{"id":623,"date":"2017-09-18T18:11:25","date_gmt":"2017-09-18T22:11:25","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/chapter\/16-2-mass-energy-and-the-theory-of-relativity\/"},"modified":"2018-06-02T12:39:48","modified_gmt":"2018-06-02T16:39:48","slug":"16-2-mass-energy-and-the-theory-of-relativity","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/chapter\/16-2-mass-energy-and-the-theory-of-relativity\/","title":{"raw":"16.2 Mass, Energy, and the Theory of Relativity","rendered":"16.2 Mass, Energy, and the Theory of Relativity"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\"><h3>Learning Objectives<\/h3><p id=\"fs-id1168583350098\">By the end of this section, you will be able to:\n\n<ul id=\"fs-id1170325072683\"><li>Explain how matter can be converted into energy<\/li><li>Describe the particles that make up atoms<\/li><li>Describe the nucleus of an atom<\/li><li>Understand the nuclear forces that hold atoms together<\/li><li>Trace the nuclear reactions in the solar interior<\/li><\/ul><\/div><p id=\"fs-id1170325354478\">As we have seen, <span class=\"no-emphasis\">energy<\/span> cannot be created or destroyed, but only converted from one form to another. One of the remarkable conclusions derived by Albert <span class=\"no-emphasis\">Einstein<\/span> (see <a href=\"#fs-id1170325040535\">Albert Einstein<\/a>) when he developed his <span class=\"no-emphasis\">theory of relativity<\/span> is that matter can be considered a form of energy too and can be converted into energy. Furthermore, energy can also be converted into matter. This seemed to contradict what humans had learned over thousands of years by studying nature. Matter is something we can see and touch, whereas energy is something objects have when they do things like move or heat up. The idea that matter or energy can be converted into each other seemed as outrageous as saying you could accelerate a car by turning the bumper into more speed, or that you could create a bigger front seat by slowing down your car. That would be pretty difficult to believe; yet, the universe actually works somewhat like that.\n\n<section id=\"fs-id1170325199520\"><h1>Converting Matter into Energy<\/h1><p id=\"fs-id1170324983265\">The remarkable equivalence between matter and energy is given in one of the most famous equations:\n\n<div id=\"fs-id1170325132817\" class=\"equation unnumbered\">$E=m{c}^{2}$<\/div><p id=\"fs-id1170325097809\">In this equation, <em>E<\/em> stands for energy, <em>m<\/em> stands for mass, and <em>c<\/em>, the constant that relates the two, is the speed of light (3 \u00d7 10<sup>8<\/sup> meters per second). Note that mass is a measure of the quantity of matter, so the significance of this equation is that matter can be converted into energy and energy can be converted into matter. Let\u2019s compare this equation of converting matter and energy to some common conversion equations that have the same form:\n\n<div id=\"fs-id1170324945270\" class=\"equation unnumbered\">$\\text{inches}=\\text{feet}\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}12,\\text{or cents}=\\text{dollars}\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}100$<\/div><p id=\"fs-id1170325078412\">Just as each conversion formula allows you to calculate the conversion of one thing into another, when we convert matter into energy, we consider how much mass the matter has. The conversion factor in this case turns out not to be either 12 or 100, as in our examples, but another constant quantity: the speed of light squared. Note that matter does not have to travel at the speed of light (or the speed of light squared) for this conversion to occur. The factor of <em>c<\/em><sup>2<\/sup> is just the number that Einstein showed must be used to relate mass and energy.\n\n<p id=\"fs-id1170325084715\">Notice that this formula does not tell us <em>how<\/em> to convert mass into energy, just as the formula for cents does not tell us where to exchange coins for a dollar bill. The formulas merely tell us what the equivalent values are if we succeed in making the conversion. When Einstein first derived his formula in 1905, no one had the faintest idea how to convert mass into energy in any practical way. Einstein himself tried to discourage speculation that the large-scale conversion of atomic mass into energy would be feasible in the near future. Today, as a result of developments in nuclear physics, we regularly convert mass into energy in power plants, nuclear weapons, and high-energy physics experiments in particle accelerators.\n\nBecause the speed of light squared (<em>c<\/em><sup>2<\/sup>) is a very large quantity, the conversion of even a small amount of mass results in a very large amount of energy. For example, the complete conversion of 1 gram of matter (about 1\/28 ounce, or approximately 1 paperclip) would produce as much energy as the burning of 15,000 barrels of oil.\n\n<p id=\"fs-id1170325357432\">Scientists soon realized that the conversion of mass into energy is the source of the Sun\u2019s heat and light. With Einstein\u2019s equation of <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>, we can calculate that the amount of energy radiated by the Sun could be produced by the complete conversion of about 4 million tons of matter into energy inside the Sun each second. Destroying 4 million tons per second sounds like a lot when compared to earthly things, but bear in mind that the Sun is a very big reservoir of matter. In fact, we will see that the Sun contains more than enough mass to destroy such huge amounts of matter and still continue shining at its present rate for billions of years.\n\n<p id=\"fs-id1170325403548\">But knowing all that still does not tell us <em>how<\/em> mass can be converted into energy. To understand the process that actually occurs in the Sun, we need to explore the structure of the atom a bit further.\n\n<div id=\"fs-id1170325040535\" class=\"note astronony voyagers-in-astronomy\"><div class=\"textbox shaded\"><div class=\"title\"><strong>Albert Einstein<\/strong><\/div><p id=\"fs-id1170325054908\">For a large part of his life, Albert <span class=\"no-emphasis\">Einstein<\/span> (<a href=\"#OSC_Astro_16_02_Albert\" class=\"autogenerated-content\">[link]<\/a>) was one of the most recognized celebrities of his day. Strangers stopped him on the street, and people all over the world asked him for endorsements, advice, and assistance. In fact, when Einstein and the great film star Charlie Chaplin met in California, they found they shared similar feelings about the loss of privacy that came with fame. Einstein\u2019s name was a household word despite the fact that most people did not understand the ideas that had made him famous.\n\n<p id=\"fs-id1170324940205\">Einstein was born in 1879 in Ulm, Germany. Legend has it that he did not do well in school (even in arithmetic), and thousands of students have since attempted to justify a bad grade by referring to this story. Alas, like many legends, this one is not true. Records indicate that although he tended to rebel against the authoritarian teaching style in vogue in Germany at that time, Einstein was a good student.\n\n<p id=\"fs-id1170325268120\">After graduating from the Federal Polytechnic Institute in Zurich, Switzerland, Einstein at first had trouble getting a job (even as a high school teacher), but he eventually became an examiner in the Swiss Patent Office. Working in his spare time, without the benefit of a university environment but using his superb physical intuition, he wrote four papers in 1905 that would ultimately transform the way physicists looked at the world.\n\n<p id=\"fs-id1170324935900\">One of these, which earned Einstein the Nobel Prize in 1921, set part of the foundation of <em>quantum mechanics<\/em>\u2014the rich, puzzling, and remarkable theory of the subatomic realm. But his most important paper presented the <em>special theory of relativity<\/em>, a reexamination of space, time, and motion that added a whole new level of sophistication to our understanding of those concepts. The famed equation <em>E<\/em> = <em>mc<\/em><sup>2<\/sup> was actually a relatively minor part of this theory, added in a later paper.\n\n<p id=\"fs-id1170325046666\">In 1916, Einstein published his <em>general theory of relativity<\/em>, which was, among other things, a fundamentally new description of gravity (see <a href=\"\/contents\/c58084cd-93fa-48ba-82a5-8bc44de393ed\" class=\"target-chapter\">Black Holes and Curved Spacetime<\/a>). When this theory was confirmed by measurements of the \u201cbending of starlight\u201d during a 1919 eclipse (<em>The New York Times<\/em> headline read, \u201cLights All Askew in the Heavens\u201d), Einstein became world famous.\n\n<p id=\"fs-id1170325052373\">In 1933, to escape Nazi persecution, Einstein left his professorship in Berlin and settled in the United States at the newly created Institute for Advanced Studies at Princeton. He remained there until his death in 1955, writing, lecturing, and espousing a variety of intellectual and political causes. For example, he agreed to sign a letter written by Leo Szilard and other scientists in 1939, alerting President Roosevelt to the dangers of allowing Nazi Germany to develop the atomic bomb first. And in 1952, Einstein was offered the second presidency of Israel. In declining the position, he said, \u201cI know a little about nature and hardly anything about men.\u201d\n\n<figure id=\"OSC_Astro_16_02_Albert\"><div class=\"title\" style=\"text-align: center\"><strong>Albert Einstein (1879\u20131955).<\/strong><\/div>[caption id=\"\" align=\"aligncenter\" width=\"325\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Albert-1.jpg\" alt=\"Photograph of Albert Einstein.\" width=\"325\" height=\"391\"> <strong>Figure 1.