\\right)+m\\left({}^{4}\\text{He}\\right)\\right]\\\\ &amp; =&amp; \\text{}\\text{239.052157 u}-\\text{239.046526 u}\\\\ &amp; =&amp; \\text{0.0005631 u.}\\end{array}[\/latex]<\/div>\n<p>Now we can find [latex]E[\/latex] by entering [latex]\\Delta m[\/latex] into the equation:<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]E=\\left(\\Delta m\\right){c}^{2}=\\left(0\\text{.005631 u}\\right){c}^{2}.[\/latex]<\/div>\n<p>We know [latex]\\text{1 u}=\\text{931.5 MeV\/}{c}^{2}[\/latex], and so<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-101\">[latex]E=\\left(0\\text{.}\\text{005631}\\right)\\left(\\text{931.5 MeV}\/{c}^{2}\\right)\\left({c}^{2}\\right)=\\text{5.25 MeV}.[\/latex]<\/div>\n<p><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1856748\">The energy released in this [latex]\\alpha [\/latex] decay is in the [latex]\\text{MeV}[\/latex] range, about [latex]{\\text{10}}^{6}[\/latex] times as great as typical chemical reaction energies, consistent with many previous discussions. Most of this energy becomes kinetic energy of the [latex]\\alpha [\/latex] particle (or [latex]{}^{4}\\text{He}[\/latex] nucleus), which moves away at high speed. The energy carried away by the recoil of the [latex]{}^{\\text{235}}\\text{U}[\/latex] nucleus is much smaller in order to conserve momentum. The [latex]{}^{\\text{235}}\\text{U}[\/latex] nucleus can be left in an excited state to later emit photons ([latex]\\gamma [\/latex] rays). This decay is spontaneous and releases energy, because the products have less mass than the parent nucleus. The question of why the products have less mass will be discussed in <a href=\"\/contents\/e12b60f5-72df-401e-a1b1-7f13fd61eee0@5\">Binding Energy<\/a>. Note that the masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> are atomic masses of neutral atoms, including their electrons. The mass of the electrons is the same before and after [latex]\\alpha [\/latex] decay, and so their masses subtract out when finding [latex]\\Delta m[\/latex]. In this case, there are 94 electrons before and after the decay.<\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Beta Decay<\/h1>\n<p id=\"import-auto-id2445383\">There are actually <em data-effect=\"italics\">three<\/em> types of <span data-type=\"term\">beta decay<\/span>. The first discovered was \u201cordinary\u201d beta decay and is called [latex]{\\beta }^{-}[\/latex] decay or electron emission. The symbol [latex]{\\beta }^{-}[\/latex] represents <em data-effect=\"italics\">an electron emitted in nuclear beta decay<\/em>. Cobalt-60 is a nuclide that [latex]{\\beta }^{-}[\/latex] decays in the following manner:<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}^{\\text{60}}\\text{Co}\\to {}^{\\text{60}}\\text{Ni}+{\\beta }^{-}+\\text{neutrino.}[\/latex]<\/div>\n<p id=\"import-auto-id3037465\">The <span data-type=\"term\" id=\"import-auto-id1917824\">neutrino<\/span> is a particle emitted in beta decay that was unanticipated and is of fundamental importance. The neutrino was not even proposed in theory until more than 20 years after beta decay was known to involve electron emissions. Neutrinos are so difficult to detect that the first direct evidence of them was not obtained until 1953. Neutrinos are nearly massless, have no charge, and do not interact with nucleons via the strong nuclear force. Traveling approximately at the speed of light, they have little time to affect any nucleus they encounter. This is, owing to the fact that they have no charge (and they are not EM waves), they do not interact through the EM force. They do interact via the relatively weak and very short range weak nuclear force. Consequently, neutrinos escape almost any detector and penetrate almost any shielding. However, neutrinos do carry energy, angular momentum (they are fermions with half-integral spin), and linear momentum away from a beta decay. When accurate measurements of beta decay were made, it became apparent that energy, angular momentum, and linear momentum were not accounted for by the daughter nucleus and electron alone. Either a previously unsuspected particle was carrying them away, or three conservation laws were being violated. Wolfgang Pauli made a formal proposal for the existence of neutrinos in 1930. The Italian-born American physicist Enrico Fermi (1901\u20131954) gave neutrinos their name, meaning little neutral ones, when he developed a sophisticated theory of beta decay (see <a href=\"#import-auto-id2672424\" class=\"autogenerated-content\">(Figure)<\/a>). Part of Fermi\u2019s theory was the identification of the weak nuclear force as being distinct from the strong nuclear force and in fact responsible for beta decay.<\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Enrico Fermi was nearly unique among 20th-century physicists\u2014he made significant contributions both as an experimentalist and a theorist. His many contributions to theoretical physics included the identification of the weak nuclear force. The fermi (fm) is named after him, as are an entire class of subatomic particles (fermions), an element (Fermium), and a major research laboratory (Fermilab). His experimental work included studies of radioactivity, for which he won the 1938 Nobel Prize in physics, and creation of the first nuclear chain reaction. (credit: United States Department of Energy, Office of Public Affairs)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1117770\" data-alt=\"Photo of physicist Enrico Fermi.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_03a.jpg\" data-media-type=\"image\/png\" alt=\"Photo of physicist Enrico Fermi.\" width=\"200\"><\/span><\/p><\/div>\n<p id=\"import-auto-id3127102\">The neutrino also reveals a new conservation law. There are various families of particles, one of which is the electron family. We propose that the number of members of the electron family is constant in any process or any closed system. In our example of beta decay, there are no members of the electron family present before the decay, but after, there is an electron and a neutrino. So electrons are given an electron family number of [latex]+1[\/latex]. The neutrino in [latex]{\\beta }^{-}[\/latex] decay is an <span data-type=\"term\">electron\u2019s antineutrino<\/span>, given the symbol [latex]{\\overline{\\nu }}_{e}[\/latex], where [latex]\\nu [\/latex] is the Greek letter nu, and the subscript <em data-effect=\"italics\">e<\/em> means this neutrino is related to the electron. The bar indicates this is a particle of <span data-type=\"term\">antimatter<\/span>. (All particles have antimatter counterparts that are nearly identical except that they have the opposite charge. Antimatter is almost entirely absent on Earth, but it is found in nuclear decay and other nuclear and particle reactions as well as in outer space.) The electron\u2019s antineutrino [latex]{\\overline{\\nu }}_{e}[\/latex], being antimatter, has an electron family number of [latex]\u20131[\/latex]. The total is zero, before and after the decay. The new conservation law, obeyed in all circumstances, states that the <em data-effect=\"italics\">total electron family number is constant<\/em>. An electron cannot be created without also creating an antimatter family member. This law is analogous to the conservation of charge in a situation where total charge is originally zero, and equal amounts of positive and negative charge must be created in a reaction to keep the total zero.<\/p>\n<p id=\"import-auto-id3199526\">If a nuclide [latex]{}_{Z}^{A}{X}_{N}[\/latex] is known to [latex]{\\beta }^{-}[\/latex] decay, then its [latex]{\\beta }^{-}[\/latex]<strong data-effect=\"bold\"> decay equation is<\/strong><\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}{}^{A}\\text{}{\\text{X}}_{N}\\to {}_{Z+1}{}^{A}\\text{}{\\text{Y}}_{N-1}+{\\beta }^{-}+{\\stackrel{-}{\\nu }}_{e}\\phantom{\\rule{0.25em}{0ex}}\\left({\\beta }^{-}\\phantom{\\rule{0.25em}{0ex}}\\text{decay}\\right),[\/latex]<\/div>\n<p id=\"import-auto-id1815384\">where Y is the nuclide having one more proton than X (see <a href=\"#import-auto-id2446798\" class=\"autogenerated-content\">(Figure)<\/a>). So if you know that a certain nuclide [latex]{\\beta }^{-}[\/latex] decays, you can find the daughter nucleus by first looking up<br>\n[latex]Z[\/latex] for the parent and then determining which element has atomic number<br>\n[latex]Z+1[\/latex]. In the example of the<br>\n[latex]{\\beta }^{-}[\/latex] decay of<br>\n[latex]{}^{\\text{60}}\\text{Co}[\/latex] given earlier, we see that [latex]Z=\\text{27}[\/latex] for Co and<br>\n[latex]Z=\\text{28}[\/latex] is Ni. It is as if one of the neutrons in the parent nucleus decays into a proton, electron, and neutrino. In fact, neutrons outside of nuclei do just that\u2014they live only an average of a few minutes and<br>\n[latex]{\\beta }^{-}[\/latex] decay in the following manner:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-828\">[latex]\\text{n}\\to \\text{p}+{\\beta }^{-}+{\\stackrel{-}{\\nu }}_{e}.[\/latex]<\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2446798\">\n<div class=\"bc-figcaption figcaption\">In [latex]{\\beta }^{-}[\/latex] decay, the parent nucleus emits an electron and an antineutrino. The daughter nucleus has one more proton and one less neutron than its parent. Neutrinos interact so weakly that they are almost never directly observed, but they play a fundamental role in particle physics.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2209887\" data-alt=\"Image shows parent nucleus before beta decay and daughter nucleus after beta decay.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_04a.jpg\" data-media-type=\"image\/jpg\" alt=\"Image shows parent nucleus before beta decay and daughter nucleus after beta decay.\" width=\"200\"><\/span><\/p><\/div>\n<p id=\"import-auto-id3178054\">We see that charge is conserved in [latex]{\\beta }^{-}[\/latex] decay, since the total charge is [latex]Z[\/latex] before and after the decay. For example, in [latex]{}^{\\text{60}}\\text{Co}[\/latex] decay, total charge is 27 before decay, since cobalt has<br>\n[latex]Z=\\text{27}[\/latex]. After decay, the daughter nucleus is Ni, which has<br>\n[latex]Z=\\text{28}[\/latex], and there is an electron, so that the total charge is also [latex]28 + \\left(\u20131\\right)[\/latex] or 27. Angular momentum is conserved, but not obviously (you have to examine the spins and angular momenta of the final products in detail to verify this). Linear momentum is also conserved, again imparting most of the decay energy to the electron and the antineutrino, since they are of low and zero mass, respectively. Another new conservation law is obeyed here and elsewhere in nature. <em data-effect=\"italics\">The total number of nucleons [latex]A[\/latex] is conserved<\/em>. In<br>\n[latex]{}^{\\text{60}}\\text{Co}[\/latex] decay, for example, there are 60 nucleons before and after the decay. Note that total<br>\n[latex]A[\/latex] is also conserved in<br>\n[latex]\\alpha [\/latex] decay. Also note that the total number of protons changes, as does the total number of neutrons, so that total<br>\n[latex]Z[\/latex] and total [latex]N[\/latex] are <em data-effect=\"italics\">not<\/em> conserved in [latex]{\\beta }^{-}[\/latex] decay, as they are in [latex]\\alpha [\/latex] decay. Energy released in [latex]{\\beta }^{-}[\/latex] decay can be calculated given the masses of the parent and products.<\/p>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1823899\">\n<div data-type=\"title\" class=\"title\">[latex]{\\beta }^{-}[\/latex] Decay Energy from Masses<\/div>\n<p id=\"import-auto-id2406059\">Find the energy emitted in the [latex]{\\beta }^{-}[\/latex] decay of [latex]{}^{\\text{60}}\\text{Co}[\/latex].<\/p>\n<p id=\"import-auto-id2673414\"><strong>Strategy and Concept<\/strong><\/p>\n<p id=\"import-auto-id2684991\">As in the preceding example, we must first find [latex]\\Delta m[\/latex], the difference in mass between the parent nucleus and the products of the decay, using masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a>. Then the emitted energy is calculated as before, using [latex]E=\\left(\\Delta m\\right){c}^{2}[\/latex]. The initial mass is just that of the parent nucleus, and the final mass is that of the daughter nucleus and the electron created in the decay. The neutrino is massless, or nearly so. However, since the masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> are for neutral atoms, the daughter nucleus has one more electron than the parent, and so the extra electron mass that corresponds to the [latex]{\\beta }^{\u2013}[\/latex] is included in the atomic mass of Ni. Thus, <\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\Delta m=m\\left({}^{\\text{60}}\\text{Co}\\right)-m\\left({}^{\\text{60}}\\text{Ni}\\right).[\/latex]<\/div>\n<p id=\"import-auto-id3257037\"><strong>Solution<\/strong><\/p>\n<p>The [latex]{\\beta }^{-}[\/latex] decay equation for [latex]{}^{\\text{60}}\\text{Co}[\/latex] is<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{\\text{27}}^{\\text{60}}{\\text{Co}}_{\\text{33}}\\to {}_{\\text{28}}^{\\text{60}}{\\text{Ni}}_{\\text{32}}+{\\beta }^{-}+{\\overline{\\nu }}_{e}.[\/latex]<\/div>\n<p>As noticed,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-371\">[latex]\\Delta m=m\\left({}^{\\text{60}}\\text{Co}\\right)-m\\left({}^{\\text{60}}\\text{Ni}\\right).[\/latex]<\/div>\n<p>Entering the masses found in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> gives<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\Delta m=\\text{59}\\text{.}\\text{933820 u}-\\text{59.930789 u}=\\text{0.003031 u}.[\/latex]<\/div>\n<p id=\"import-auto-id2209670\">Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]E=\\left(\\Delta m\\right){c}^{2}=\\left(\\text{0.003031 u}\\right){c}^{2}.[\/latex]<\/div>\n<p id=\"import-auto-id3259992\">Using [latex]1 u=931.5 MeV\/{c}^{2}[\/latex], we obtain<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]E=\\left(0\\text{.}\\text{003031}\\right)\\left(931.5 MeV\/{c}^{2}\\right)\\left({c}^{2}\\right)=2\\text{.}\\text{82 MeV.}[\/latex]<\/div>\n<p id=\"import-auto-id3421994\"><strong>Discussion and Implications<\/strong><\/p>\n<p id=\"import-auto-id3054780\">Perhaps the most difficult thing about this example is convincing yourself that the [latex]{\\beta }^{-}[\/latex] mass is included in the atomic mass of [latex]{}^{\\text{60}}\\text{Ni}[\/latex]. Beyond that are other implications. Again the decay energy is in the MeV range. This energy is shared by all of the products of the decay. In many [latex]{}^{\\text{60}}\\text{Co}[\/latex] decays, the daughter nucleus [latex]{}^{\\text{60}}\\text{Ni}[\/latex] is left in an excited state and emits photons (<br>\n[latex]\\gamma [\/latex] rays). Most of the remaining energy goes to the electron and neutrino, since the recoil kinetic energy of the daughter nucleus is small. One final note: the electron emitted in [latex]{\\beta }^{-}[\/latex] decay is created in the nucleus at the time of decay.<\/p>\n<\/div>\n<p id=\"import-auto-id3063962\">The second type of beta decay is less common than the first. It is [latex]{\\beta }^{+}[\/latex]decay. Certain nuclides decay by the emission of a <em data-effect=\"italics\">positive<\/em> electron. This is <span data-type=\"term\" id=\"import-auto-id1539094\">antielectron<\/span> or <span data-type=\"term\" id=\"import-auto-id3340946\">positron decay<\/span> (see <a href=\"#import-auto-id3250027\" class=\"autogenerated-content\">(Figure)<\/a>).<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id3250027\">\n<div class=\"bc-figcaption figcaption\">[latex]{\\beta }^{+}[\/latex] decay is the emission of a positron that eventually finds an electron to annihilate, characteristically producing gammas in opposite directions.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3250028\" data-alt=\"Image shows parent nucleus before beta plus decay and daughter nucleus after beta plus decay, which results in a positively charged electron called a positron.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_05a.jpg\" data-media-type=\"image\/jpg\" alt=\"Image shows parent nucleus before beta plus decay and daughter nucleus after beta plus decay, which results in a positively charged electron called a positron.