<\/strong> This portrait of Einstein was taken in 1912. (credit: modification of work by J. F. Langhans)[\/caption]<\/figure><\/div>&nbsp;\n\n<\/div><\/section><section><h1>Elementary Particles<\/h1><p id=\"fs-id1170324918878\">The fundamental components of atoms are the proton, neutron, and electron (see <a href=\"\/contents\/22d9d199-7c88-418f-92bd-6cb72d0e1a53\" class=\"target-chapter\">The Structure of the Atom<\/a>).\n\n<p id=\"fs-id1170325103467\">Protons, neutrons, and electrons are by no means all the particles that exist. First, for each kind of particle, there is a corresponding but opposite <em>antiparticle<\/em>. If the particle carries a charge, its <span class=\"no-emphasis\">antiparticle<\/span> has the opposite charge. The antielectron is the <em>positron<\/em>, which has the same mass as the electron but is positively charged. Similarly, the antiproton has a negative charge. The remarkable thing about such <em>antimatter<\/em> is that when a particle comes into contact with its antiparticle, the original particles are annihilated, and substantial amounts of energy in the form of photons are produced.\n\n<p id=\"fs-id1170325024112\">Since our world is made exclusively of ordinary particles of matter, <span class=\"no-emphasis\">antimatter<\/span> cannot survive for very long. But individual antiparticles are found in cosmic rays (particles that arrive at the top of Earth\u2019s atmosphere from space) and can be created in particle accelerators. And, as we will see in a moment, antimatter is created in the core of the Sun and other stars.\n\n<p id=\"fs-id1170325234700\">Science fiction fans may be familiar with antimatter from the <em>Star Trek<\/em> television series and films. The Starship Enterprise is propelled by the careful combining of matter and antimatter in the ship\u2019s engine room. According to <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>, the annihilation of matter and antimatter can produce a huge amount of energy, but keeping the antimatter fuel from touching the ship before it is needed must be a big problem. No wonder Scotty, the chief engineer in the original TV show, always looked worried!\n\n<p id=\"fs-id1170325083688\">In 1933, physicist Wolfgang <span class=\"no-emphasis\">Pauli<\/span> (<a href=\"#OSC_Astro_16_02_Pauli\" class=\"autogenerated-content\">[link]<\/a>) suggested that there might be another type of elementary particle. Energy seemed to disappear when certain types of nuclear reactions took place, violating the law of conservation of energy. Pauli was reluctant to accept the idea that one of the basic laws of physics was wrong, and he suggested a \u201cdesperate remedy.\u201d Perhaps a so-far-undetected particle, which was given the name <span>neutrino<\/span> (\u201clittle neutral one\u201d), carried away the \u201cmissing\u201d energy. He suggested that neutrinos were particles with zero mass, and that like photons, they moved with the speed of light.\n\n<figure id=\"OSC_Astro_16_02_Pauli\"><div class=\"title\" style=\"text-align: center\"><strong>Wolfgang Pauli in 1945.<\/strong><\/div>[caption id=\"\" align=\"aligncenter\" width=\"325\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Pauli-1.jpg\" alt=\"Photograph of Wolfgang Pauli.\" width=\"325\" height=\"460\"> <strong>Figure 2.<\/strong> Pauli is considered the \u201cfather\u201d of the neutrino, having conceived of it in 1933.[\/caption]<\/figure><p id=\"fs-id1170325104048\">The elusive neutrino was not detected until 1956. The reason it was so hard to find is that neutrinos interact very weakly with other matter and therefore are very difficult to detect. Earth is more transparent to a neutrino than the thinnest and cleanest pane of glass is to a photon of light. In fact, most neutrinos can pass completely through a star or planet without being absorbed. As we shall see, this behavior of neutrinos makes them a very important tool for studying the Sun. Since Pauli\u2019s prediction, scientists have learned a lot more about the neutrino. We now know that there are three different types of neutrinos, and in 1998, neutrinos were discovered to have a tiny amount of mass. Indeed, it is so tiny that electrons are at least 500,000 times more massive. Ongoing research is focused on determining the mass of neutrinos more precisely, and it may still turn out that one of the three types is massless. We will return to the subject of neutrinos later in this chapter.\n\n<p id=\"fs-id1170325169909\">Some of the properties of the proton, electron, neutron, and neutrino are summarized in <a href=\"#fs-id1170325216952\" class=\"autogenerated-content\">[link]<\/a>. (Other subatomic particles have been produced by experiments with particle accelerators, but they do not play a role in the generation of solar energy.)\n\n&lt;table id=\"fs-id1170325216952\" class=\"span-all\" summary=\"This table contains 3 columns and 5 rows. The first row is a header row and contains the values, \u201cParticle\u201d, \u201cMass (kg)\u201d, and \u201cCharge\u201d. Under the \u201cParticle\u201d column are the values, \u201cProton\u201d, \u201cNeutron\u201d, \u201cElectron\u201d, and \u201cNeutrino\u201d. Under the \u201cMass (kg)\u201d column are the values, \u201c1.67265 \u00d7 10\u201327\u201d, \u201c1.67495 \u00d7 10\u201327\u201d, \u201c9.11 \u00d7 10\u201331\u201d, and \u201c\n\n<thead><tr><th colspan=\"3\">Properties of Some Common Particles<\/th><\/tr><tr valign=\"top\"><th>Particle<\/th><th>Mass (kg)<\/th><th>Charge<\/th><\/tr><\/thead><tbody><tr valign=\"top\"><td>Proton<\/td><td>1.67265 \u00d7 10<sup>\u221227<\/sup><\/td><td>+1<\/td><\/tr><tr valign=\"top\"><td>Neutron<\/td><td>1.67495 \u00d7 10<sup>\u221227<\/sup><\/td><td>0<\/td><\/tr><tr valign=\"top\"><td>Electron<\/td><td>9.11 \u00d7 10<sup>\u221231<\/sup><\/td><td>\u22121<\/td><\/tr><tr valign=\"top\"><td>Neutrino<\/td><td>&lt;2 \u00d7 10<sup>\u221236<\/sup> (uncertain)<\/td><td>0<\/td><\/tr><\/tbody><\/section><section id=\"fs-id1170324929199\"><h1>The Atomic Nucleus<\/h1><p id=\"fs-id1170324945566\">The nucleus of an atom is not just a loose collection of elementary particles. Inside the nucleus, particles are held together by a very powerful force called the <span class=\"no-emphasis\">strong nuclear force<\/span>. This is short-range force, only capable of acting over distances about the size of the atomic nucleus. A quick thought experiment shows how important this force is. Take a look at your finger and consider the atoms composing it. Among them is carbon, one of the basic elements of life. Focus your imagination on the nucleus of one of your carbon atoms. It contains six protons, which have a positive charge, and six neutrons, which are neutral. Thus, the nucleus has a net charge of six positives. If only the electrical force were acting, the protons in this and every carbon atom would find each other very repulsive and fly apart.\n\n<p id=\"fs-id1170324934944\">The strong nuclear force is an attractive force, stronger than the electrical force, and it keeps the particles of the nucleus tightly bound together. We saw earlier that if under the force of gravity a star \u201cshrinks\u201d\u2014bringing its atoms closer together\u2014gravitational energy is released. In the same way, if particles come together under the strong nuclear force and unite to form an atomic nucleus, some of the nuclear energy is released. The energy given up in such a process is called the <em>binding energy<\/em> of the nucleus.\n\n<p id=\"fs-id1170325342849\">When such <span class=\"no-emphasis\">binding energy<\/span> is released, the resulting nucleus has slightly less mass than the sum of the masses of the particles that came together to form it. In other words, the energy comes from the loss of mass. This slight deficit in mass is only a small fraction of the mass of one proton. But because each bit of lost mass can provide a lot of energy (remember, <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>), this nuclear energy release can be quite substantial.\n\n<p id=\"fs-id1170325065963\">Measurements show that the binding energy is greatest for atoms with a mass near that of the iron nucleus (with a combined number of protons and neutrons equal to 56) and less for both the lighter and the heavier nuclei. Iron, therefore, is the most stable element: since it gives up the most energy when it forms, it would require the most energy to break it back down into its component particles.\n\n<p id=\"fs-id1170325355088\">What this means is that, in general, when light atomic nuclei come together to form a heavier one (up to iron), mass is lost and energy is released. This joining together of atomic nuclei is called nuclear <span>fusion<\/span>.\n\n<p id=\"fs-id1170325073328\">Energy can also be produced by breaking up heavy atomic nuclei into lighter ones (down to iron); this process is called nuclear <span>fission<\/span>. Nuclear fission was the process we learned to use first\u2014in atomic bombs and in nuclear reactors used to generate electrical power\u2014and it may therefore be more familiar to you. Fission also sometimes occurs spontaneously in some unstable nuclei through the process of natural radioactivity. But fission requires big, complex nuclei, whereas we know that the stars are made up predominantly of small, simple nuclei. So we must look to fusion first to explain the energy of the Sun and the stars (<a href=\"#OSC_Astro_16_02_FissFusion\" class=\"autogenerated-content\">[link]<\/a>).\n\n<figure id=\"OSC_Astro_16_02_FissFusion\"><div class=\"title\" style=\"text-align: center\"><strong>Fusion and Fission.<\/strong><\/div>[caption id=\"\" align=\"aligncenter\" width=\"465\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_FissFusion-1.jpg\" alt=\"In (a) one white sphere and one green sphere join together. In (b), a ball consisting of many smaller white and green spheres breaks apart into two smaller balls of green and white spheres.\" width=\"465\" height=\"294\"> <strong>Figure 3.<\/strong> (a) In fusion, light atomic nuclei join together to form a heavier nuclei, releasing energy in the process. (b) In fission, energy is produced by the breaking up of heavy, complex nuclei into lighter ones.[\/caption]<\/figure><\/section><section id=\"fs-id1170322739286\"><h1>Nuclear Attraction versus Electrical Repulsion<\/h1><p id=\"fs-id1170325124283\">So far, we seem to have a very attractive prescription for producing the energy emitted by the Sun: \u201croll\u201d some nuclei together and join them via nuclear fusion. This will cause them to lose some of their mass, which then turns into energy. However, every nucleus, even simple hydrogen, has protons\u2014and protons all have positive charges. Since like charges repel via the electrical force, the closer we get two nuclei to each other, the more they repel. It\u2019s true that if we can get them within \u201cstriking distance\u201d of the nuclear force, they will then come together with a much stronger attraction. But that striking distance is very tiny, about the size of a nucleus. How can we get nuclei close enough to participate in fusion?\n\n<p id=\"fs-id1170325176178\">The answer turns out to be heat\u2014tremendous heat\u2014which speeds the protons up enough to overcome the electrical forces that try to keep protons apart. Inside the Sun, as we saw, the most common element is hydrogen, whose nucleus contains only a single proton. Two protons can fuse only in regions where the temperature is greater than about 12 million K, and the speed of the protons average around 1000 kilometers per second or more. (In old-fashioned units, that\u2019s over 2 million miles per hour!)\n\n<p id=\"fs-id1170325244913\">In our Sun, such extreme temperatures are reached only in the regions near its center, which has a temperature of 15 million K. Calculations show that nearly all of the Sun\u2019s energy is generated within about 150,000 kilometers of its core, or within less than 10% of its total volume.\n\n<p id=\"fs-id1170325088211\">Even at these high temperatures, it is exceedingly difficult to force two protons to combine. On average, a proton will rebound from other protons in the Sun\u2019s crowded core for about 14 billion years, at the rate of <em>100 million collisions per second<\/em>, before it fuses with a second proton. This is, however, only the <em>average<\/em> waiting time. Some of the enormous numbers of protons in the Sun\u2019s inner region are \u201clucky\u201d and take only a few collisions to achieve a fusion reaction: they are the protons responsible for producing the energy radiated by the Sun. Since the Sun is about 4.5 billion years old, most of its protons have not yet been involved in fusion reactions.\n\n<\/section><section><h1>Nuclear Reactions in the Sun\u2019s Interior<\/h1><p id=\"fs-id1170324933114\">The <span class=\"no-emphasis\">Sun<\/span>, then, taps the energy contained in the nuclei of atoms through nuclear <span class=\"no-emphasis\">fusion<\/span>. Let\u2019s look at what happens in more detail. Deep inside the Sun, a three-step process takes four hydrogen nuclei and fuses them together to form a single helium nucleus. The helium nucleus is slightly less massive than the four hydrogen nuclei that combine to form it, and that mass is converted into energy.\n\n<p id=\"fs-id1170324902364\">The initial step required to form one helium nucleus from four hydrogen nuclei is shown in <a href=\"#OSC_Astro_16_02_Step1\" class=\"autogenerated-content\">[link]<\/a>. At the high temperatures inside the Sun\u2019s core, two protons combine to make a <em>deuterium<\/em> nucleus, which is an isotope (or version) of hydrogen that contains one proton and one neutron. In effect, one of the original protons has been converted into a neutron in the fusion reaction. Electric charge has to be conserved in nuclear reactions, and it is conserved in this one. A <span>positron<\/span> (antimatter electron) emerges from the reaction and carries away the positive charge originally associated with one of the protons.\n\n<figure id=\"OSC_Astro_16_02_Step1\"><div class=\"title\" style=\"text-align: center\"><strong>Proton-Proton Chain, Step 1.<\/strong><\/div>[caption id=\"\" align=\"aligncenter\" width=\"414\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Step1-1.jpg\" alt=\"Diagram of the First Step in the Proton-Proton Chain. At left are shown two protons drawn in blue, and labeled as \u201c1H\u201d. An arrow is drawn from each proton toward the right and converge at an illustration of a small explosion. This explosion represents the release of energy and mass from the collision of the high energy protons. Three arrows are drawn moving away from the explosion toward the right. At the point of the topmost arrow is a neutrino drawn in light blue and labeled \u201cNeutrino\u201d. At the point of the central arrow is a deuterium nucleus drawn as a blue dot (proton) and a red dot (neutron) and labeled \u201c2H\u201d. At the point of the lower arrow is a positron drawn in purple and labeled \u201cPositron\u201d.\" width=\"414\" height=\"152\"> <strong>Figure 4.<\/strong> This is the first step in the process of fusing hydrogen into helium in the Sun. High temperatures are required because this reaction starts with two hydrogen nuclei, which are protons (shown in blue at left) that must overcome electrical repulsion to combine, forming a hydrogen nucleus with a proton and a neutron (shown in red). Note that hydrogen containing one proton and one neutron is given its own name: deuterium. Also produced in this reaction are a positron, which is an antielectron, and an elusive particle named the neutrino.[\/caption]<\/figure><p id=\"fs-id1170324919204\">Since it is antimatter, this positron will instantly collide with a nearby electron, and both will be annihilated, producing electromagnetic energy in the form of gamma-ray photons. This gamma ray, which has been created in the center of the Sun, finds itself in a world crammed full of fast-moving nuclei and electrons. The gamma ray collides with particles of matter and transfers its energy to one of them. The particle later emits another gamma-ray photon, but often the emitted photon has a bit less energy than the one that was absorbed.\n\n<p id=\"fs-id1170325195828\">Such interactions happen to gamma rays again and again and again as they make their way slowly toward the outer layers of the Sun, until their energy becomes so reduced that they are no longer gamma rays but X-rays (recall what you learned in <a href=\"\/contents\/15eec1a9-5e3c-4e2b-abac-8cd61748d4a0\" class=\"target-chapter\">The Electromagnetic Spectrum<\/a>). Later, as the photons lose still more energy through collisions in the crowded center of the Sun, they become ultraviolet photons.\n\n<p id=\"fs-id1170324919096\">By the time they reach the Sun\u2019s surface, most of the photons have given up enough energy to be ordinary light\u2014and they are the sunlight we see coming from our star. (To be precise, each gamma-ray photon is ultimately converted into many separate lower-energy photons of sunlight.) So, the sunlight given off by the Sun today had its origin as a gamma ray produced by nuclear reactions deep in the Sun\u2019s core. The length of time that photons require to reach the surface depends on how far a photon on average travels between collisions, and the travel time depends on what model of the complicated solar interior we accept. Estimates are somewhat uncertain but indicate that the emission of energy from the surface of the Sun can lag its production in the interior by 100,000 years to as much as 1,000,000 years.\n\n<p id=\"fs-id1170325010258\">In addition to the positron, the fusion of two hydrogen atoms to form deuterium results in the emission of a <span class=\"no-emphasis\">neutrino<\/span>. Because neutrinos interact so little with ordinary matter, those produced by fusion reactions near the center of the Sun travel directly to the Sun\u2019s surface and then out into space, in all directions. Neutrinos move at nearly the speed of light, and they escape the Sun about two seconds after they are created.\n\n<figure id=\"OSC_Astro_16_02_Step2\"><div class=\"title\" style=\"text-align: center\"><strong>Proton-Proton Chain, Step 2.<\/strong><\/div><figcaption><\/figcaption>[caption id=\"\" align=\"aligncenter\" width=\"383\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Step2-1.jpg\" alt=\"Diagram of the Second Step in the Proton-Proton Chain. At upper left is the deuterium nucleus from the first step drawn as a blue dot (proton) and a red dot (neutron) and labeled \u201c2H\u201d. At lower left is a proton drawn in blue, and labeled as \u201c1H\u201d. An arrow is drawn from each object toward the right and converge at an illustration of a small explosion. This explosion represents the release of energy and mass from the collision of the deuterium and proton. A single arrow is drawn emerging from the explosion pointing toward the right. At the point of the arrow is an isotope of helium, known as deuterium, drawn as 2 blue dots (protons) and 1 red dot (neutron) and labeled \u201c3He\u201d. A single wavy arrow is drawn moving away from the deuterium nucleus and is labeled \u201cGamma ray\u201d.\" width=\"383\" height=\"176\"> <strong>Figure 5.<\/strong> This is the second step of the proton-proton chain, the fusion reaction that converts hydrogen into helium in the Sun. This step combines one hydrogen nucleus, which is a proton (shown in blue), with the deuterium nucleus from the previous step (shown as a red and blue particle). The product of this is an isotope of helium with two protons (blue) and one neutron (red) and energy in the form of gamma-ray radiation.[\/caption]<\/figure><p id=\"fs-id1170324960240\">The second step in forming helium from hydrogen is to add another proton to the deuterium nucleus to create a helium nucleus that contains two protons and one neutron (<a href=\"#OSC_Astro_16_02_Step2\" class=\"autogenerated-content\">[link]<\/a>). In the process, some mass is again lost and more gamma radiation is emitted. Such a nucleus is helium because an element is defined by its number of protons; any nucleus with two protons is called helium. But this form of helium, which we call helium-3 (and write in shorthand as <sup>3<\/sup>He) is not the isotope we see in the Sun\u2019s atmosphere or on Earth. That helium has two neutrons and two protons and hence is called helium-4 (<sup>4<\/sup>He).