\" width=\"200\"><\/span><\/p><\/div>\n<p>The antielectron is often represented by the symbol [latex]{e}^{+}[\/latex], but in beta decay it is written as [latex]{\\beta }^{+}[\/latex] to indicate the antielectron was emitted in a nuclear decay. Antielectrons are the antimatter counterpart to electrons, being nearly identical, having the same mass, spin, and so on, but having a positive charge and an electron family number of [latex]\u20131[\/latex]. When a <span data-type=\"term\">positron<\/span> encounters an electron, there is a mutual annihilation in which all the mass of the antielectron-electron pair is converted into pure photon energy. (The reaction, [latex]{e}^{+}+{e}^{-}\\to \\gamma +\\gamma [\/latex], conserves electron family number as well as all other conserved quantities.) If a nuclide [latex]{}_{Z}^{A}{X}_{N}[\/latex] is known to [latex]{\\beta }^{+}[\/latex] decay, then its [latex]{\\beta }^{+}[\/latex]<strong data-effect=\"bold\"><span data-type=\"term\" id=\"import-auto-id3102703\">decay equation<\/span> is<\/strong><\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}^{A}{\\text{X}}_{N}\\to {}_{Z-1}{}^{A}\\text{}{\\text{Y}}_{N+1}+{\\beta }^{+}+{\\nu }_{e}\\phantom{\\rule{0.25em}{0ex}}\\left({\\beta }^{+}\\phantom{\\rule{0.25em}{0ex}}\\text{decay}\\right),[\/latex]<\/div>\n<p id=\"import-auto-id1447217\">where Y is the nuclide having one less proton than X (to conserve charge) and [latex]{\\nu }_{e}[\/latex] is the symbol for the <span data-type=\"term\" id=\"import-auto-id1815789\">electron\u2019s neutrino<\/span>, which has an electron family number of [latex]+1[\/latex]. Since an antimatter member of the electron family (the [latex]{\\beta }^{+}[\/latex]) is created in the decay, a matter member of the family (here the [latex]{\\nu }_{e}[\/latex]) must also be created. Given, for example, that<br>\n[latex]{}^{\\text{22}}\\text{Na}[\/latex]<br>\n[latex]{\\beta }^{+}[\/latex] decays, you can write its full decay equation by first finding that [latex]Z=\\text{11}[\/latex] for [latex]{}^{\\text{22}}\\text{Na}[\/latex], so that the daughter nuclide will have<br>\n[latex]Z=\\text{10}[\/latex], the atomic number for neon. Thus the [latex]{\\beta }^{+}[\/latex] decay equation for [latex]{}^{\\text{22}}\\text{Na}[\/latex] is<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{\\text{11}}^{\\text{22}}{\\text{Na}}_{\\text{11}}\\to {}_{\\text{10}}^{\\text{22}}{\\text{Ne}}_{\\text{12}}+{\\beta }^{+}+{\\nu }_{e}.[\/latex]<\/div>\n<p id=\"import-auto-id2429706\">In [latex]{\\beta }^{+}[\/latex] decay, it is as if one of the protons in the parent nucleus decays into a neutron, a positron, and a neutrino. Protons do not do this outside of the nucleus, and so the decay is due to the complexities of the nuclear force. Note again that the total number of nucleons is constant in this and any other reaction. To find the energy emitted in [latex]{\\beta }^{+}[\/latex] decay, you must again count the number of electrons in the neutral atoms, since atomic masses are used. The daughter has one less electron than the parent, and one electron mass is created in the decay. Thus, in [latex]{\\beta }^{+}[\/latex] decay,<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]\\Delta m=m\\left(\\text{parent}\\right)-\\left[m\\left(\\text{daughter}\\right)+{2m}_{e}\\right],[\/latex]<\/div>\n<p id=\"import-auto-id3397934\">since we use the masses of neutral atoms.<\/p>\n<p><span data-type=\"term\">Electron capture<\/span> is the third type of beta decay. Here, a nucleus captures an inner-shell electron and undergoes a nuclear reaction that has the same effect as [latex]{\\beta }^{+}[\/latex] decay. Electron capture is sometimes denoted by the letters EC. We know that electrons cannot reside in the nucleus, but this is a nuclear reaction that consumes the electron and occurs spontaneously only when the products have less mass than the parent plus the electron. If a nuclide [latex]{}_{Z}^{A}{X}_{N}[\/latex] is known to undergo electron capture, then its <span data-type=\"term\" id=\"import-auto-id3137718\">electron capture equation<\/span> is<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"fs-id877331\">[latex]{}_{Z}^{A}{\\text{X}}_{N}+{e}^{-}\\to {}_{Z-1}{}^{A}\\text{}{\\text{Y}}_{N+1}+{\\nu }_{e}\\left(\\text{electron capture, or EC}\\right)\\text{.}[\/latex]<\/div>\n<p id=\"import-auto-id2654139\">Any nuclide that can [latex]{\\beta }^{+}[\/latex] decay can also undergo electron capture (and often does both). The same conservation laws are obeyed for EC as for [latex]{\\beta }^{+}[\/latex] decay. It is good practice to confirm these for yourself.<\/p>\n<p id=\"import-auto-id3163016\">All forms of beta decay occur because the parent nuclide is unstable and lies outside the region of stability in the chart of nuclides. Those nuclides that have relatively more neutrons than those in the region of stability will [latex]{\\beta }^{-}[\/latex] decay to produce a daughter with fewer neutrons, producing a daughter nearer the region of stability. Similarly, those nuclides having relatively more protons than those in the region of stability will [latex]{\\beta }^{-}[\/latex] decay or undergo electron capture to produce a daughter with fewer protons, nearer the region of stability.<\/p>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id3012414\">\n<h1 data-type=\"title\">Gamma Decay<\/h1>\n<p id=\"import-auto-id2928558\"><span data-type=\"term\">Gamma decay<\/span> is the simplest form of nuclear decay\u2014it is the emission of energetic photons by nuclei left in an excited state by some earlier process. Protons and neutrons in an excited nucleus are in higher orbitals, and they fall to lower levels by photon emission (analogous to electrons in excited atoms). Nuclear excited states have lifetimes typically of only about [latex]{\\text{10}}^{-\\text{14}}[\/latex] s, an indication of the great strength of the forces pulling the nucleons to lower states. The [latex]\\gamma [\/latex] decay equation is simply<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"fs-id1253157\">[latex]{}_{Z}^{A}{\\text{X}}_{N}^{*}\\to {}_{Z}{}^{A}\\text{}{\\text{X}}_{N}+{\\gamma }_{1}+{\\gamma }_{2}+\\cdots \\phantom{\\rule{0.25em}{0ex}}\\left(\\gamma \\phantom{\\rule{0.25em}{0ex}}\\text{decay}\\right)[\/latex]<\/div>\n<p id=\"import-auto-id3402401\">where the asterisk indicates the nucleus is in an excited state. There may be one or more [latex]\\gamma [\/latex] s emitted, depending on how the nuclide de-excites. In radioactive decay, [latex]\\gamma [\/latex] emission is common and is preceded by [latex]\\gamma [\/latex] or [latex]\\beta [\/latex] decay. For example, when [latex]{}^{\\text{60}}\\text{Co}[\/latex] [latex]{\\beta }^{-}[\/latex] decays, it most often leaves the daughter nucleus in an excited state, written [latex]{}^{\\text{60}}\\text{Ni*}[\/latex]. Then the nickel nucleus quickly [latex]\\gamma [\/latex] decays by the emission of two penetrating [latex]\\gamma [\/latex] s:<\/p>\n<div data-type=\"equation\" class=\"equation\">[latex]{}^{\\text{60}}\\text{Ni*}\\to {}^{\\text{60}}\\text{Ni}+{\\gamma }_{1}+{\\gamma }_{2}.[\/latex]<\/div>\n<p id=\"import-auto-id3008135\">These are called cobalt [latex]\\gamma [\/latex] rays, although they come from nickel\u2014they are used for cancer therapy, for example. It is again constructive to verify the conservation laws for gamma decay. Finally, since [latex]\\gamma [\/latex] decay does not change the nuclide to another species, it is not prominently featured in charts of decay series, such as that in <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a>.<\/p>\n<p id=\"import-auto-id1473699\">There are other types of nuclear decay, but they occur less commonly than [latex]\\alpha [\/latex], <\/p>\n<p>[latex]\\beta [\/latex], and [latex]\\gamma [\/latex] decay. Spontaneous fission is the most important of the other forms of nuclear decay because of its applications in nuclear power and weapons. It is covered in the next chapter.<\/p>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id3032498\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id2621009\">\n<li id=\"import-auto-id2681094\">When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay, called alpha [latex]\\left(\\alpha \\right),[\/latex] beta [latex]\\left(\\beta \\right),[\/latex] and gamma [latex]\\left(\\gamma \\right)[\/latex]. The [latex]\\alpha [\/latex]  decay equation is\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}^{A}{X}_{N}\\to {}_{Z-2}^{A-4}{\\text{Y}}_{N-2}+{}_{2}^{4}{\\text{He}}_{2}.[\/latex]<\/div>\n<\/li>\n<li id=\"import-auto-id2402192\">Nuclear decay releases an amount of energy [latex]E[\/latex] related to the mass destroyed [latex]\\Delta m[\/latex] by\n<div data-type=\"equation\" class=\"equation\">[latex]E=\\left(\\Delta m\\right){c}^{2}.[\/latex]<\/div>\n<\/li>\n<li id=\"import-auto-id3450034\">There are three forms of beta decay. The [latex]{\\beta }^{-}[\/latex]decay equation is\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}^{A}{X}_{N}\\to {}_{Z+1}^{A}{\\text{Y}}_{N-1}+{\\beta }^{-}+{\\overline{\\nu }}_{e}.[\/latex]<\/div>\n<\/li>\n<li id=\"import-auto-id1614644\">The [latex]{\\beta }^{+}[\/latex] decay equation is\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}^{A}{X}_{N}\\to {}_{Z-1}^{A}{\\text{Y}}_{N+1}+{\\beta }^{+}+{\\nu }_{e}.[\/latex]<\/div>\n<\/li>\n<li id=\"import-auto-id3149618\">The electron capture equation is\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}^{A}{X}_{N}+{e}^{-}\\to {}_{Z-1}^{A}{\\text{Y}}_{N+1}+{\\nu }_{e}.[\/latex]<\/div>\n<\/li>\n<li id=\"import-auto-id2600265\">[latex]{\\beta }^{-}[\/latex] is an electron, [latex]{\\beta }^{+}[\/latex] is an antielectron or positron, [latex]{\\nu }_{e}[\/latex] represents an electron\u2019s neutrino, and  [latex]{\\overline{\\nu }}_{e}[\/latex] is an electron\u2019s antineutrino. In addition to all previously known conservation laws, two new ones arise\u2014 conservation of electron family number  and conservation of the total number of nucleons.  The [latex]\\gamma [\/latex] decay equation is\n<div data-type=\"equation\" class=\"equation\">[latex]{}_{Z}{}^{A}\\text{}{\\text{X}}_{N}^{*}\\to {}_{Z}{}^{A}\\text{}{\\text{X}}_{N}+{\\gamma }_{1}+{\\gamma }_{2}+\\cdots [\/latex]<\/div>\n<p>[latex]\\gamma [\/latex] is a high-energy photon originating in a nucleus.<\/p><\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id2929463\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2209498\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3388708\">\n<p id=\"import-auto-id3112726\">Star Trek fans have often heard the term \u201cantimatter drive.\u201d Describe how you could use a magnetic field to trap antimatter, such as produced by nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the fraction of matter converted into energy.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1485777\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3164070\">\n<p id=\"import-auto-id1617379\">What conservation law requires an electron\u2019s neutrino to be produced in electron capture? Note that the electron no longer exists after it is captured by the nucleus.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1576428\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3179513\">\n<p id=\"import-auto-id2659009\">Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern Hemisphere and some 100,000 light-years away from Earth, neutrinos from the explosion were observed at about the same time as the light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2006022\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2932053\">\n<p id=\"import-auto-id3385870\">What do the three types of beta decay have in common that is distinctly different from alpha decay?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<p id=\"import-auto-id3033441\">In the following eight problems, write the complete decay equation for the given nuclide in the complete [latex]{}_{Z}^{A}{X}_{N}[\/latex] notation. Refer to the periodic table for values of [latex]Z[\/latex].<\/p>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2405551\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2661400\">\n<p id=\"import-auto-id1947269\">[latex]{\\beta }^{-}[\/latex] decay of [latex]{}^{3}\\text{H}[\/latex] (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3234485\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2384056\">[latex]{}_{1}^{3}{\\text{H}}_{2}\\to {}_{2}^{3}{\\text{He}}_{1}+{\\beta }^{-}+{\\overline{\\nu }}_{e}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1907192\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2621600\">\n<p id=\"import-auto-id1569981\">[latex]{\\beta }^{-}[\/latex] decay of [latex]{}^{\\text{40}}K[\/latex], a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2670256\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3065078\">\n<p id=\"import-auto-id2449142\">[latex]{\\beta }^{+}[\/latex] decay of [latex]{}^{\\text{50}}\\text{Mn}[\/latex].<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2382245\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id3253996\">[latex]{}_{\\text{25}}^{\\text{50}}{M}_{\\text{25}}\\to {}_{\\text{24}}^{\\text{50}}{\\text{Cr}}_{\\text{26}}+{\\beta }^{+}+{\\nu }_{e}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1860601\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2672908\">\n<p id=\"import-auto-id1845794\">[latex]{\\beta }^{+}[\/latex] decay of [latex]{}^{\\text{52}}\\text{Fe}[\/latex].<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2640350\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2615661\">\n<p id=\"import-auto-id2400416\">Electron capture by [latex]{}^{7}\\text{Be}[\/latex].<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2628798\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1488206\">[latex]{}_{4}^{7}{\\text{Be}}_{3}+{e}^{-}\\to {}_{3}^{7}{\\text{Li}}_{4}+{\\nu }_{e}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1917574\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1917578\">\n<p>Electron capture by [latex]{}^{\\text{106}}\\text{In}[\/latex].<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2626117\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3257711\">\n<p id=\"import-auto-id3422558\">[latex]\\alpha [\/latex] decay of [latex]{}^{\\text{210}}\\text{Po}[\/latex], the isotope of polonium in the decay series of [latex]{}^{\\text{238}}\\text{U}[\/latex] that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2654425\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id3076865\">[latex]{}_{\\text{84}}^{\\text{210}}{\\text{Po}}_{\\text{126}}\\to {}_{\\text{82}}^{\\text{206}}{\\text{Pb}}_{\\text{124}}+{}_{2}^{4}{\\text{He}}_{2}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3010127\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3175592\">\n<p id=\"import-auto-id3094872\">[latex]\\alpha [\/latex] decay of [latex]{}^{\\text{226}}\\text{Ra}[\/latex], another isotope in the decay series of [latex]{}^{\\text{238}}\\text{U}[\/latex], first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas.<\/p>\n<\/div>\n<\/div>\n<p id=\"import-auto-id1434739\">In the following four problems, identify the parent nuclide and write the complete decay equation in the [latex]{}_{Z}^{A}{X}_{N}[\/latex] notation. Refer to the periodic table for values of [latex]Z[\/latex].<\/p>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1473021\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3399081\">\n<p id=\"import-auto-id3402679\">[latex]{\\beta }^{-}[\/latex] decay producing [latex]{}^{\\text{137}}\\text{Ba}[\/latex]. The parent nuclide is a major waste product of reactors and has chemistry similar to potassium and sodium, resulting in its concentration in your cells if ingested.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2017287\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id3036694\">[latex]{}_{\\text{55}}^{\\text{137}}{\\text{Cs}}_{\\text{82}}\\to {}_{\\text{56}}^{\\text{137}}{\\text{Ba}}_{\\text{81}}+{\\beta }^{-}+{\\overline{\\nu }}_{e}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3418134\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3418136\">\n<p id=\"import-auto-id2397673\">[latex]{\\beta }^{-}[\/latex] decay producing [latex]{}^{\\text{90}}\\text{Y}[\/latex]. The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested ([latex]{}^{\\text{90}}\\text{Y}[\/latex] is also radioactive.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2011306\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2011309\">\n<p id=\"import-auto-id2962207\">[latex]\\alpha [\/latex] decay producing [latex]{}^{\\text{228}}\\text{Ra}[\/latex]. The parent nuclide is nearly 100% of the natural element and is found in gas lantern mantles and in metal alloys used in jets ([latex]{}^{\\text{228}}\\text{Ra}[\/latex] is also radioactive).<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3355264\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1894648\">[latex]{}_{\\text{90}}^{\\text{232}}{\\text{Th}}_{\\text{142}}\\to {}_{\\text{88}}^{\\text{228}}{\\text{Ra}}_{\\text{140}}+{}_{2}^{4}{\\text{He}}_{2}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3033134\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3033137\">\n<p id=\"import-auto-id3354561\">[latex]\\alpha [\/latex] decay producing [latex]{}^{\\text{208}}\\text{Pb}[\/latex]. The parent nuclide is in the decay series produced by [latex]{}^{\\text{232}}\\text{Th}[\/latex], the only naturally occurring isotope of thorium.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3164080\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3164082\">\n<p id=\"import-auto-id3028935\">When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation [latex]{e}^{+}+{e}^{-}\\to \\gamma +\\gamma [\/latex]<em data-effect=\"italics\"> conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation. (b) Find the energy of each [latex]\\gamma [\/latex] ray, assuming the electron and positron are initially nearly at rest. (c) Explain why the two [latex]\\gamma [\/latex] rays travel in exactly opposite directions if the center of mass of the electron-positron system is initially at rest.<\/em><\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3176709\">\n<p id=\"import-auto-id2953315\">(a) [latex]\\text{charge:}\\left(+1\\right)+\\left(-1\\right)=0;\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\text{electron family number:}\\phantom{\\rule{0.25em}{0ex}}\\left(+1\\right)+\\left(-1\\right)=0;\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}A: 0+0=0[\/latex]<\/p>\n<p id=\"import-auto-id2953320\">(b) 0.511 MeV<\/p>\n<p id=\"import-auto-id1932189\">(c) The two [latex]\\gamma [\/latex] rays must travel in exactly opposite directions in order to conserve momentum, since initially there is zero momentum if the center of mass is initially at rest.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2442449\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2442452\">\n<p id=\"import-auto-id3062765\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for [latex]\\alpha [\/latex] decay given in the equation [latex]{}_{Z}^{A}{X}_{N}\\to {}_{Z-2}^{A-4}{\\text{Y}}_{N-2}+{}_{2}^{4}{\\text{He}}_{2}[\/latex]. To do this, identify the values of each before and after the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3291026\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3291029\">\n<p id=\"import-auto-id2626320\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for<br>\n[latex]{\\beta }^{-}[\/latex] decay given in the equation<br>\n[latex]{}_{Z}^{A}{X}_{N}\\to {}_{Z+1}^{A}{\\text{Y}}_{N-1}+{\\beta }^{-}+{\\overline{\\nu }}_{e}[\/latex]. To do this, identify the values of each before and after the decay.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2453152\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1464681\">[latex]Z=\\left(Z+1\\right)-1;\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}A=A\\text{;}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\text{efn : 0}=\\left(+1\\right)+\\left(-1\\right)[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2460264\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3077530\">\n<p id=\"import-auto-id3246240\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for [latex]{\\beta }^{-}[\/latex] decay given in the equation [latex]{}_{Z}^{A}{X}_{N}\\to {}_{Z-1}^{A}{\\text{Y}}_{N-1}+{\\beta }^{-}+{\\nu }_{e}[\/latex]. To do this, identify the values of each before and after the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3178618\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3178621\">\n<p id=\"import-auto-id3422948\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in the equation [latex]{}_{Z}^{A}{X}_{N}+{e}^{-}\\to {}_{Z-1}^{A}{\\text{Y}}_{N+1}+{\\nu }_{e}[\/latex]. To do this, identify the values of each before and after the capture.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3035818\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2648112\">[latex]Z-1=Z-1;\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}A=A;\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\phantom{\\rule{0.25em}{0ex}}\\text{efn :}\\left(+1\\right)=\\left(+1\\right)[\/latex]<\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2590538\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2590541\">\n<p id=\"import-auto-id3163760\">A rare decay mode has been observed in which [latex]{}^{\\text{222}}\\text{Ra}[\/latex] emits a<br>\n[latex]{}^{\\text{14}}C[\/latex] nucleus. (a) The decay equation is<br>\n[latex]{}^{\\text{222}}\\text{Ra}{\\to }^{A}{\\text{X+}}^{\\text{14}}\\text{C}[\/latex]. Identify the nuclide [latex]{}^{A}X[\/latex]. (b) Find the energy emitted in the decay. The mass of [latex]{}^{\\text{222}}\\text{Ra}[\/latex] is 222.015353 u.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2062598\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2062601\">\n<p>(a) Write the complete [latex]\\alpha [\/latex] decay equation for [latex]{}^{\\text{226}}\\text{Ra}[\/latex].<\/p>\n<p id=\"import-auto-id1981359\">(b) Find the energy released in the decay.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3062624\">\n<p id=\"import-auto-id1998676\">(a) [latex]{}_{\\text{88}}^{\\text{226}}{\\text{Ra}}_{138}\\to {}_{\\text{86}}^{\\text{222}}{\\text{Rn}}_{\\text{136}}+{}_{2}^{4}{\\text{He}}_{2}[\/latex]<\/p>\n<p id=\"import-auto-id3081154\">(b) 4.87 MeV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1893984\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2401213\">\n<p id=\"import-auto-id3253435\">(a) Write the complete [latex]\\alpha [\/latex] decay equation for [latex]{}^{\\text{249}}\\text{Cf}[\/latex].<\/p>\n<p id=\"import-auto-id2929542\">(b) Find the energy released in the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1871366\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2963343\">\n<p id=\"import-auto-id2670189\">(a) Write the complete [latex]{\\beta }^{-}[\/latex] decay equation for the neutron. (b) Find the energy released in the decay.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3254531\">\n<p id=\"import-auto-id2452615\">(a) [latex]\\text{n}\\to \\text{p}+{\\beta }^{-}+{\\overline{\\nu }}_{e}[\/latex]<\/p>\n<p id=\"import-auto-id3356256\">(b) ) 0.783 MeV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1116905\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1116908\">\n<p id=\"import-auto-id2449067\">(a) Write the complete [latex]{\\beta }^{-}[\/latex] decay equation for [latex]{}^{\\text{90}}\\text{Sr}[\/latex], a major waste product of nuclear reactors. (b) Find the energy released in the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3028069\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3028072\">\n<p>Calculate the energy released in the [latex]{\\beta }^{+}[\/latex] decay of [latex]{}^{\\text{22}}\\text{Na}[\/latex], the equation for which is given in the text. The masses of<br>\n[latex]{}^{\\text{22}}\\text{Na}[\/latex] and<br>\n[latex]{}^{\\text{22}}\\text{Ne}[\/latex] are 21.994434 and 21.991383 u, respectively.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2391615\">\n<p id=\"import-auto-id3033703\">1.82 MeV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1441536\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1863870\">\n<p id=\"import-auto-id2074557\">(a) Write the complete [latex]{\\beta }^{+}[\/latex] decay equation for [latex]{}^{\\text{11}}\\text{C}[\/latex].<\/p>\n<p id=\"import-auto-id2639096\">(b) Calculate the energy released in the decay. The masses of [latex]{}^{\\text{11}}\\text{C}[\/latex] and [latex]{}^{\\text{11}}\\text{B}[\/latex] are 11.011433 and 11.009305 u, respectively.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3402996\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3176786\">\n<p id=\"import-auto-id1848510\">(a) Calculate the energy released in the [latex]\\alpha [\/latex] decay of [latex]{}^{\\text{238}}\\text{U}[\/latex].<\/p>\n<p id=\"import-auto-id3354600\">(b) What fraction of the mass of a single [latex]{}^{\\text{238}}\\text{U}[\/latex] is destroyed in the decay? The mass of [latex]{}^{\\text{234}}\\text{Th}[\/latex] is 234.043593 u.<\/p>\n<p id=\"import-auto-id3229174\">(c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1951662\">\n<p id=\"import-auto-id1486163\">(a) 4.274 MeV<\/p>\n<p id=\"import-auto-id2920736\">(b) [latex]1\\text{.}\\text{927}\u00d7{\\text{10}}^{-5}[\/latex]<\/p>\n<p id=\"import-auto-id3091706\">(c) Since U-238 is a slowly decaying substance, only a very small number of nuclei decay on human timescales; therefore, although those nuclei that decay lose a noticeable fraction of their mass, the change in the total mass of the sample is not detectable for a macroscopic sample.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3121887\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3285569\">\n<p id=\"import-auto-id2962661\">(a) Write the complete reaction equation for electron capture by [latex]{}^{7}\\text{Be.}[\/latex]<\/p>\n<p id=\"eip-id1826968\">(b) Calculate the energy released.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2600565\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2600568\">\n<p id=\"import-auto-id3109373\">(a) Write the complete reaction equation for electron capture by [latex]{}^{\\text{15}}\\text{O}[\/latex].<\/p>\n<p id=\"import-auto-id2979269\">(b) Calculate the energy released.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3180437\">\n<p id=\"import-auto-id2662509\">(a) [latex]{}_{8}^{\\text{15}}{O}_{7}+{e}^{-}\\to {}_{7}^{\\text{15}}{N}_{8}+{\\nu }_{e}[\/latex]<\/p>\n<p id=\"import-auto-id2365629\">(b) 2.754 MeV<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id3008963\">\n<dt>parent<\/dt>\n<dd id=\"fs-id2640151\">the original state of nucleus before decay<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1615990\">\n<dt>daughter<\/dt>\n<dd id=\"fs-id2443752\">the nucleus obtained when parent nucleus decays and produces another nucleus following the rules and the conservation laws<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1615993\">\n<dt>positron<\/dt>\n<dd id=\"fs-id3062638\">the particle that results from positive beta decay; also known as an antielectron<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"fs-id2234366\">\n<dt>decay<\/dt>\n<dd>the process by which an atomic nucleus of an unstable atom loses mass and energy by emitting ionizing particles<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1981401\">\n<dt>alpha decay<\/dt>\n<dd id=\"fs-id1517548\">type of radioactive decay in which an atomic nucleus emits an alpha particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1981403\">\n<dt>beta decay<\/dt>\n<dd id=\"fs-id3410683\">type of radioactive decay in which an atomic nucleus emits a beta particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2668157\">\n<dt>gamma decay<\/dt>\n<dd id=\"fs-id3098191\">type of radioactive decay in which an atomic nucleus emits a gamma particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2668160\">\n<dt>decay equation<\/dt>\n<dd id=\"fs-id3109833\">the equation to find out how much of a radioactive material is left after a given period of time<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2449377\">\n<dt>nuclear reaction energy<\/dt>\n<dd id=\"fs-id1995255\">the energy created in a nuclear reaction<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2449379\">\n<dt>neutrino<\/dt>\n<dd id=\"fs-id1587883\">an electrically neutral, weakly interacting elementary subatomic particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2382824\">\n<dt>electron\u2019s antineutrino<\/dt>\n<dd id=\"fs-id1977528\">antiparticle of electron\u2019s neutrino<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2382826\">\n<dt>positron decay<\/dt>\n<dd id=\"fs-id3163006\">type of beta decay in which a proton is converted to a neutron, releasing a positron and a neutrino<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"fs-id2850141\">\n<dt>antielectron<\/dt>\n<dd id=\"fs-id1825605\">another term for positron<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"fs-id1825608\">\n<dt>decay series<\/dt>\n<dd id=\"fs-id1853690\">process whereby subsequent nuclides decay until a stable nuclide is produced<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3209969\">\n<dt>electron\u2019s neutrino<\/dt>\n<dd id=\"fs-id3223437\">a subatomic elementary particle which has no net electric charge<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1954183\">\n<dt>antimatter<\/dt>\n<dd id=\"fs-id1474720\">composed of antiparticles<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1954185\">\n<dt>electron capture<\/dt>\n<dd id=\"fs-id3401137\">the process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3175197\">\n<dt>electron capture equation<\/dt>\n<dd id=\"fs-id3054581\">equation representing the electron capture<\/dd>\n<\/dl>\n<\/div>\n\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3 itemprop=\"educationalUse\">Learning Objectives<\/h3>\n<ul>\n<li>Define and discuss nuclear decay.<\/li>\n<li>State the conservation laws.<\/li>\n<li>Explain parent and daughter nucleus.<\/li>\n<li>Calculate the energy emitted during nuclear decay.<\/li>\n<\/ul>\n<\/div>\n<p id=\"import-auto-id3035108\">Nuclear <span data-type=\"term\">decay<\/span> has provided an amazing window into the realm of the very small. Nuclear decay gave the first indication of the connection between mass and energy, and it revealed the existence of two of the four basic forces in nature. In this section, we explore the major modes of nuclear decay; and, like those who first explored them, we will discover evidence of previously unknown particles and conservation laws.<\/p>\n<p id=\"import-auto-id2688849\">Some nuclides are stable, apparently living forever. Unstable nuclides decay (that is, they are radioactive), eventually producing a stable nuclide after many decays. We call the original nuclide the <span data-type=\"term\">parent<\/span> and its decay products the <span data-type=\"term\" id=\"import-auto-id2429491\">daughters<\/span>. Some radioactive nuclides decay in a single step to a stable nucleus. For example, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> is unstable and decays directly to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d3927179b7e5ccb2da584c63f799945f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/>, which is stable. Others, such as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/>, decay to another unstable nuclide, resulting in a <span data-type=\"term\" id=\"import-auto-id1518523\">decay series<\/span> in which each subsequent nuclide decays until a stable nuclide is finally produced. The decay series that starts from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> is of particular interest, since it produces the radioactive isotopes <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7b08416be47f546450c758843fe2335a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#54;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-17b3cef778b462e0624b7c858c3e7348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#49;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/>, which the Curies first discovered (see <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a>). Radon gas is also produced (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1cfcefb195e95766b510813e87356e89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"44\" style=\"vertical-align: 0px;\" \/> in the series), an increasingly recognized naturally occurring hazard. Since radon is a noble gas, it emanates from materials, such as soil, containing even trace amounts of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> and can be inhaled. The decay of radon and its daughters produces internal damage. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> decay series ends with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9dcc08220dfc486f18427471b7426a6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#54;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/>, a stable isotope of lead.<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id1930472\">\n<div class=\"bc-figcaption figcaption\">The decay series produced by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/>, the most common uranium isotope. Nuclides are graphed in the same manner as in the chart of nuclides. The type of decay for each member of the series is shown, as well as the half-lives. Note that some nuclides decay by more than one mode. You can see why radium and polonium are found in uranium ore. A stable isotope of lead is the end product of the series.<\/div>\n<p><span data-type=\"media\" data-alt=\"A graph is shown in which decay of alpha and beta is shown. Also half lives of each isotope are shown. Uranium decays in one mode but some isotopes decay by more than one mode. Finally a stable isotope of lead results.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_01a.jpg\" data-media-type=\"image\/jpg\" alt=\"A graph is shown in which decay of alpha and beta is shown. Also half lives of each isotope are shown. Uranium decays in one mode but some isotopes decay by more than one mode. Finally a stable isotope of lead results.\" width=\"360\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id1916253\">Note that the daughters of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay shown in <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a> always have two fewer protons and two fewer neutrons than the parent. This seems reasonable, since we know that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay is the emission of a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7de192413d8e61d4f9df89fac3b04770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/> nucleus, which has two protons and two neutrons. The daughters of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-39ffee81b79fbfa10c128d48495e8b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\" \/> decay have one less neutron and one more proton than their parent. Beta decay is a little more subtle, as we shall see. No <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> decays are shown in the figure, because they do not produce a daughter that differs from the parent.