\n\n<p id=\"fs-id1170325194210\">To get to helium-4 in the Sun, helium-3 must combine with another helium-3 in the third step of fusion (illustrated in <a href=\"#OSC_Astro_16_02_Step3\" class=\"autogenerated-content\">[link]<\/a>). Note that two energetic protons are left over from this step; each of them comes out of the reaction ready to collide with other protons and to start step 1 in the chain of reactions all over again.\n\n<figure id=\"OSC_Astro_16_02_Step3\"><div class=\"title\" style=\"text-align: center\"><strong>Proton-Proton Chain, Step 3.<\/strong><\/div><figcaption><\/figcaption>[caption id=\"\" align=\"aligncenter\" width=\"397\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Step3-1.jpg\" alt=\"Diagram of the Third Step in the Proton-Proton Chain. At left are two deuterium nuclei each drawn as 2 blue dots (protons) and 1 red dot (neutron), and labeled \u201c3He\u201d. An arrow is drawn from each nucleus toward the right and converge at an illustration of a small explosion. This explosion represents the release of energy and mass from the collision of the deuterium nuclei. Three arrows are drawn moving away from the explosion toward the right. At the point of the topmost arrow is a proton drawn in blue and labeled \u201c1H\u201d. At the point of the center arrow a helium nucleus is drawn as two blue dots (protons) and two red dots (neutrons) and labeled \u201c4He\u201d. At the point of the lower arrow is a proton drawn in blue and labeled \u201c1H\u201d.\" width=\"397\" height=\"164\"> <strong>Figure 6.<\/strong> This is the third step in the fusion of hydrogen into helium in the Sun. Note that the two helium-3 nuclei from the second step (see [link]) must combine before the third step becomes possible. The two protons that come out of this step have the energy to collide with other protons in the Sun and start step one again.[\/caption]<\/figure><div id=\"fs-id1170325443812\" class=\"note astronomy link-to-learning\"><div class=\"textbox shaded\">These animations of <a href=\"https:\/\/openstaxcollege.org\/l\/30proproreactio\">proton-proton reactions<\/a> show the steps required for fusion of hydrogen into helium in the Sun.<\/div><\/div><div id=\"fs-id1170325345072\" class=\"note astronomy link-to-learning\"><div class=\"textbox shaded\">Visit the <a href=\"https:\/\/openstaxcollege.org\/l\/30tokamakfusrea\">Tokamak Fusion Reactor<\/a> at the General Atomics Lab in San Diego, CA, for an 8-minute tour.<\/div><\/div><\/section><section id=\"fs-id1170324978329\"><h1>The Proton-Proton Chain<\/h1><p id=\"fs-id1170324959823\">The nuclear reactions in the Sun that we have been discussing can be described succinctly through the following nuclear formulas:\n\n<div id=\"fs-id1170325088312\" class=\"equation unnumbered\">$\\begin{array}{c}{}_{}^{1}\\text{H}+{}_{}^{1}\\text{H}\u27f6{}_{}^{2}\\text{H}+{\\text{e}}^{+}+v\\hfill \\\\ {}_{}^{2}\\text{H}+{}_{}^{1}\\text{H}\u27f6{}_{}^{3}\\text{He}+\\gamma \\hfill \\\\ {}_{}^{3}\\text{He}+{}_{}^{3}\\text{He}\u27f6{}_{}^{4}\\text{He}+{}_{}^{1}\\text{H}+{}_{}^{1}\\text{H}\\hfill \\end{array}$<\/div><p id=\"fs-id1170325090920\">Here, the superscripts indicate the total number of neutrons plus protons in the nucleus, e<sup>+<\/sup> is the positron, <em>v<\/em> is the neutrino, and <em>\u03b3<\/em> indicates that gamma rays are emitted. Note that the third step requires two helium-3 nuclei to start; the first two steps must happen twice before the third step can occur.\n\n<p id=\"fs-id1170324920113\">Although, as we discussed, the first step in this chain of reactions is very difficult and generally takes a long time, the other steps happen more quickly. After the deuterium nucleus is formed, it survives an average of only about 6 seconds before being converted into <sup>3<\/sup>He. About a million years after that (on average), the <sup>3<\/sup>He nucleus will combine with another to form <sup>4<\/sup>He.\n\n<p id=\"fs-id1170325159055\">We can compute the amount of energy these reactions generate by calculating the difference in the initial and final masses. The masses of hydrogen and helium atoms in the units normally used by scientists are 1.007825 <em>u<\/em> and 4.00268 <em>u<\/em>, respectively. (The unit of mass, <em>u<\/em>, is defined to be 1\/12 the mass of an atom of carbon, or approximately the mass of a proton.) Here, we include the mass of the entire atom, not just the nucleus, because electrons are involved as well. When hydrogen is converted into helium, two positrons are created (remember, the first step happens twice), and these are annihilated with two free electrons, adding to the energy produced.\n\n<div id=\"fs-id1170325080568\" class=\"equation unnumbered\">$\\begin{array}{cc}\\hfill 4\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}1.007825&amp; =4.03130\\phantom{\\rule{0.2em}{0ex}}u\\phantom{\\rule{0.2em}{0ex}}\\text{(mass of initial hydrogen atoms)}\\hfill \\\\ &amp; \\phantom{\\rule{0.2em}{0ex}}\\text{\u2212}\\phantom{\\rule{0.3em}{0ex}}4.00268\\phantom{\\rule{0.2em}{0ex}}u\\phantom{\\rule{0.2em}{0ex}}\\text{(mass of final helium atoms)}\\hfill \\\\ &amp; =0.02862\\phantom{\\rule{0.2em}{0ex}}u\\phantom{\\rule{0.2em}{0ex}}\\text{(mass lost in the transformation)}\\hfill \\end{array}$<\/div><p id=\"fs-id1170324914897\">The mass lost, 0.02862 <em>u<\/em>, is 0.71% of the mass of the initial hydrogen. Thus, if 1 kilogram of hydrogen is converted into helium, then the mass of the helium is only 0.9929 kilogram, and 0.0071 kilogram of material is converted into energy. The speed of light (<em>c<\/em>) is 3 \u00d7 10<sup>8<\/sup> meters per second, so the energy released by the conversion of just 1 kilogram of hydrogen into helium is:\n\n<div id=\"fs-id1170325354129\" class=\"equation unnumbered\">$\\begin{array}{}\\\\ \\\\ E=m{c}^{2}\\hfill \\\\ E=0.0071\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}{\\left(3\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}{10}^{8}\\text{m\/s}\\right)}^{2}=6.4\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}{10}^{14}\\phantom{\\rule{0.2em}{0ex}}\\text{J}\\hfill \\end{array}$<\/div><p id=\"fs-id1170325078026\">This amount, the energy released when a single kilogram (2.2 pounds) of hydrogen undergoes fusion, would supply all of the electricity used in the United States for about 2 weeks.\n\n<p id=\"fs-id1170325240627\">To produce the Sun\u2019s luminosity of 4 \u00d7 10<sup>26<\/sup> watts, some 600 million tons of hydrogen must be converted into helium <em>each second<\/em>, of which about 4 million tons are converted from matter into energy. As large as these numbers are, the store of hydrogen (and thus of nuclear energy) in the Sun is still <em>more<\/em> enormous, and can last a long time\u2014billions of years, in fact.\n\n<p id=\"fs-id1170325210554\">At the temperatures inside the stars with masses smaller than about 1.2 times the mass of our Sun (a category that includes the Sun itself), most of the energy is produced by the reactions we have just described, and this set of reactions is called the <span>proton-proton chain<\/span> (or sometimes, the p-p chain). In the proton-proton chain, protons collide directly with other protons to form helium nuclei.\n\n<p id=\"fs-id1170325195013\">In hotter stars, another set of reactions, called the carbon-nitrogen-oxygen (CNO) cycle, accomplishes the same net result. In the <span class=\"no-emphasis\">CNO cycle<\/span>, carbon and hydrogen nuclei collide to initiate a series of reactions that form nitrogen, oxygen, and ultimately, helium. The nitrogen and oxygen nuclei do not survive but interact to form carbon again. Therefore, the outcome is the same as in the proton-proton chain: four hydrogen atoms disappear, and in their place, a single helium atom is created. The CNO cycle plays only a minor role in the Sun but is the main source of energy for stars with masses greater than about the mass of the Sun.\n\n<p id=\"fs-id1170325206822\">So you can see that we have solved the puzzle that so worried scientists at the end of the nineteenth century. The Sun can maintain its high temperature and energy output for billions of years through the fusion of the simplest element in the universe, hydrogen. Because most of the Sun (and the other stars) is made of hydrogen, it is an ideal \u201cfuel\u201d for powering a star. As will be discussed in the following chapters, we can define a star as a ball of gas capable of getting its core hot enough to initiate the fusion of hydrogen. There are balls of gas that lack the mass required to do this (Jupiter is a local example); like so many hopefuls in Hollywood, they will never be stars.\n\n<div id=\"fs-id1170325047754\" class=\"note astronomy making-connections\"><div class=\"textbox shaded\"><div class=\"title\"><strong>Fusion on Earth<\/strong><\/div><p id=\"fs-id1170324943586\">Wouldn\u2019t it be wonderful if we could duplicate the Sun\u2019s energy mechanism in a controlled way on Earth? (We have already duplicated it in an uncontrolled way in hydrogen bombs, but we hope our storehouses of these will never be used.) Fusion energy would have many advantages: it would use hydrogen (or deuterium, which is heavy hydrogen) as fuel, and there is abundant hydrogen in Earth\u2019s lakes and oceans. Water is much more evenly distributed around the world than oil or uranium, meaning that a few countries would no longer hold an energy advantage over the others. And unlike fission, which leaves dangerous byproducts, the nuclei that result from fusion are perfectly safe.\n\n<p id=\"fs-id1170325091806\">The problem is that, as we saw, it takes extremely high temperatures for nuclei to overcome their electrical repulsion and undergo fusion. When the first hydrogen bombs were exploded in tests in the 1950s, the \u201cfuses\u201d to get them hot enough were fission bombs. Interactions at such temperatures are difficult to sustain and control. To make fusion power on Earth, after all, we have to do what the Sun does: produce temperatures and pressures high enough to get hydrogen nuclei on intimate terms with one another.\n\n<p id=\"fs-id1170325206600\">The European Union, the United States, South Korea, Japan, China, Russia, Switzerland, and India are collaborating on the <span class=\"no-emphasis\">International Thermonuclear Experimental Reactor (ITER)<\/span>, a project to demonstrate the feasibility of controlled fusion (<a href=\"#OSC_Astro_16_02_ITER\" class=\"autogenerated-content\">[link]<\/a>). The facility is being built in France. Construction will require over 10,000,000 components and 2000 workers for assembly. The date for the start of operations is yet to be determined.\n\n<p id=\"fs-id1170325062203\">ITER is based on the Tokamak design, in which a large doughnut-shaped container is surrounded by superconducting magnets to confine and control the hydrogen nuclei in a strong magnetic field. Previous fusion experiments have produced about 15 million watts of energy, but only for a second or two, and they have required 100 million watts to produce the conditions necessary to achieve fusion. The goal of ITER is to build the first fusion device capable of producing 500 million watts of fusion energy for up to 1000 seconds. The challenge is keeping the deuterium and tritium\u2014which will participate in fusion reactions\u2014hot enough and dense enough, for a long enough time to produce energy.\n\n<figure id=\"OSC_Astro_16_02_ITER\"><div class=\"title\" style=\"text-align: center\"><strong>ITER Design.<\/strong><\/div>[caption id=\"\" align=\"aligncenter\" width=\"487\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_ITER-1.jpg\" alt=\"Cutaway Model of the ITER Design. In the center of this model are two pink kidney shaped areas that represents the hollow chamber wherein the particles will travel. The bright yellow areas surrounding the chamber are the superconducting magnets. Surrounding these two structures are a myriad of pipes, wires, conduits and other components of this highly complex machine.\" width=\"487\" height=\"541\"> <strong>Figure 7.<\/strong> The bright yellow areas in this model show where the superconducting magnets will circle the chamber within which fusion will take place. A huge magnet will keep the charged nuclei of heavy hydrogen confined. The goal is to produce 500 megawatts of energy. (credit: modification of work by Stephan Mosel)[\/caption]<\/figure><\/div>&nbsp;\n\n<\/div><\/section><section id=\"fs-id1170325048064\" class=\"summary\"><h1>Key Concepts and Summary<\/h1><p id=\"fs-id1170325447484\">Solar energy is produced by interactions of particles\u2014that is, protons, neutrons, electrons, positrons, and neutrinos. Specifically, the source of the Sun\u2019s energy is the fusion of hydrogen to form helium. The series of reactions required to convert hydrogen to helium is called the proton-proton chain. A helium atom is about 0.71% less massive than the four hydrogen atoms that combine to form it, and that lost mass is converted to energy (with the amount of energy given by the formula <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>).\n\n<\/section><div><h2>Glossary<\/h2><dl id=\"fs-id1170325276212\" class=\"definition\"><dt>fission<\/dt><dd id=\"fs-id1170325265957\">breaking up of heavier atomic nuclei into lighter ones<\/dd><\/dl><dl id=\"fs-id1170325016080\" class=\"definition\"><dt>fusion<\/dt><dd id=\"fs-id1170325182961\">building up of heavier atomic nuclei from lighter ones<\/dd><\/dl><dl id=\"fs-id1170325187140\" class=\"definition\"><dt>neutrino<\/dt><dd id=\"fs-id1170322673782\">fundamental particle that has no charge and a mass that is tiny relative to an electron; it rarely interacts with ordinary matter and comes in three different types<\/dd><\/dl><dl id=\"fs-id1170325200011\" class=\"definition\"><dt>positron<\/dt><dd id=\"fs-id1170325159136\">particle with the same mass as an electron, but positively charged<\/dd><\/dl><dl id=\"fs-id1170325181179\" class=\"definition\"><dt>proton-proton chain<\/dt><dd id=\"fs-id1170325250566\">series of thermonuclear reactions by which nuclei of hydrogen are built up into nuclei of helium<\/dd><\/dl><\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p id=\"fs-id1168583350098\">By the end of this section, you will be able to:<\/p>\n<ul id=\"fs-id1170325072683\">\n<li>Explain how matter can be converted into energy<\/li>\n<li>Describe the particles that make up atoms<\/li>\n<li>Describe the nucleus of an atom<\/li>\n<li>Understand the nuclear forces that hold atoms together<\/li>\n<li>Trace the nuclear reactions in the solar interior<\/li>\n<\/ul>\n<\/div>\n<p id=\"fs-id1170325354478\">As we have seen, <span class=\"no-emphasis\">energy<\/span> cannot be created or destroyed, but only converted from one form to another. One of the remarkable conclusions derived by Albert <span class=\"no-emphasis\">Einstein<\/span> (see <a href=\"#fs-id1170325040535\">Albert Einstein<\/a>) when he developed his <span class=\"no-emphasis\">theory of relativity<\/span> is that matter can be considered a form of energy too and can be converted into energy. Furthermore, energy can also be converted into matter. This seemed to contradict what humans had learned over thousands of years by studying nature. Matter is something we can see and touch, whereas energy is something objects have when they do things like move or heat up. The idea that matter or energy can be converted into each other seemed as outrageous as saying you could accelerate a car by turning the bumper into more speed, or that you could create a bigger front seat by slowing down your car. That would be pretty difficult to believe; yet, the universe actually works somewhat like that.<\/p>\n<section id=\"fs-id1170325199520\">\n<h1>Converting Matter into Energy<\/h1>\n<p id=\"fs-id1170324983265\">The remarkable equivalence between matter and energy is given in one of the most famous equations:<\/p>\n<div id=\"fs-id1170325132817\" class=\"equation unnumbered\">$E=m{c}^{2}$<\/div>\n<p id=\"fs-id1170325097809\">In this equation, <em>E<\/em> stands for energy, <em>m<\/em> stands for mass, and <em>c<\/em>, the constant that relates the two, is the speed of light (3 \u00d7 10<sup>8<\/sup> meters per second). Note that mass is a measure of the quantity of matter, so the significance of this equation is that matter can be converted into energy and energy can be converted into matter. Let\u2019s compare this equation of converting matter and energy to some common conversion equations that have the same form:<\/p>\n<div id=\"fs-id1170324945270\" class=\"equation unnumbered\">$\\text{inches}=\\text{feet}\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}12,\\text{or cents}=\\text{dollars}\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}100$<\/div>\n<p id=\"fs-id1170325078412\">Just as each conversion formula allows you to calculate the conversion of one thing into another, when we convert matter into energy, we consider how much mass the matter has. The conversion factor in this case turns out not to be either 12 or 100, as in our examples, but another constant quantity: the speed of light squared. Note that matter does not have to travel at the speed of light (or the speed of light squared) for this conversion to occur. The factor of <em>c<\/em><sup>2<\/sup> is just the number that Einstein showed must be used to relate mass and energy.<\/p>\n<p id=\"fs-id1170325084715\">Notice that this formula does not tell us <em>how<\/em> to convert mass into energy, just as the formula for cents does not tell us where to exchange coins for a dollar bill. The formulas merely tell us what the equivalent values are if we succeed in making the conversion. When Einstein first derived his formula in 1905, no one had the faintest idea how to convert mass into energy in any practical way. Einstein himself tried to discourage speculation that the large-scale conversion of atomic mass into energy would be feasible in the near future. Today, as a result of developments in nuclear physics, we regularly convert mass into energy in power plants, nuclear weapons, and high-energy physics experiments in particle accelerators.<\/p>\n<p>Because the speed of light squared (<em>c<\/em><sup>2<\/sup>) is a very large quantity, the conversion of even a small amount of mass results in a very large amount of energy. For example, the complete conversion of 1 gram of matter (about 1\/28 ounce, or approximately 1 paperclip) would produce as much energy as the burning of 15,000 barrels of oil.<\/p>\n<p id=\"fs-id1170325357432\">Scientists soon realized that the conversion of mass into energy is the source of the Sun\u2019s heat and light. With Einstein\u2019s equation of <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>, we can calculate that the amount of energy radiated by the Sun could be produced by the complete conversion of about 4 million tons of matter into energy inside the Sun each second. Destroying 4 million tons per second sounds like a lot when compared to earthly things, but bear in mind that the Sun is a very big reservoir of matter. In fact, we will see that the Sun contains more than enough mass to destroy such huge amounts of matter and still continue shining at its present rate for billions of years.<\/p>\n<p id=\"fs-id1170325403548\">But knowing all that still does not tell us <em>how<\/em> mass can be converted into energy. To understand the process that actually occurs in the Sun, we need to explore the structure of the atom a bit further.