<\/p>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Alpha Decay<\/h1>\n<p id=\"import-auto-id1206958\">In <span data-type=\"term\">alpha decay<\/span>, a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7de192413d8e61d4f9df89fac3b04770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/> nucleus simply breaks away from the parent nucleus, leaving a daughter with two fewer protons and two fewer neutrons than the parent (see <a href=\"#import-auto-id3078027\" class=\"autogenerated-content\">(Figure)<\/a>). One example of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay is shown in <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/>. Another nuclide that undergoes <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e34dfdc14badef18d2b00fd03aaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/>. The decay equations for these two nuclides are<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-eaf19a022878af555bc0fff2c34b62bf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#52;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#50;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#52;&#125;&#125;&#43;&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"178\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"import-auto-id1403527\">and<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ebbf6b1111932710da6db4d303179ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;&#43;&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"160\" style=\"vertical-align: -2px;\" \/><\/div>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Alpha decay is the separation of a <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7de192413d8e61d4f9df89fac3b04770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/> nucleus from the parent. The daughter nucleus has two fewer protons and two fewer neutrons than the parent. Alpha decay occurs spontaneously only if the daughter and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7de192413d8e61d4f9df89fac3b04770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/> nucleus have less total mass than the parent.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1386075\" data-alt=\"The image shows conditions before and after alpha decay. Before alpha decay the nucleus is labeled parent and after decay the nucleus is labeled daughter.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_02a.jpg\" data-media-type=\"image\/jpg\" alt=\"The image shows conditions before and after alpha decay. Before alpha decay the nucleus is labeled parent and after decay the nucleus is labeled daughter.\" width=\"200\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id3007716\">If you examine the periodic table of the elements, you will find that Th has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5199388adf3dc521b72db4be84eaf7e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"54\" style=\"vertical-align: 0px;\" \/>, two fewer than U, which has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bb51dda6ed4f921d8e7e5225e2cd2dae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"53\" style=\"vertical-align: 0px;\" \/>. Similarly, in the second <span data-type=\"term\">decay equation<\/span>, we see that U has two fewer protons than Pu, which has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-445d77ec5cd365270f24d421c17f2019_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: -1px;\" \/>. The general rule for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay is best written in the format <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ab573359ef47f3d525804ad06735b3df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"36\" style=\"vertical-align: -5px;\" \/>. If a certain nuclide is known to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay (generally this information must be looked up in a table of isotopes, such as in <a href=\"\/contents\/666f5335-e742-451e-b7ff-245efeff8bd9@2\">Appendix B<\/a>), its <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/><span data-type=\"term\" id=\"import-auto-id2930041\"> decay equation<\/span> is<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d963c57391360f0f5c63b6ea170ec858_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#50;&#125;&#94;&#123;&#65;&#45;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#50;&#125;&#43;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#97;&#108;&#112;&#104;&#97;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#101;&#99;&#97;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"284\" style=\"vertical-align: -6px;\" \/><\/div>\n<p id=\"import-auto-id1825060\">where Y is the nuclide that has two fewer protons than X, such as Th having two fewer than U. So if you were told that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e34dfdc14badef18d2b00fd03aaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decays and were asked to write the complete decay equation, you would first look up which element has two fewer protons (an atomic number two lower) and find that this is uranium. Then since four nucleons have broken away from the original 239, its atomic mass would be 235.<\/p>\n<p id=\"import-auto-id2639290\">It is instructive to examine conservation laws related to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay. You can see from the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bf1f0f78759d3963c0800bb97d298ac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#50;&#125;&#94;&#123;&#65;&#45;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#50;&#125;&#43;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"195\" style=\"vertical-align: -6px;\" \/>  that total charge is conserved. Linear and angular momentum are conserved, too. Although conserved angular momentum is not of great consequence in this type of decay, conservation of linear momentum has interesting consequences. If the nucleus is at rest when it decays, its momentum is zero. In that case, the fragments must fly in opposite directions with equal-magnitude momenta so that total momentum remains zero. This results in the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/><em data-effect=\"italics\"> particle carrying away most of the energy, as a bullet from a heavy rifle carries away most of the energy of the powder burned to shoot it. Total mass\u2013energy is also conserved: the energy produced in the decay comes from conversion of a fraction of the original mass. As discussed in <a href=\"\/contents\/05208266-2374-4008-9060-7ddddbe877f2@2\">Atomic Physics<\/a>, the general relationship is<\/em><\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-63bb1f1a10b35e8dbd4feb985613f679_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#49;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"import-auto-id3181645\">Here, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e1c770271f92700e1a4fbce46c668_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> is the <span data-type=\"term\" id=\"import-auto-id3403043\">nuclear reaction energy<\/span> (the reaction can be nuclear decay or any other reaction), and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> is the difference in mass between initial and final products. When the final products have less total mass, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> is positive, and the reaction releases energy (is exothermic). When the products have greater total mass, the reaction is endothermic (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> is negative) and must be induced with an energy input. For <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay to be spontaneous, the decay products must have smaller mass than the parent.<\/p>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1816061\">\n<div data-type=\"title\" class=\"title\">Alpha Decay Energy Found from Nuclear Masses<\/div>\n<p id=\"import-auto-id1547918\">Find the energy emitted in the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e34dfdc14badef18d2b00fd03aaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"import-auto-id3013051\"><strong>Strategy<\/strong><\/p>\n<p id=\"import-auto-id2661877\">Nuclear reaction energy, such as released in <em data-effect=\"italics\">\u03b1<\/em> decay, can be found using the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0b2dcc59c56363236d7149830491831d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"100\" style=\"vertical-align: -4px;\" \/>. We must first find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>, the difference in mass between the parent nucleus and the products of the decay. This is easily done using masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a>.<\/p>\n<p id=\"import-auto-id2662636\"><strong>Solution<\/strong><\/p>\n<p id=\"import-auto-id3095513\">The decay equation was given earlier for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e34dfdc14badef18d2b00fd03aaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/> ; it is<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ebbf6b1111932710da6db4d303179ece_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;&#43;&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"160\" style=\"vertical-align: -2px;\" \/><\/div>\n<p id=\"import-auto-id2684784\">Thus the pertinent masses are those of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e34dfdc14badef18d2b00fd03aaa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e21a942a7a4ab383d7397e0d76e5d890_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/>, and the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> particle or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7de192413d8e61d4f9df89fac3b04770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/>, all of which are listed in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a>. The initial mass was <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-08ffb4480a9fe2314969ac3018be3272_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#53;&#50;&#49;&#53;&#55;&#32;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"199\" style=\"vertical-align: -7px;\" \/>. The final mass is the sum <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0059d4529c4f492b384d4216705f5c70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#109;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#61;&#32;&#50;&#51;&#53;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#52;&#51;&#57;&#50;&#52;&#32;&#117;&#32;&#43;&#32;&#52;&#46;&#48;&#48;&#50;&#54;&#48;&#50;&#32;&#117;&#32;&#61;&#32;&#50;&#51;&#57;&#46;&#48;&#52;&#54;&#53;&#50;&#54;&#32;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"502\" style=\"vertical-align: -7px;\" \/>. Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5259ac8c349b6e3885c561db544c0eb2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#108;&#108;&#125;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#38;&#32;&#61;&#38;&#32;&#109;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#117;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#91;&#109;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#92;&#92;&#32;&#38;&#32;&#61;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#46;&#48;&#53;&#50;&#49;&#53;&#55;&#32;&#117;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#57;&#46;&#48;&#52;&#54;&#53;&#50;&#54;&#32;&#117;&#125;&#92;&#92;&#32;&#38;&#32;&#61;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#48;&#48;&#48;&#53;&#54;&#51;&#49;&#32;&#117;&#46;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"337\" style=\"vertical-align: -23px;\" \/><\/div>\n<p>Now we can find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e1c770271f92700e1a4fbce46c668_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> by entering <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> into the equation:<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-720a8548f19ec625565b0549c10c00f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#48;&#48;&#53;&#54;&#51;&#49;&#32;&#117;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"243\" style=\"vertical-align: -4px;\" \/><\/div>\n<p>We know <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4190abb5c6f58588cf876cd2708803e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#32;&#117;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#51;&#49;&#46;&#53;&#32;&#77;&#101;&#86;&#47;&#125;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -4px;\" \/>, and so<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-101\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a4c270d2075ab579372e435b449b95fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#53;&#54;&#51;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#51;&#49;&#46;&#53;&#32;&#77;&#101;&#86;&#125;&#47;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#46;&#50;&#53;&#32;&#77;&#101;&#86;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"383\" style=\"vertical-align: -7px;\" \/><\/div>\n<p><strong>Discussion<\/strong><\/p>\n<p id=\"import-auto-id1856748\">The energy released in this <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay is in the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9c8b19875b7157b4573c479b392e86cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#101;&#86;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"37\" style=\"vertical-align: -1px;\" \/> range, about <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bb4f3b6229e4491678fa3397b38ae5cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"24\" style=\"vertical-align: -1px;\" \/> times as great as typical chemical reaction energies, consistent with many previous discussions. Most of this energy becomes kinetic energy of the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> particle (or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7de192413d8e61d4f9df89fac3b04770_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#52;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/> nucleus), which moves away at high speed. The energy carried away by the recoil of the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e21a942a7a4ab383d7397e0d76e5d890_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> nucleus is much smaller in order to conserve momentum. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e21a942a7a4ab383d7397e0d76e5d890_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> nucleus can be left in an excited state to later emit photons (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> rays). This decay is spontaneous and releases energy, because the products have less mass than the parent nucleus. The question of why the products have less mass will be discussed in <a href=\"\/contents\/e12b60f5-72df-401e-a1b1-7f13fd61eee0@5\">Binding Energy<\/a>. Note that the masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> are atomic masses of neutral atoms, including their electrons. The mass of the electrons is the same before and after <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay, and so their masses subtract out when finding <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>. In this case, there are 94 electrons before and after the decay.<\/p>\n<\/div>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\">\n<h1 data-type=\"title\">Beta Decay<\/h1>\n<p id=\"import-auto-id2445383\">There are actually <em data-effect=\"italics\">three<\/em> types of <span data-type=\"term\">beta decay<\/span>. The first discovered was \u201cordinary\u201d beta decay and is called <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay or electron emission. The symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> represents <em data-effect=\"italics\">an electron emitted in nuclear beta decay<\/em>. Cobalt-60 is a nuclide that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decays in the following manner:<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-36c34e3bc18ada07eb5125f755fe64b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#101;&#117;&#116;&#114;&#105;&#110;&#111;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"232\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"import-auto-id3037465\">The <span data-type=\"term\" id=\"import-auto-id1917824\">neutrino<\/span> is a particle emitted in beta decay that was unanticipated and is of fundamental importance. The neutrino was not even proposed in theory until more than 20 years after beta decay was known to involve electron emissions. Neutrinos are so difficult to detect that the first direct evidence of them was not obtained until 1953. Neutrinos are nearly massless, have no charge, and do not interact with nucleons via the strong nuclear force. Traveling approximately at the speed of light, they have little time to affect any nucleus they encounter. This is, owing to the fact that they have no charge (and they are not EM waves), they do not interact through the EM force. They do interact via the relatively weak and very short range weak nuclear force. Consequently, neutrinos escape almost any detector and penetrate almost any shielding. However, neutrinos do carry energy, angular momentum (they are fermions with half-integral spin), and linear momentum away from a beta decay. When accurate measurements of beta decay were made, it became apparent that energy, angular momentum, and linear momentum were not accounted for by the daughter nucleus and electron alone. Either a previously unsuspected particle was carrying them away, or three conservation laws were being violated. Wolfgang Pauli made a formal proposal for the existence of neutrinos in 1930. The Italian-born American physicist Enrico Fermi (1901\u20131954) gave neutrinos their name, meaning little neutral ones, when he developed a sophisticated theory of beta decay (see <a href=\"#import-auto-id2672424\" class=\"autogenerated-content\">(Figure)<\/a>). Part of Fermi\u2019s theory was the identification of the weak nuclear force as being distinct from the strong nuclear force and in fact responsible for beta decay.