<\/p>\n<div id=\"fs-id1170325040535\" class=\"note astronony voyagers-in-astronomy\">\n<div class=\"textbox shaded\">\n<div class=\"title\"><strong>Albert Einstein<\/strong><\/div>\n<p id=\"fs-id1170325054908\">For a large part of his life, Albert <span class=\"no-emphasis\">Einstein<\/span> (<a href=\"#OSC_Astro_16_02_Albert\" class=\"autogenerated-content\">[link]<\/a>) was one of the most recognized celebrities of his day. Strangers stopped him on the street, and people all over the world asked him for endorsements, advice, and assistance. In fact, when Einstein and the great film star Charlie Chaplin met in California, they found they shared similar feelings about the loss of privacy that came with fame. Einstein\u2019s name was a household word despite the fact that most people did not understand the ideas that had made him famous.<\/p>\n<p id=\"fs-id1170324940205\">Einstein was born in 1879 in Ulm, Germany. Legend has it that he did not do well in school (even in arithmetic), and thousands of students have since attempted to justify a bad grade by referring to this story. Alas, like many legends, this one is not true. Records indicate that although he tended to rebel against the authoritarian teaching style in vogue in Germany at that time, Einstein was a good student.<\/p>\n<p id=\"fs-id1170325268120\">After graduating from the Federal Polytechnic Institute in Zurich, Switzerland, Einstein at first had trouble getting a job (even as a high school teacher), but he eventually became an examiner in the Swiss Patent Office. Working in his spare time, without the benefit of a university environment but using his superb physical intuition, he wrote four papers in 1905 that would ultimately transform the way physicists looked at the world.<\/p>\n<p id=\"fs-id1170324935900\">One of these, which earned Einstein the Nobel Prize in 1921, set part of the foundation of <em>quantum mechanics<\/em>\u2014the rich, puzzling, and remarkable theory of the subatomic realm. But his most important paper presented the <em>special theory of relativity<\/em>, a reexamination of space, time, and motion that added a whole new level of sophistication to our understanding of those concepts. The famed equation <em>E<\/em> = <em>mc<\/em><sup>2<\/sup> was actually a relatively minor part of this theory, added in a later paper.<\/p>\n<p id=\"fs-id1170325046666\">In 1916, Einstein published his <em>general theory of relativity<\/em>, which was, among other things, a fundamentally new description of gravity (see <a href=\"\/contents\/c58084cd-93fa-48ba-82a5-8bc44de393ed\" class=\"target-chapter\">Black Holes and Curved Spacetime<\/a>). When this theory was confirmed by measurements of the \u201cbending of starlight\u201d during a 1919 eclipse (<em>The New York Times<\/em> headline read, \u201cLights All Askew in the Heavens\u201d), Einstein became world famous.<\/p>\n<p id=\"fs-id1170325052373\">In 1933, to escape Nazi persecution, Einstein left his professorship in Berlin and settled in the United States at the newly created Institute for Advanced Studies at Princeton. He remained there until his death in 1955, writing, lecturing, and espousing a variety of intellectual and political causes. For example, he agreed to sign a letter written by Leo Szilard and other scientists in 1939, alerting President Roosevelt to the dangers of allowing Nazi Germany to develop the atomic bomb first. And in 1952, Einstein was offered the second presidency of Israel. In declining the position, he said, \u201cI know a little about nature and hardly anything about men.\u201d<\/p>\n<figure id=\"OSC_Astro_16_02_Albert\">\n<div class=\"title\" style=\"text-align: center\"><strong>Albert Einstein (1879\u20131955).<\/strong><\/div>\n<figure style=\"width: 325px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Albert-1.jpg\" alt=\"Photograph of Albert Einstein.\" width=\"325\" height=\"391\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 1.<\/strong> This portrait of Einstein was taken in 1912. (credit: modification of work by J. F. Langhans)<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/section>\n<section>\n<h1>Elementary Particles<\/h1>\n<p id=\"fs-id1170324918878\">The fundamental components of atoms are the proton, neutron, and electron (see <a href=\"\/contents\/22d9d199-7c88-418f-92bd-6cb72d0e1a53\" class=\"target-chapter\">The Structure of the Atom<\/a>).<\/p>\n<p id=\"fs-id1170325103467\">Protons, neutrons, and electrons are by no means all the particles that exist. First, for each kind of particle, there is a corresponding but opposite <em>antiparticle<\/em>. If the particle carries a charge, its <span class=\"no-emphasis\">antiparticle<\/span> has the opposite charge. The antielectron is the <em>positron<\/em>, which has the same mass as the electron but is positively charged. Similarly, the antiproton has a negative charge. The remarkable thing about such <em>antimatter<\/em> is that when a particle comes into contact with its antiparticle, the original particles are annihilated, and substantial amounts of energy in the form of photons are produced.<\/p>\n<p id=\"fs-id1170325024112\">Since our world is made exclusively of ordinary particles of matter, <span class=\"no-emphasis\">antimatter<\/span> cannot survive for very long. But individual antiparticles are found in cosmic rays (particles that arrive at the top of Earth\u2019s atmosphere from space) and can be created in particle accelerators. And, as we will see in a moment, antimatter is created in the core of the Sun and other stars.<\/p>\n<p id=\"fs-id1170325234700\">Science fiction fans may be familiar with antimatter from the <em>Star Trek<\/em> television series and films. The Starship Enterprise is propelled by the careful combining of matter and antimatter in the ship\u2019s engine room. According to <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>, the annihilation of matter and antimatter can produce a huge amount of energy, but keeping the antimatter fuel from touching the ship before it is needed must be a big problem. No wonder Scotty, the chief engineer in the original TV show, always looked worried!<\/p>\n<p id=\"fs-id1170325083688\">In 1933, physicist Wolfgang <span class=\"no-emphasis\">Pauli<\/span> (<a href=\"#OSC_Astro_16_02_Pauli\" class=\"autogenerated-content\">[link]<\/a>) suggested that there might be another type of elementary particle. Energy seemed to disappear when certain types of nuclear reactions took place, violating the law of conservation of energy. Pauli was reluctant to accept the idea that one of the basic laws of physics was wrong, and he suggested a \u201cdesperate remedy.\u201d Perhaps a so-far-undetected particle, which was given the name <span>neutrino<\/span> (\u201clittle neutral one\u201d), carried away the \u201cmissing\u201d energy. He suggested that neutrinos were particles with zero mass, and that like photons, they moved with the speed of light.<\/p>\n<figure id=\"OSC_Astro_16_02_Pauli\">\n<div class=\"title\" style=\"text-align: center\"><strong>Wolfgang Pauli in 1945.<\/strong><\/div>\n<figure style=\"width: 325px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Pauli-1.jpg\" alt=\"Photograph of Wolfgang Pauli.\" width=\"325\" height=\"460\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 2.<\/strong> Pauli is considered the \u201cfather\u201d of the neutrino, having conceived of it in 1933.<\/figcaption><\/figure>\n<\/figure>\n<p id=\"fs-id1170325104048\">The elusive neutrino was not detected until 1956. The reason it was so hard to find is that neutrinos interact very weakly with other matter and therefore are very difficult to detect. Earth is more transparent to a neutrino than the thinnest and cleanest pane of glass is to a photon of light. In fact, most neutrinos can pass completely through a star or planet without being absorbed. As we shall see, this behavior of neutrinos makes them a very important tool for studying the Sun. Since Pauli\u2019s prediction, scientists have learned a lot more about the neutrino. We now know that there are three different types of neutrinos, and in 1998, neutrinos were discovered to have a tiny amount of mass. Indeed, it is so tiny that electrons are at least 500,000 times more massive. Ongoing research is focused on determining the mass of neutrinos more precisely, and it may still turn out that one of the three types is massless. We will return to the subject of neutrinos later in this chapter.<\/p>\n<p id=\"fs-id1170325169909\">Some of the properties of the proton, electron, neutron, and neutrino are summarized in <a href=\"#fs-id1170325216952\" class=\"autogenerated-content\">[link]<\/a>. (Other subatomic particles have been produced by experiments with particle accelerators, but they do not play a role in the generation of solar energy.)<\/p>\n<p>&lt;table id=&#8221;fs-id1170325216952&#8243; class=&#8221;span-all&#8221; summary=&#8221;This table contains 3 columns and 5 rows. The first row is a header row and contains the values, \u201cParticle\u201d, \u201cMass (kg)\u201d, and \u201cCharge\u201d. Under the \u201cParticle\u201d column are the values, \u201cProton\u201d, \u201cNeutron\u201d, \u201cElectron\u201d, and \u201cNeutrino\u201d. Under the \u201cMass (kg)\u201d column are the values, \u201c1.67265 \u00d7 10\u201327\u201d, \u201c1.67495 \u00d7 10\u201327\u201d, \u201c9.11 \u00d7 10\u201331\u201d, and \u201c<\/p>\n<p>Properties of Some Common ParticlesParticleMass (kg)ChargeProton1.67265 \u00d7 10<sup>\u221227<\/sup>+1Neutron1.67495 \u00d7 10<sup>\u221227<\/sup>0Electron9.11 \u00d7 10<sup>\u221231<\/sup>\u22121Neutrino&lt;2 \u00d7 10<sup>\u221236<\/sup> (uncertain)0<\/section>\n<section id=\"fs-id1170324929199\">\n<h1>The Atomic Nucleus<\/h1>\n<p id=\"fs-id1170324945566\">The nucleus of an atom is not just a loose collection of elementary particles. Inside the nucleus, particles are held together by a very powerful force called the <span class=\"no-emphasis\">strong nuclear force<\/span>. This is short-range force, only capable of acting over distances about the size of the atomic nucleus. A quick thought experiment shows how important this force is. Take a look at your finger and consider the atoms composing it. Among them is carbon, one of the basic elements of life. Focus your imagination on the nucleus of one of your carbon atoms. It contains six protons, which have a positive charge, and six neutrons, which are neutral. Thus, the nucleus has a net charge of six positives. If only the electrical force were acting, the protons in this and every carbon atom would find each other very repulsive and fly apart.