<\/p>\n<div class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">Enrico Fermi was nearly unique among 20th-century physicists\u2014he made significant contributions both as an experimentalist and a theorist. His many contributions to theoretical physics included the identification of the weak nuclear force. The fermi (fm) is named after him, as are an entire class of subatomic particles (fermions), an element (Fermium), and a major research laboratory (Fermilab). His experimental work included studies of radioactivity, for which he won the 1938 Nobel Prize in physics, and creation of the first nuclear chain reaction. (credit: United States Department of Energy, Office of Public Affairs)<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id1117770\" data-alt=\"Photo of physicist Enrico Fermi.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_03a.jpg\" data-media-type=\"image\/png\" alt=\"Photo of physicist Enrico Fermi.\" width=\"200\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id3127102\">The neutrino also reveals a new conservation law. There are various families of particles, one of which is the electron family. We propose that the number of members of the electron family is constant in any process or any closed system. In our example of beta decay, there are no members of the electron family present before the decay, but after, there is an electron and a neutrino. So electrons are given an electron family number of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d4932b1a489a055f2908670bac049524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"22\" style=\"vertical-align: -2px;\" \/>. The neutrino in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay is an <span data-type=\"term\">electron\u2019s antineutrino<\/span>, given the symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b26bf8421e3994d90214b7643c77280c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-af49fe31d80f9a073f85c0e48aa43d1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#110;&#117;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> is the Greek letter nu, and the subscript <em data-effect=\"italics\">e<\/em> means this neutrino is related to the electron. The bar indicates this is a particle of <span data-type=\"term\">antimatter<\/span>. (All particles have antimatter counterparts that are nearly identical except that they have the opposite charge. Antimatter is almost entirely absent on Earth, but it is found in nuclear decay and other nuclear and particle reactions as well as in outer space.) The electron\u2019s antineutrino <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b26bf8421e3994d90214b7643c77280c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\" \/>, being antimatter, has an electron family number of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2a61410f041331e606d64882668a12b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>. The total is zero, before and after the decay. The new conservation law, obeyed in all circumstances, states that the <em data-effect=\"italics\">total electron family number is constant<\/em>. An electron cannot be created without also creating an antimatter family member. This law is analogous to the conservation of charge in a situation where total charge is originally zero, and equal amounts of positive and negative charge must be created in a reaction to keep the total zero.<\/p>\n<p id=\"import-auto-id3199526\">If a nuclide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c719fef559590cd824e0d022d9e1a1eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"38\" style=\"vertical-align: -5px;\" \/> is known to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay, then its <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/><strong data-effect=\"bold\"> decay equation is<\/strong><\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2d7ffbb8453456200db31387ff3f59b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#123;&#125;&#94;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#43;&#49;&#125;&#123;&#125;&#94;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#49;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#45;&#125;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#101;&#99;&#97;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"342\" style=\"vertical-align: -5px;\" \/><\/div>\n<p id=\"import-auto-id1815384\">where Y is the nuclide having one more proton than X (see <a href=\"#import-auto-id2446798\" class=\"autogenerated-content\">(Figure)<\/a>). So if you know that a certain nuclide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decays, you can find the daughter nucleus by first looking up<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> for the parent and then determining which element has atomic number<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6bb61b3be106adb4c45fbd05bbd17cc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"42\" style=\"vertical-align: -2px;\" \/>. In the example of the<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay of<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> given earlier, we see that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bcf56b0b0267ea2ebdcb2e5395534b75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: 0px;\" \/> for Co and<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9aee692097dab20f76275a0f6f2814bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"54\" style=\"vertical-align: 0px;\" \/> is Ni. It is as if one of the neutrons in the parent nucleus decays into a proton, electron, and neutrino. In fact, neutrons outside of nuclei do just that\u2014they live only an average of a few minutes and<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay in the following manner:<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-828\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8a810b1db67aa70f4f2e2d4d39c0a8ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#125;&#92;&#116;&#111;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#115;&#116;&#97;&#99;&#107;&#114;&#101;&#108;&#123;&#45;&#125;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"135\" style=\"vertical-align: -4px;\" \/><\/div>\n<div class=\"bc-figure figure\" id=\"import-auto-id2446798\">\n<div class=\"bc-figcaption figcaption\">In <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay, the parent nucleus emits an electron and an antineutrino. The daughter nucleus has one more proton and one less neutron than its parent. Neutrinos interact so weakly that they are almost never directly observed, but they play a fundamental role in particle physics.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id2209887\" data-alt=\"Image shows parent nucleus before beta decay and daughter nucleus after beta decay.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_04a.jpg\" data-media-type=\"image\/jpg\" alt=\"Image shows parent nucleus before beta decay and daughter nucleus after beta decay.\" width=\"200\" \/><\/span><\/p>\n<\/div>\n<p id=\"import-auto-id3178054\">We see that charge is conserved in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay, since the total charge is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> before and after the decay. For example, in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> decay, total charge is 27 before decay, since cobalt has<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bcf56b0b0267ea2ebdcb2e5395534b75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: 0px;\" \/>. After decay, the daughter nucleus is Ni, which has<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9aee692097dab20f76275a0f6f2814bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"54\" style=\"vertical-align: 0px;\" \/>, and there is an electron, so that the total charge is also <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-696a795921c3877647f2767a3b7beb71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#32;&#43;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"75\" style=\"vertical-align: -4px;\" \/> or 27. Angular momentum is conserved, but not obviously (you have to examine the spins and angular momenta of the final products in detail to verify this). Linear momentum is also conserved, again imparting most of the decay energy to the electron and the antineutrino, since they are of low and zero mass, respectively. Another new conservation law is obeyed here and elsewhere in nature. <em data-effect=\"italics\">The total number of nucleons <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/> is conserved<\/em>. In<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> decay, for example, there are 60 nucleons before and after the decay. Note that total<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#65;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\" \/> is also conserved in<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay. Also note that the total number of protons changes, as does the total number of neutrons, so that total<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> and total <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5793832f979c2268e3694c246d53b1bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#78;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"16\" style=\"vertical-align: 0px;\" \/> are <em data-effect=\"italics\">not<\/em> conserved in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay, as they are in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay. Energy released in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay can be calculated given the masses of the parent and products.<\/p>\n<div data-type=\"example\" class=\"textbox examples\" id=\"fs-id1823899\">\n<div data-type=\"title\" class=\"title\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> Decay Energy from Masses<\/div>\n<p id=\"import-auto-id2406059\">Find the energy emitted in the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id2673414\"><strong>Strategy and Concept<\/strong><\/p>\n<p id=\"import-auto-id2684991\">As in the preceding example, we must first find <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/>, the difference in mass between the parent nucleus and the products of the decay, using masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a>. Then the emitted energy is calculated as before, using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0b2dcc59c56363236d7149830491831d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"100\" style=\"vertical-align: -4px;\" \/>. The initial mass is just that of the parent nucleus, and the final mass is that of the daughter nucleus and the electron created in the decay. The neutrino is massless, or nearly so. However, since the masses given in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> are for neutral atoms, the daughter nucleus has one more electron than the parent, and so the extra electron mass that corresponds to the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-440ae4ca344f27eef5ed1d3596773d04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> is included in the atomic mass of Ni. Thus, <\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-38d23377f2d9e83e751b607ebf43ac6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"221\" style=\"vertical-align: -7px;\" \/><\/div>\n<p id=\"import-auto-id3257037\"><strong>Solution<\/strong><\/p>\n<p>The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> is<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6dc7b930275abf04bc122517790bc3f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#55;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#51;&#125;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#56;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#51;&#50;&#125;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"213\" style=\"vertical-align: -5px;\" \/><\/div>\n<p>As noticed,<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"eip-371\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-38d23377f2d9e83e751b607ebf43ac6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"221\" style=\"vertical-align: -7px;\" \/><\/div>\n<p>Entering the masses found in <a href=\"\/contents\/aaf30a54-a356-4c5f-8c0d-2f55e4d20556@3\">Appendix A<\/a> gives<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-cc22f50558da37d701637d22d45eda56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#57;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#51;&#51;&#56;&#50;&#48;&#32;&#117;&#125;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#57;&#46;&#57;&#51;&#48;&#55;&#56;&#57;&#32;&#117;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#48;&#48;&#51;&#48;&#51;&#49;&#32;&#117;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"369\" style=\"vertical-align: -1px;\" \/><\/div>\n<p id=\"import-auto-id2209670\">Thus,<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8f8c350bd00005d532eef1901a105587_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#46;&#48;&#48;&#51;&#48;&#51;&#49;&#32;&#117;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"243\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"import-auto-id3259992\">Using <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1a403e8606cbe65a49d4897a6e0fce26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#32;&#117;&#61;&#57;&#51;&#49;&#46;&#53;&#32;&#77;&#101;&#86;&#47;&#123;&#99;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"146\" style=\"vertical-align: -5px;\" \/>, we obtain<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a588dfeef9daf117e93c26f031664468_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#48;&#48;&#51;&#48;&#51;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#51;&#49;&#46;&#53;&#32;&#77;&#101;&#86;&#47;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#50;&#32;&#77;&#101;&#86;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"379\" style=\"vertical-align: -7px;\" \/><\/div>\n<p id=\"import-auto-id3421994\"><strong>Discussion and Implications<\/strong><\/p>\n<p id=\"import-auto-id3054780\">Perhaps the most difficult thing about this example is convincing yourself that the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> mass is included in the atomic mass of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d3927179b7e5ccb2da584c63f799945f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/>. Beyond that are other implications. Again the decay energy is in the MeV range. This energy is shared by all of the products of the decay. In many <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> decays, the daughter nucleus <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d3927179b7e5ccb2da584c63f799945f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/> is left in an excited state and emits photons (<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> rays). Most of the remaining energy goes to the electron and neutrino, since the recoil kinetic energy of the daughter nucleus is small. One final note: the electron emitted in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay is created in the nucleus at the time of decay.<\/p>\n<\/div>\n<p id=\"import-auto-id3063962\">The second type of beta decay is less common than the first. It is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/>decay. Certain nuclides decay by the emission of a <em data-effect=\"italics\">positive<\/em> electron. This is <span data-type=\"term\" id=\"import-auto-id1539094\">antielectron<\/span> or <span data-type=\"term\" id=\"import-auto-id3340946\">positron decay<\/span> (see <a href=\"#import-auto-id3250027\" class=\"autogenerated-content\">(Figure)<\/a>).<\/p>\n<div class=\"bc-figure figure\" id=\"import-auto-id3250027\">\n<div class=\"bc-figcaption figcaption\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay is the emission of a positron that eventually finds an electron to annihilate, characteristically producing gammas in opposite directions.<\/div>\n<p><span data-type=\"media\" id=\"import-auto-id3250028\" data-alt=\"Image shows parent nucleus before beta plus decay and daughter nucleus after beta plus decay, which results in a positively charged electron called a positron.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/clalonde\/wp-content\/uploads\/sites\/280\/2017\/10\/Figure_32_04_05a.jpg\" data-media-type=\"image\/jpg\" alt=\"Image shows parent nucleus before beta plus decay and daughter nucleus after beta plus decay, which results in a positively charged electron called a positron.