<\/p>\n<p id=\"fs-id1170324934944\">The strong nuclear force is an attractive force, stronger than the electrical force, and it keeps the particles of the nucleus tightly bound together. We saw earlier that if under the force of gravity a star \u201cshrinks\u201d\u2014bringing its atoms closer together\u2014gravitational energy is released. In the same way, if particles come together under the strong nuclear force and unite to form an atomic nucleus, some of the nuclear energy is released. The energy given up in such a process is called the <em>binding energy<\/em> of the nucleus.<\/p>\n<p id=\"fs-id1170325342849\">When such <span class=\"no-emphasis\">binding energy<\/span> is released, the resulting nucleus has slightly less mass than the sum of the masses of the particles that came together to form it. In other words, the energy comes from the loss of mass. This slight deficit in mass is only a small fraction of the mass of one proton. But because each bit of lost mass can provide a lot of energy (remember, <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>), this nuclear energy release can be quite substantial.<\/p>\n<p id=\"fs-id1170325065963\">Measurements show that the binding energy is greatest for atoms with a mass near that of the iron nucleus (with a combined number of protons and neutrons equal to 56) and less for both the lighter and the heavier nuclei. Iron, therefore, is the most stable element: since it gives up the most energy when it forms, it would require the most energy to break it back down into its component particles.<\/p>\n<p id=\"fs-id1170325355088\">What this means is that, in general, when light atomic nuclei come together to form a heavier one (up to iron), mass is lost and energy is released. This joining together of atomic nuclei is called nuclear <span>fusion<\/span>.<\/p>\n<p id=\"fs-id1170325073328\">Energy can also be produced by breaking up heavy atomic nuclei into lighter ones (down to iron); this process is called nuclear <span>fission<\/span>. Nuclear fission was the process we learned to use first\u2014in atomic bombs and in nuclear reactors used to generate electrical power\u2014and it may therefore be more familiar to you. Fission also sometimes occurs spontaneously in some unstable nuclei through the process of natural radioactivity. But fission requires big, complex nuclei, whereas we know that the stars are made up predominantly of small, simple nuclei. So we must look to fusion first to explain the energy of the Sun and the stars (<a href=\"#OSC_Astro_16_02_FissFusion\" class=\"autogenerated-content\">[link]<\/a>).<\/p>\n<figure id=\"OSC_Astro_16_02_FissFusion\">\n<div class=\"title\" style=\"text-align: center\"><strong>Fusion and Fission.<\/strong><\/div>\n<figure style=\"width: 465px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_FissFusion-1.jpg\" alt=\"In (a) one white sphere and one green sphere join together. In (b), a ball consisting of many smaller white and green spheres breaks apart into two smaller balls of green and white spheres.\" width=\"465\" height=\"294\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 3.<\/strong> (a) In fusion, light atomic nuclei join together to form a heavier nuclei, releasing energy in the process. (b) In fission, energy is produced by the breaking up of heavy, complex nuclei into lighter ones.<\/figcaption><\/figure>\n<\/figure>\n<\/section>\n<section id=\"fs-id1170322739286\">\n<h1>Nuclear Attraction versus Electrical Repulsion<\/h1>\n<p id=\"fs-id1170325124283\">So far, we seem to have a very attractive prescription for producing the energy emitted by the Sun: \u201croll\u201d some nuclei together and join them via nuclear fusion. This will cause them to lose some of their mass, which then turns into energy. However, every nucleus, even simple hydrogen, has protons\u2014and protons all have positive charges. Since like charges repel via the electrical force, the closer we get two nuclei to each other, the more they repel. It\u2019s true that if we can get them within \u201cstriking distance\u201d of the nuclear force, they will then come together with a much stronger attraction. But that striking distance is very tiny, about the size of a nucleus. How can we get nuclei close enough to participate in fusion?<\/p>\n<p id=\"fs-id1170325176178\">The answer turns out to be heat\u2014tremendous heat\u2014which speeds the protons up enough to overcome the electrical forces that try to keep protons apart. Inside the Sun, as we saw, the most common element is hydrogen, whose nucleus contains only a single proton. Two protons can fuse only in regions where the temperature is greater than about 12 million K, and the speed of the protons average around 1000 kilometers per second or more. (In old-fashioned units, that\u2019s over 2 million miles per hour!)<\/p>\n<p id=\"fs-id1170325244913\">In our Sun, such extreme temperatures are reached only in the regions near its center, which has a temperature of 15 million K. Calculations show that nearly all of the Sun\u2019s energy is generated within about 150,000 kilometers of its core, or within less than 10% of its total volume.<\/p>\n<p id=\"fs-id1170325088211\">Even at these high temperatures, it is exceedingly difficult to force two protons to combine. On average, a proton will rebound from other protons in the Sun\u2019s crowded core for about 14 billion years, at the rate of <em>100 million collisions per second<\/em>, before it fuses with a second proton. This is, however, only the <em>average<\/em> waiting time. Some of the enormous numbers of protons in the Sun\u2019s inner region are \u201clucky\u201d and take only a few collisions to achieve a fusion reaction: they are the protons responsible for producing the energy radiated by the Sun. Since the Sun is about 4.5 billion years old, most of its protons have not yet been involved in fusion reactions.<\/p>\n<\/section>\n<section>\n<h1>Nuclear Reactions in the Sun\u2019s Interior<\/h1>\n<p id=\"fs-id1170324933114\">The <span class=\"no-emphasis\">Sun<\/span>, then, taps the energy contained in the nuclei of atoms through nuclear <span class=\"no-emphasis\">fusion<\/span>. Let\u2019s look at what happens in more detail. Deep inside the Sun, a three-step process takes four hydrogen nuclei and fuses them together to form a single helium nucleus. The helium nucleus is slightly less massive than the four hydrogen nuclei that combine to form it, and that mass is converted into energy.<\/p>\n<p id=\"fs-id1170324902364\">The initial step required to form one helium nucleus from four hydrogen nuclei is shown in <a href=\"#OSC_Astro_16_02_Step1\" class=\"autogenerated-content\">[link]<\/a>. At the high temperatures inside the Sun\u2019s core, two protons combine to make a <em>deuterium<\/em> nucleus, which is an isotope (or version) of hydrogen that contains one proton and one neutron. In effect, one of the original protons has been converted into a neutron in the fusion reaction. Electric charge has to be conserved in nuclear reactions, and it is conserved in this one. A <span>positron<\/span> (antimatter electron) emerges from the reaction and carries away the positive charge originally associated with one of the protons.<\/p>\n<figure id=\"OSC_Astro_16_02_Step1\">\n<div class=\"title\" style=\"text-align: center\"><strong>Proton-Proton Chain, Step 1.<\/strong><\/div>\n<figure style=\"width: 414px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Step1-1.jpg\" alt=\"Diagram of the First Step in the Proton-Proton Chain. At left are shown two protons drawn in blue, and labeled as \u201c1H\u201d. An arrow is drawn from each proton toward the right and converge at an illustration of a small explosion. This explosion represents the release of energy and mass from the collision of the high energy protons. Three arrows are drawn moving away from the explosion toward the right. At the point of the topmost arrow is a neutrino drawn in light blue and labeled \u201cNeutrino\u201d. At the point of the central arrow is a deuterium nucleus drawn as a blue dot (proton) and a red dot (neutron) and labeled \u201c2H\u201d. At the point of the lower arrow is a positron drawn in purple and labeled \u201cPositron\u201d.\" width=\"414\" height=\"152\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 4.<\/strong> This is the first step in the process of fusing hydrogen into helium in the Sun. High temperatures are required because this reaction starts with two hydrogen nuclei, which are protons (shown in blue at left) that must overcome electrical repulsion to combine, forming a hydrogen nucleus with a proton and a neutron (shown in red). Note that hydrogen containing one proton and one neutron is given its own name: deuterium. Also produced in this reaction are a positron, which is an antielectron, and an elusive particle named the neutrino.<\/figcaption><\/figure>\n<\/figure>\n<p id=\"fs-id1170324919204\">Since it is antimatter, this positron will instantly collide with a nearby electron, and both will be annihilated, producing electromagnetic energy in the form of gamma-ray photons. This gamma ray, which has been created in the center of the Sun, finds itself in a world crammed full of fast-moving nuclei and electrons. The gamma ray collides with particles of matter and transfers its energy to one of them. The particle later emits another gamma-ray photon, but often the emitted photon has a bit less energy than the one that was absorbed.