\" width=\"200\" \/><\/span><\/p>\n<\/div>\n<p>The antielectron is often represented by the symbol <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1aa956987d669d924ff3a36e9925f094_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#101;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: 0px;\" \/>, but in beta decay it is written as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> to indicate the antielectron was emitted in a nuclear decay. Antielectrons are the antimatter counterpart to electrons, being nearly identical, having the same mass, spin, and so on, but having a positive charge and an electron family number of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2a61410f041331e606d64882668a12b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: -1px;\" \/>. When a <span data-type=\"term\">positron<\/span> encounters an electron, there is a mutual annihilation in which all the mass of the antielectron-electron pair is converted into pure photon energy. (The reaction, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9107dfe0a6feb5fcadfa3d9741b1d8d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#101;&#125;&#94;&#123;&#43;&#125;&#43;&#123;&#101;&#125;&#94;&#123;&#45;&#125;&#92;&#116;&#111;&#32;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#43;&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -4px;\" \/>, conserves electron family number as well as all other conserved quantities.) If a nuclide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c719fef559590cd824e0d022d9e1a1eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"38\" style=\"vertical-align: -5px;\" \/> is known to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay, then its <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/><strong data-effect=\"bold\"><span data-type=\"term\" id=\"import-auto-id3102703\">decay equation<\/span> is<\/strong><\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2e252faf272f6ec1192f9ac609270f97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#49;&#125;&#123;&#125;&#94;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#43;&#49;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#101;&#99;&#97;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"329\" style=\"vertical-align: -5px;\" \/><\/div>\n<p id=\"import-auto-id1447217\">where Y is the nuclide having one less proton than X (to conserve charge) and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-80f78aaf563a079d3048244927e0704b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\" \/> is the symbol for the <span data-type=\"term\" id=\"import-auto-id1815789\">electron\u2019s neutrino<\/span>, which has an electron family number of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d4932b1a489a055f2908670bac049524_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"22\" style=\"vertical-align: -2px;\" \/>. Since an antimatter member of the electron family (the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/>) is created in the decay, a matter member of the family (here the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-80f78aaf563a079d3048244927e0704b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\" \/>) must also be created. Given, for example, that<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f2c6236e7b3ffc0ce3945577257fc876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decays, you can write its full decay equation by first finding that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-33ce3444c42037ac6afd41ba4df927a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: -1px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f2c6236e7b3ffc0ce3945577257fc876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/>, so that the daughter nuclide will have<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-74ef91538e7bfffd9c9181dbb26566da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: -1px;\" \/>, the atomic number for neon. Thus the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f2c6236e7b3ffc0ce3945577257fc876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> is<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d966a1dffe88985381e311b5b8576b14_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#97;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#101;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#125;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"215\" style=\"vertical-align: -6px;\" \/><\/div>\n<p id=\"import-auto-id2429706\">In <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay, it is as if one of the protons in the parent nucleus decays into a neutron, a positron, and a neutrino. Protons do not do this outside of the nucleus, and so the decay is due to the complexities of the nuclear force. Note again that the total number of nucleons is constant in this and any other reaction. To find the energy emitted in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay, you must again count the number of electrons in the neutral atoms, since atomic masses are used. The daughter has one less electron than the parent, and one electron mass is created in the decay. Thus, in <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay,<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a8f2a308c4190ae17858989af8b14aec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#61;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#97;&#114;&#101;&#110;&#116;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#91;&#109;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#97;&#117;&#103;&#104;&#116;&#101;&#114;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#123;&#50;&#109;&#125;&#95;&#123;&#101;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#93;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"329\" style=\"vertical-align: -5px;\" \/><\/div>\n<p id=\"import-auto-id3397934\">since we use the masses of neutral atoms.<\/p>\n<p><span data-type=\"term\">Electron capture<\/span> is the third type of beta decay. Here, a nucleus captures an inner-shell electron and undergoes a nuclear reaction that has the same effect as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay. Electron capture is sometimes denoted by the letters EC. We know that electrons cannot reside in the nucleus, but this is a nuclear reaction that consumes the electron and occurs spontaneously only when the products have less mass than the parent plus the electron. If a nuclide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c719fef559590cd824e0d022d9e1a1eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"38\" style=\"vertical-align: -5px;\" \/> is known to undergo electron capture, then its <span data-type=\"term\" id=\"import-auto-id3137718\">electron capture equation<\/span> is<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"fs-id877331\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7981a9f397953a5431baf4201feea4a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#43;&#123;&#101;&#125;&#94;&#123;&#45;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#49;&#125;&#123;&#125;&#94;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#43;&#49;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#108;&#101;&#99;&#116;&#114;&#111;&#110;&#32;&#99;&#97;&#112;&#116;&#117;&#114;&#101;&#44;&#32;&#111;&#114;&#32;&#69;&#67;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"434\" style=\"vertical-align: -5px;\" \/><\/div>\n<p id=\"import-auto-id2654139\">Any nuclide that can <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay can also undergo electron capture (and often does both). The same conservation laws are obeyed for EC as for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay. It is good practice to confirm these for yourself.<\/p>\n<p id=\"import-auto-id3163016\">All forms of beta decay occur because the parent nuclide is unstable and lies outside the region of stability in the chart of nuclides. Those nuclides that have relatively more neutrons than those in the region of stability will <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay to produce a daughter with fewer neutrons, producing a daughter nearer the region of stability. Similarly, those nuclides having relatively more protons than those in the region of stability will <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay or undergo electron capture to produce a daughter with fewer protons, nearer the region of stability.<\/p>\n<\/div>\n<div class=\"bc-section section\" data-depth=\"1\" id=\"fs-id3012414\">\n<h1 data-type=\"title\">Gamma Decay<\/h1>\n<p id=\"import-auto-id2928558\"><span data-type=\"term\">Gamma decay<\/span> is the simplest form of nuclear decay\u2014it is the emission of energetic photons by nuclei left in an excited state by some earlier process. Protons and neutrons in an excited nucleus are in higher orbitals, and they fall to lower levels by photon emission (analogous to electrons in excited atoms). Nuclear excited states have lifetimes typically of only about <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c903d3020122e97084703d427a723b81_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/> s, an indication of the great strength of the forces pulling the nucleons to lower states. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> decay equation is simply<\/p>\n<div data-type=\"equation\" class=\"equation\" id=\"fs-id1253157\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c26bfa410e29043fdf681617466c61c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#94;&#123;&#42;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#125;&#123;&#125;&#94;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#43;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#95;&#123;&#49;&#125;&#43;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#95;&#123;&#50;&#125;&#43;&#92;&#99;&#100;&#111;&#116;&#115;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#100;&#101;&#99;&#97;&#121;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"314\" style=\"vertical-align: -5px;\" \/><\/div>\n<p id=\"import-auto-id3402401\">where the asterisk indicates the nucleus is in an excited state. There may be one or more <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> s emitted, depending on how the nuclide de-excites. In radioactive decay, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> emission is common and is preceded by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-39ffee81b79fbfa10c128d48495e8b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\" \/> decay. For example, when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-bc6a3afb9b0a408f6a3c28695d58fe41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decays, it most often leaves the daughter nucleus in an excited state, written <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0c1a3ed0307c5663ea5f6a86f3b5ff0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"41\" style=\"vertical-align: 0px;\" \/>. Then the nickel nucleus quickly <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> decays by the emission of two penetrating <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> s:<\/p>\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-1b40d1fb44e97d7fcc86aca36eace400_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#42;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#54;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#105;&#125;&#43;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#95;&#123;&#49;&#125;&#43;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#95;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -4px;\" \/><\/div>\n<p id=\"import-auto-id3008135\">These are called cobalt <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> rays, although they come from nickel\u2014they are used for cancer therapy, for example. It is again constructive to verify the conservation laws for gamma decay. Finally, since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> decay does not change the nuclide to another species, it is not prominently featured in charts of decay series, such as that in <a href=\"#import-auto-id1930472\" class=\"autogenerated-content\">(Figure)<\/a>.<\/p>\n<p id=\"import-auto-id1473699\">There are other types of nuclear decay, but they occur less commonly than <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-39ffee81b79fbfa10c128d48495e8b8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#116;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\" \/>, and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> decay. Spontaneous fission is the most important of the other forms of nuclear decay because of its applications in nuclear power and weapons. It is covered in the next chapter.<\/p>\n<\/div>\n<div class=\"section-summary\" data-depth=\"1\" id=\"fs-id3032498\">\n<h1 data-type=\"title\">Section Summary<\/h1>\n<ul id=\"fs-id2621009\">\n<li id=\"import-auto-id2681094\">When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay, called alpha <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-81a760d58ae66945a9a03ea68e6f331f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#97;&#108;&#112;&#104;&#97;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"31\" style=\"vertical-align: -4px;\" \/> beta <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-3fa961ff31f56f49e963b6a00745fb85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#98;&#101;&#116;&#97;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#44;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"31\" style=\"vertical-align: -4px;\" \/> and gamma <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c60d1c626d991f2c014fb1e98cbe7ef1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"22\" style=\"vertical-align: -4px;\" \/>. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>  decay equation is\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-07c8258e7b88f48797ea908960899806_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#50;&#125;&#94;&#123;&#65;&#45;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#50;&#125;&#43;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"201\" style=\"vertical-align: -6px;\" \/><\/div>\n<\/li>\n<li id=\"import-auto-id2402192\">Nuclear decay releases an amount of energy <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-764e1c770271f92700e1a4fbce46c668_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> related to the mass destroyed <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8b54ad14e30444378952afb43fab8c57_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"30\" style=\"vertical-align: 0px;\" \/> by\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2d3b923eb52760aee3266c6275d09b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#68;&#101;&#108;&#116;&#97;&#32;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#99;&#125;&#94;&#123;&#50;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/li>\n<li id=\"import-auto-id3450034\">There are three forms of beta decay. The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/>decay equation is\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-66e8c98c47e1b9d1ff7cb82a9c7ef958_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#43;&#49;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#49;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"226\" style=\"vertical-align: -7px;\" \/><\/div>\n<\/li>\n<li id=\"import-auto-id1614644\">The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay equation is\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fa2b5dc5295ba49f4119903c03faeceb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#49;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#43;&#49;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"225\" style=\"vertical-align: -6px;\" \/><\/div>\n<\/li>\n<li id=\"import-auto-id3149618\">The electron capture equation is\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7f1abe8aac53e6bd08b7ec5fc4f504ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#43;&#123;&#101;&#125;&#94;&#123;&#45;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#49;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#43;&#49;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;&#46;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"222\" style=\"vertical-align: -6px;\" \/><\/div>\n<\/li>\n<li id=\"import-auto-id2600265\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> is an electron, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> is an antielectron or positron, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-80f78aaf563a079d3048244927e0704b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\" \/> represents an electron\u2019s neutrino, and  <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-b26bf8421e3994d90214b7643c77280c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -3px;\" \/> is an electron\u2019s antineutrino. In addition to all previously known conservation laws, two new ones arise\u2014 conservation of electron family number  and conservation of the total number of nucleons.  The <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> decay equation is\n<div data-type=\"equation\" class=\"equation\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a69936473c286a6910ae1607da530e1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#123;&#125;&#94;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#94;&#123;&#42;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#125;&#123;&#125;&#94;&#123;&#65;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#125;&#125;&#95;&#123;&#78;&#125;&#43;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#95;&#123;&#49;&#125;&#43;&#123;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#125;&#95;&#123;&#50;&#125;&#43;&#92;&#99;&#100;&#111;&#116;&#115;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"243\" style=\"vertical-align: -5px;\" \/><\/div>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> is a high-energy photon originating in a nucleus.<\/p>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"conceptual-questions\" data-depth=\"1\" id=\"fs-id2929463\" data-element-type=\"conceptual-questions\">\n<h1 data-type=\"title\">Conceptual Questions<\/h1>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2209498\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3388708\">\n<p id=\"import-auto-id3112726\">Star Trek fans have often heard the term \u201cantimatter drive.\u201d Describe how you could use a magnetic field to trap antimatter, such as produced by nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the fraction of matter converted into energy.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1485777\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3164070\">\n<p id=\"import-auto-id1617379\">What conservation law requires an electron\u2019s neutrino to be produced in electron capture? Note that the electron no longer exists after it is captured by the nucleus.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1576428\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3179513\">\n<p id=\"import-auto-id2659009\">Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern Hemisphere and some 100,000 light-years away from Earth, neutrinos from the explosion were observed at about the same time as the light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2006022\" data-element-type=\"conceptual-questions\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2932053\">\n<p id=\"import-auto-id3385870\">What do the three types of beta decay have in common that is distinctly different from alpha decay?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"problems-exercises\" data-depth=\"1\" data-element-type=\"problems-exercises\">\n<h1 data-type=\"title\">Problems &amp; Exercises<\/h1>\n<p id=\"import-auto-id3033441\">In the following eight problems, write the complete decay equation for the given nuclide in the complete <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c719fef559590cd824e0d022d9e1a1eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"38\" style=\"vertical-align: -5px;\" \/> notation. Refer to the periodic table for values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2405551\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2661400\">\n<p id=\"import-auto-id1947269\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ffd38ded86d8ab0f01ba91761b4695f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#51;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -1px;\" \/> (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3234485\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2384056\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-443aa08e0eb7465a55a2e98cb4b2437a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#49;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#125;&#125;&#95;&#123;&#50;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#49;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"175\" style=\"vertical-align: -6px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1907192\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2621600\">\n<p id=\"import-auto-id1569981\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-a5f34b49c719363ef2df3abc94e272ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#52;&#48;&#125;&#125;&#75;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"31\" style=\"vertical-align: 0px;\" \/>, a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2670256\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3065078\">\n<p id=\"import-auto-id2449142\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-852f4dda27a0a3fab0823e5a0a47f32b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#77;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2382245\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id3253996\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e4607ed477c4d7489d96e33608c78094_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#48;&#125;&#125;&#123;&#77;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#53;&#125;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#52;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#48;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#114;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#54;&#125;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"204\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1860601\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2672908\">\n<p id=\"import-auto-id1845794\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6589f1c2e32c3e60de0c94d529db2b6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"33\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2640350\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2615661\">\n<p id=\"import-auto-id2400416\">Electron capture by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-33c449964338a3b473c579fd589f948f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"29\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2628798\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1488206\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7bf754276251a6a7c3aefd00f392628c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#52;&#125;&#94;&#123;&#55;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#101;&#125;&#125;&#95;&#123;&#51;&#125;&#43;&#123;&#101;&#125;&#94;&#123;&#45;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#51;&#125;&#94;&#123;&#55;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#105;&#125;&#125;&#95;&#123;&#52;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"173\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1917574\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1917578\">\n<p>Electron capture by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5fffe0dc2334c2b657caf3fb01438514_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#54;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#110;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"36\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2626117\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3257711\">\n<p id=\"import-auto-id3422558\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-17b3cef778b462e0624b7c858c3e7348_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#49;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#111;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"42\" style=\"vertical-align: -1px;\" \/>, the isotope of polonium in the decay series of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2654425\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id3076865\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e14a89de014286eec98eb943839f9d12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#52;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#49;&#48;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#111;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#54;&#125;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#50;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#54;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#98;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#50;&#52;&#125;&#125;&#43;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"213\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3010127\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3175592\">\n<p id=\"import-auto-id3094872\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7b08416be47f546450c758843fe2335a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#54;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/>, another isotope in the decay series of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/>, first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas.<\/p>\n<\/div>\n<\/div>\n<p id=\"import-auto-id1434739\">In the following four problems, identify the parent nuclide and write the complete decay equation in the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c719fef559590cd824e0d022d9e1a1eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"38\" style=\"vertical-align: -5px;\" \/> notation. Refer to the periodic table for values of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-761fd3ca09ad29ba6f86aa02ff540254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1473021\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3399081\">\n<p id=\"import-auto-id3402679\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay producing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5ddac940218d4fba943be33d250c744d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#51;&#55;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"42\" style=\"vertical-align: 0px;\" \/>. The parent nuclide is a major waste product of reactors and has chemistry similar to potassium and sodium, resulting in its concentration in your cells if ingested.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2017287\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id3036694\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-ea29c2103b2cd748441f347247b93745_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#53;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#51;&#55;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#115;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#50;&#125;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#53;&#54;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#51;&#55;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#97;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#49;&#125;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"223\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3418134\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3418136\">\n<p id=\"import-auto-id2397673\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay producing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fca9c8645b5f21f1955792def40089b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/>. The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-fca9c8645b5f21f1955792def40089b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"29\" style=\"vertical-align: -1px;\" \/> is also radioactive.)<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2011306\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2011309\">\n<p id=\"import-auto-id2962207\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay producing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-668a1220b6097f3ef3a99f9685db92d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/>. The parent nuclide is nearly 100% of the natural element and is found in gas lantern mantles and in metal alloys used in jets (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-668a1220b6097f3ef3a99f9685db92d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/> is also radioactive).<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3355264\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1894648\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-6a646b0768dad0e684a608a72d5a7dd5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#50;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#50;&#125;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#56;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#56;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#48;&#125;&#125;&#43;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"215\" style=\"vertical-align: -5px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3033134\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3033137\">\n<p id=\"import-auto-id3354561\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay producing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9a5ed4b535344f2702df2de82b0a2d54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#48;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#80;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"43\" style=\"vertical-align: -1px;\" \/>. The parent nuclide is in the decay series produced by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-adc925504a5ecc4495e67b487f645619_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"44\" style=\"vertical-align: -1px;\" \/>, the only naturally occurring isotope of thorium.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3164080\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3164082\">\n<p id=\"import-auto-id3028935\">When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9107dfe0a6feb5fcadfa3d9741b1d8d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#101;&#125;&#94;&#123;&#43;&#125;&#43;&#123;&#101;&#125;&#94;&#123;&#45;&#125;&#92;&#116;&#111;&#32;&#92;&#103;&#97;&#109;&#109;&#97;&#32;&#43;&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -4px;\" \/><em data-effect=\"italics\"> conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation. (b) Find the energy of each <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> ray, assuming the electron and positron are initially nearly at rest. (c) Explain why the two <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> rays travel in exactly opposite directions if the center of mass of the electron-positron system is initially at rest.<\/em><\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3176709\">\n<p id=\"import-auto-id2953315\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-5eb1e6d97d887db9c4dc5526039c52d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#104;&#97;&#114;&#103;&#101;&#58;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#108;&#101;&#99;&#116;&#114;&#111;&#110;&#32;&#102;&#97;&#109;&#105;&#108;&#121;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#58;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#65;&#58;&#32;&#48;&#43;&#48;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"582\" style=\"vertical-align: -2px;\" \/><\/p>\n<p id=\"import-auto-id2953320\">(b) 0.511 MeV<\/p>\n<p id=\"import-auto-id1932189\">(c) The two <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-4dfd339d0f13026ff7af56aa6f129380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#103;&#97;&#109;&#109;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\" \/> rays must travel in exactly opposite directions in order to conserve momentum, since initially there is zero momentum if the center of mass is initially at rest.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2442449\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2442452\">\n<p id=\"import-auto-id3062765\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay given in the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f4e0a67f6e48b1007d40ccfc42e21126_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#50;&#125;&#94;&#123;&#65;&#45;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#50;&#125;&#43;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"197\" style=\"vertical-align: -6px;\" \/>. To do this, identify the values of each before and after the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3291026\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3291029\">\n<p id=\"import-auto-id2626320\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay given in the equation<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-d57396aff92cc3ad0a8b9147bd1a7499_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#43;&#49;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#49;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"221\" style=\"vertical-align: -7px;\" \/>. To do this, identify the values of each before and after the decay.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2453152\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id1464681\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-3b6538d1322aa6bb2ba33bd02fdf7b74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#90;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#65;&#61;&#65;&#92;&#116;&#101;&#120;&#116;&#123;&#59;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#102;&#110;&#32;&#58;&#32;&#48;&#125;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"382\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2460264\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3077530\">\n<p id=\"import-auto-id3246240\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay given in the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c77affe7012695ffdc27420ef2b23edb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#49;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#45;&#49;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"220\" style=\"vertical-align: -6px;\" \/>. To do this, identify the values of each before and after the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3178618\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3178621\">\n<p id=\"import-auto-id3422948\">Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in the equation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-02afb431a9ce291477d70677eaec273f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#90;&#125;&#94;&#123;&#65;&#125;&#123;&#88;&#125;&#95;&#123;&#78;&#125;&#43;&#123;&#101;&#125;&#94;&#123;&#45;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#90;&#45;&#49;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#89;&#125;&#125;&#95;&#123;&#78;&#43;&#49;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"217\" style=\"vertical-align: -6px;\" \/>. To do this, identify the values of each before and after the capture.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3035818\">\n<div data-type=\"equation\" class=\"equation\" id=\"import-auto-id2648112\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-0b82d78078f79ca575f590682a68c035_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#90;&#45;&#49;&#61;&#90;&#45;&#49;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#65;&#61;&#65;&#59;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#101;&#102;&#110;&#32;&#58;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"336\" style=\"vertical-align: -4px;\" \/><\/div>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2590538\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2590541\">\n<p id=\"import-auto-id3163760\">A rare decay mode has been observed in which <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9cca4e4737d8e20244423ef517665aa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/> emits a<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-c53e5c35bfd38901e95a8c8feaa59039_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#125;&#125;&#67;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"28\" style=\"vertical-align: 0px;\" \/> nucleus. (a) The decay equation is<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-589df0ff01818d1f691b5ac944c39a7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;&#123;&#92;&#116;&#111;&#32;&#125;&#94;&#123;&#65;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#88;&#43;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#52;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"126\" style=\"vertical-align: -2px;\" \/>. Identify the nuclide <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-8eb62a96c47785a406bf1f0112f93380_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#65;&#125;&#88;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/>. (b) Find the energy emitted in the decay. The mass of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9cca4e4737d8e20244423ef517665aa1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/> is 222.015353 u.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2062598\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2062601\">\n<p>(a) Write the complete <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-7b08416be47f546450c758843fe2335a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#54;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id1981359\">(b) Find the energy released in the decay.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3062624\">\n<p id=\"import-auto-id1998676\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-21aa9fbbd86b0f0d9a5b2ddacc1953b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#56;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#54;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#97;&#125;&#125;&#95;&#123;&#49;&#51;&#56;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#56;&#54;&#125;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#50;&#125;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#82;&#110;&#125;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#51;&#54;&#125;&#125;&#43;&#123;&#125;&#95;&#123;&#50;&#125;&#94;&#123;&#52;&#125;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#72;&#101;&#125;&#125;&#95;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"216\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"import-auto-id3081154\">(b) 4.87 MeV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1893984\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2401213\">\n<p id=\"import-auto-id3253435\">(a) Write the complete <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e9b9abb3bbb700af7a972014c2b64a24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#52;&#57;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#102;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p id=\"import-auto-id2929542\">(b) Find the energy released in the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1871366\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2963343\">\n<p id=\"import-auto-id2670189\">(a) Write the complete <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay equation for the neutron. (b) Find the energy released in the decay.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3254531\">\n<p id=\"import-auto-id2452615\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-088a0befe014e94d316cee2d5e54fd59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#110;&#125;&#92;&#116;&#111;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#112;&#125;&#43;&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;&#43;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#92;&#110;&#117;&#32;&#125;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"129\" style=\"vertical-align: -4px;\" \/><\/p>\n<p id=\"import-auto-id3356256\">(b) ) 0.783 MeV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1116905\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1116908\">\n<p id=\"import-auto-id2449067\">(a) Write the complete <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-11b606b25e9e398c430d53f0bcda3707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#45;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-776b042c1eba5679fca98b71acccec06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#48;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#83;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"32\" style=\"vertical-align: -1px;\" \/>, a major waste product of nuclear reactors. (b) Find the energy released in the decay.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3028069\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3028072\">\n<p>Calculate the energy released in the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f2c6236e7b3ffc0ce3945577257fc876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/>, the equation for which is given in the text. The masses of<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-f2c6236e7b3ffc0ce3945577257fc876_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"37\" style=\"vertical-align: 0px;\" \/> and<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-38906eee50740f16896aacb6fc13ee85_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#50;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#78;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"36\" style=\"vertical-align: 0px;\" \/> are 21.994434 and 21.991383 u, respectively.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id2391615\">\n<p id=\"import-auto-id3033703\">1.82 MeV<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id1441536\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id1863870\">\n<p id=\"import-auto-id2074557\">(a) Write the complete <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-77aea07b1c09110b6d6b6fd5249abec2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#92;&#98;&#101;&#116;&#97;&#32;&#125;&#94;&#123;&#43;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"21\" style=\"vertical-align: -4px;\" \/> decay equation for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2310288ae7338e0eaa48732f7b2425c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id2639096\">(b) Calculate the energy released in the decay. The masses of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-2310288ae7338e0eaa48732f7b2425c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#67;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-642aa94a727d64fb59934376024a103f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#49;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> are 11.011433 and 11.009305 u, respectively.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3402996\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3176786\">\n<p id=\"import-auto-id1848510\">(a) Calculate the energy released in the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-946f8144d4e3d460c8621773145884d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;&#32;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> decay of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id3354600\">(b) What fraction of the mass of a single <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-abe150575b2640caeb07853d026ce87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#56;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> is destroyed in the decay? The mass of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-675c432dd3b9a93e68a313af02880e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#51;&#52;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#84;&#104;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"44\" style=\"vertical-align: -1px;\" \/> is 234.043593 u.<\/p>\n<p id=\"import-auto-id3229174\">(c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id1951662\">\n<p id=\"import-auto-id1486163\">(a) 4.274 MeV<\/p>\n<p id=\"import-auto-id2920736\">(b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-9db6c16f217e56f6688d8d9c993021ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#57;&#50;&#55;&#125;&times;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#48;&#125;&#125;&#94;&#123;&#45;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"75\" style=\"vertical-align: -1px;\" \/><\/p>\n<p id=\"import-auto-id3091706\">(c) Since U-238 is a slowly decaying substance, only a very small number of nuclei decay on human timescales; therefore, although those nuclei that decay lose a noticeable fraction of their mass, the change in the total mass of the sample is not detectable for a macroscopic sample.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id3121887\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id3285569\">\n<p id=\"import-auto-id2962661\">(a) Write the complete reaction equation for electron capture by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-25dfac00e84f47c991adb3cf24efac74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#55;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#101;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"eip-id1826968\">(b) Calculate the energy released.<\/p>\n<\/div>\n<\/div>\n<div data-type=\"exercise\" class=\"exercise\" id=\"fs-id2600565\" data-element-type=\"problem-exercises\">\n<div data-type=\"problem\" class=\"problem\" id=\"fs-id2600568\">\n<p id=\"import-auto-id3109373\">(a) Write the complete reaction equation for electron capture by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-27b0a599ab5841682143221800a4f148_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#79;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"27\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"import-auto-id2979269\">(b) Calculate the energy released.<\/p>\n<\/div>\n<div data-type=\"solution\" class=\"solution\" id=\"fs-id3180437\">\n<p id=\"import-auto-id2662509\">(a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-content\/ql-cache\/quicklatex.com-e00ed201741ea1ee5d6174e2c72fa588_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#123;&#125;&#95;&#123;&#56;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;&#123;&#79;&#125;&#95;&#123;&#55;&#125;&#43;&#123;&#101;&#125;&#94;&#123;&#45;&#125;&#92;&#116;&#111;&#32;&#123;&#125;&#95;&#123;&#55;&#125;&#94;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#53;&#125;&#125;&#123;&#78;&#125;&#95;&#123;&#56;&#125;&#43;&#123;&#92;&#110;&#117;&#32;&#125;&#95;&#123;&#101;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"178\" style=\"vertical-align: -5px;\" \/><\/p>\n<p id=\"import-auto-id2365629\">(b) 2.754 MeV<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"glossary\" class=\"textbox shaded\">\n<h2 data-type=\"glossary-title\">Glossary<\/h2>\n<dl class=\"definition\" id=\"import-auto-id3008963\">\n<dt>parent<\/dt>\n<dd id=\"fs-id2640151\">the original state of nucleus before decay<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1615990\">\n<dt>daughter<\/dt>\n<dd id=\"fs-id2443752\">the nucleus obtained when parent nucleus decays and produces another nucleus following the rules and the conservation laws<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1615993\">\n<dt>positron<\/dt>\n<dd id=\"fs-id3062638\">the particle that results from positive beta decay; also known as an antielectron<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"fs-id2234366\">\n<dt>decay<\/dt>\n<dd>the process by which an atomic nucleus of an unstable atom loses mass and energy by emitting ionizing particles<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1981401\">\n<dt>alpha decay<\/dt>\n<dd id=\"fs-id1517548\">type of radioactive decay in which an atomic nucleus emits an alpha particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1981403\">\n<dt>beta decay<\/dt>\n<dd id=\"fs-id3410683\">type of radioactive decay in which an atomic nucleus emits a beta particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2668157\">\n<dt>gamma decay<\/dt>\n<dd id=\"fs-id3098191\">type of radioactive decay in which an atomic nucleus emits a gamma particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2668160\">\n<dt>decay equation<\/dt>\n<dd id=\"fs-id3109833\">the equation to find out how much of a radioactive material is left after a given period of time<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2449377\">\n<dt>nuclear reaction energy<\/dt>\n<dd id=\"fs-id1995255\">the energy created in a nuclear reaction<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2449379\">\n<dt>neutrino<\/dt>\n<dd id=\"fs-id1587883\">an electrically neutral, weakly interacting elementary subatomic particle<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2382824\">\n<dt>electron\u2019s antineutrino<\/dt>\n<dd id=\"fs-id1977528\">antiparticle of electron\u2019s neutrino<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id2382826\">\n<dt>positron decay<\/dt>\n<dd id=\"fs-id3163006\">type of beta decay in which a proton is converted to a neutron, releasing a positron and a neutrino<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"fs-id2850141\">\n<dt>antielectron<\/dt>\n<dd id=\"fs-id1825605\">another term for positron<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"fs-id1825608\">\n<dt>decay series<\/dt>\n<dd id=\"fs-id1853690\">process whereby subsequent nuclides decay until a stable nuclide is produced<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3209969\">\n<dt>electron\u2019s neutrino<\/dt>\n<dd id=\"fs-id3223437\">a subatomic elementary particle which has no net electric charge<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1954183\">\n<dt>antimatter<\/dt>\n<dd id=\"fs-id1474720\">composed of antiparticles<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id1954185\">\n<dt>electron capture<\/dt>\n<dd id=\"fs-id3401137\">the process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino<\/dd>\n<\/dl>\n<dl class=\"definition\" id=\"import-auto-id3175197\">\n<dt>electron capture equation<\/dt>\n<dd id=\"fs-id3054581\">equation representing the electron capture<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":211,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"all-rights-reserved"},"chapter-type":[],"contributor":[],"license":[56],"class_list":["post-1690","chapter","type-chapter","status-publish","hentry","license-all-rights-reserved"],"part":1663,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1690","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/users\/211"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1690\/revisions"}],"predecessor-version":[{"id":1691,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1690\/revisions\/1691"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/parts\/1663"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapters\/1690\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/media?parent=1690"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/pressbooks\/v2\/chapter-type?post=1690"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/contributor?post=1690"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/ubcbatessandbox\/wp-json\/wp\/v2\/license?post=1690"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}