<\/p>\n<p id=\"fs-id1170325195828\">Such interactions happen to gamma rays again and again and again as they make their way slowly toward the outer layers of the Sun, until their energy becomes so reduced that they are no longer gamma rays but X-rays (recall what you learned in <a href=\"\/contents\/15eec1a9-5e3c-4e2b-abac-8cd61748d4a0\" class=\"target-chapter\">The Electromagnetic Spectrum<\/a>). Later, as the photons lose still more energy through collisions in the crowded center of the Sun, they become ultraviolet photons.<\/p>\n<p id=\"fs-id1170324919096\">By the time they reach the Sun\u2019s surface, most of the photons have given up enough energy to be ordinary light\u2014and they are the sunlight we see coming from our star. (To be precise, each gamma-ray photon is ultimately converted into many separate lower-energy photons of sunlight.) So, the sunlight given off by the Sun today had its origin as a gamma ray produced by nuclear reactions deep in the Sun\u2019s core. The length of time that photons require to reach the surface depends on how far a photon on average travels between collisions, and the travel time depends on what model of the complicated solar interior we accept. Estimates are somewhat uncertain but indicate that the emission of energy from the surface of the Sun can lag its production in the interior by 100,000 years to as much as 1,000,000 years.<\/p>\n<p id=\"fs-id1170325010258\">In addition to the positron, the fusion of two hydrogen atoms to form deuterium results in the emission of a <span class=\"no-emphasis\">neutrino<\/span>. Because neutrinos interact so little with ordinary matter, those produced by fusion reactions near the center of the Sun travel directly to the Sun\u2019s surface and then out into space, in all directions. Neutrinos move at nearly the speed of light, and they escape the Sun about two seconds after they are created.<\/p>\n<figure id=\"OSC_Astro_16_02_Step2\">\n<div class=\"title\" style=\"text-align: center\"><strong>Proton-Proton Chain, Step 2.<\/strong><\/div><figcaption><\/figcaption><figure style=\"width: 383px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Step2-1.jpg\" alt=\"Diagram of the Second Step in the Proton-Proton Chain. At upper left is the deuterium nucleus from the first step drawn as a blue dot (proton) and a red dot (neutron) and labeled \u201c2H\u201d. At lower left is a proton drawn in blue, and labeled as \u201c1H\u201d. An arrow is drawn from each object toward the right and converge at an illustration of a small explosion. This explosion represents the release of energy and mass from the collision of the deuterium and proton. A single arrow is drawn emerging from the explosion pointing toward the right. At the point of the arrow is an isotope of helium, known as deuterium, drawn as 2 blue dots (protons) and 1 red dot (neutron) and labeled \u201c3He\u201d. A single wavy arrow is drawn moving away from the deuterium nucleus and is labeled \u201cGamma ray\u201d.\" width=\"383\" height=\"176\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 5.<\/strong> This is the second step of the proton-proton chain, the fusion reaction that converts hydrogen into helium in the Sun. This step combines one hydrogen nucleus, which is a proton (shown in blue), with the deuterium nucleus from the previous step (shown as a red and blue particle). The product of this is an isotope of helium with two protons (blue) and one neutron (red) and energy in the form of gamma-ray radiation.<\/figcaption><\/figure>\n<\/figure>\n<p id=\"fs-id1170324960240\">The second step in forming helium from hydrogen is to add another proton to the deuterium nucleus to create a helium nucleus that contains two protons and one neutron (<a href=\"#OSC_Astro_16_02_Step2\" class=\"autogenerated-content\">[link]<\/a>). In the process, some mass is again lost and more gamma radiation is emitted. Such a nucleus is helium because an element is defined by its number of protons; any nucleus with two protons is called helium. But this form of helium, which we call helium-3 (and write in shorthand as <sup>3<\/sup>He) is not the isotope we see in the Sun\u2019s atmosphere or on Earth. That helium has two neutrons and two protons and hence is called helium-4 (<sup>4<\/sup>He).<\/p>\n<p id=\"fs-id1170325194210\">To get to helium-4 in the Sun, helium-3 must combine with another helium-3 in the third step of fusion (illustrated in <a href=\"#OSC_Astro_16_02_Step3\" class=\"autogenerated-content\">[link]<\/a>). Note that two energetic protons are left over from this step; each of them comes out of the reaction ready to collide with other protons and to start step 1 in the chain of reactions all over again.<\/p>\n<figure id=\"OSC_Astro_16_02_Step3\">\n<div class=\"title\" style=\"text-align: center\"><strong>Proton-Proton Chain, Step 3.<\/strong><\/div><figcaption><\/figcaption><figure style=\"width: 397px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_Step3-1.jpg\" alt=\"Diagram of the Third Step in the Proton-Proton Chain. At left are two deuterium nuclei each drawn as 2 blue dots (protons) and 1 red dot (neutron), and labeled \u201c3He\u201d. An arrow is drawn from each nucleus toward the right and converge at an illustration of a small explosion. This explosion represents the release of energy and mass from the collision of the deuterium nuclei. Three arrows are drawn moving away from the explosion toward the right. At the point of the topmost arrow is a proton drawn in blue and labeled \u201c1H\u201d. At the point of the center arrow a helium nucleus is drawn as two blue dots (protons) and two red dots (neutrons) and labeled \u201c4He\u201d. At the point of the lower arrow is a proton drawn in blue and labeled \u201c1H\u201d.\" width=\"397\" height=\"164\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 6.<\/strong> This is the third step in the fusion of hydrogen into helium in the Sun. Note that the two helium-3 nuclei from the second step (see [link]) must combine before the third step becomes possible. The two protons that come out of this step have the energy to collide with other protons in the Sun and start step one again.<\/figcaption><\/figure>\n<\/figure>\n<div id=\"fs-id1170325443812\" class=\"note astronomy link-to-learning\">\n<div class=\"textbox shaded\">These animations of <a href=\"https:\/\/openstaxcollege.org\/l\/30proproreactio\">proton-proton reactions<\/a> show the steps required for fusion of hydrogen into helium in the Sun.<\/div>\n<\/div>\n<div id=\"fs-id1170325345072\" class=\"note astronomy link-to-learning\">\n<div class=\"textbox shaded\">Visit the <a href=\"https:\/\/openstaxcollege.org\/l\/30tokamakfusrea\">Tokamak Fusion Reactor<\/a> at the General Atomics Lab in San Diego, CA, for an 8-minute tour.<\/div>\n<\/div>\n<\/section>\n<section id=\"fs-id1170324978329\">\n<h1>The Proton-Proton Chain<\/h1>\n<p id=\"fs-id1170324959823\">The nuclear reactions in the Sun that we have been discussing can be described succinctly through the following nuclear formulas:<\/p>\n<div id=\"fs-id1170325088312\" class=\"equation unnumbered\">$\\begin{array}{c}{}_{}^{1}\\text{H}+{}_{}^{1}\\text{H}\u27f6{}_{}^{2}\\text{H}+{\\text{e}}^{+}+v\\hfill \\\\ {}_{}^{2}\\text{H}+{}_{}^{1}\\text{H}\u27f6{}_{}^{3}\\text{He}+\\gamma \\hfill \\\\ {}_{}^{3}\\text{He}+{}_{}^{3}\\text{He}\u27f6{}_{}^{4}\\text{He}+{}_{}^{1}\\text{H}+{}_{}^{1}\\text{H}\\hfill \\end{array}$<\/div>\n<p id=\"fs-id1170325090920\">Here, the superscripts indicate the total number of neutrons plus protons in the nucleus, e<sup>+<\/sup> is the positron, <em>v<\/em> is the neutrino, and <em>\u03b3<\/em> indicates that gamma rays are emitted. Note that the third step requires two helium-3 nuclei to start; the first two steps must happen twice before the third step can occur.<\/p>\n<p id=\"fs-id1170324920113\">Although, as we discussed, the first step in this chain of reactions is very difficult and generally takes a long time, the other steps happen more quickly. After the deuterium nucleus is formed, it survives an average of only about 6 seconds before being converted into <sup>3<\/sup>He. About a million years after that (on average), the <sup>3<\/sup>He nucleus will combine with another to form <sup>4<\/sup>He.<\/p>\n<p id=\"fs-id1170325159055\">We can compute the amount of energy these reactions generate by calculating the difference in the initial and final masses. The masses of hydrogen and helium atoms in the units normally used by scientists are 1.007825 <em>u<\/em> and 4.00268 <em>u<\/em>, respectively. (The unit of mass, <em>u<\/em>, is defined to be 1\/12 the mass of an atom of carbon, or approximately the mass of a proton.) Here, we include the mass of the entire atom, not just the nucleus, because electrons are involved as well. When hydrogen is converted into helium, two positrons are created (remember, the first step happens twice), and these are annihilated with two free electrons, adding to the energy produced.<\/p>\n<div id=\"fs-id1170325080568\" class=\"equation unnumbered\">$\\begin{array}{cc}\\hfill 4\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}1.007825&amp; =4.03130\\phantom{\\rule{0.2em}{0ex}}u\\phantom{\\rule{0.2em}{0ex}}\\text{(mass of initial hydrogen atoms)}\\hfill \\\\ &amp; \\phantom{\\rule{0.2em}{0ex}}\\text{\u2212}\\phantom{\\rule{0.3em}{0ex}}4.00268\\phantom{\\rule{0.2em}{0ex}}u\\phantom{\\rule{0.2em}{0ex}}\\text{(mass of final helium atoms)}\\hfill \\\\ &amp; =0.02862\\phantom{\\rule{0.2em}{0ex}}u\\phantom{\\rule{0.2em}{0ex}}\\text{(mass lost in the transformation)}\\hfill \\end{array}$<\/div>\n<p id=\"fs-id1170324914897\">The mass lost, 0.02862 <em>u<\/em>, is 0.71% of the mass of the initial hydrogen. Thus, if 1 kilogram of hydrogen is converted into helium, then the mass of the helium is only 0.9929 kilogram, and 0.0071 kilogram of material is converted into energy. The speed of light (<em>c<\/em>) is 3 \u00d7 10<sup>8<\/sup> meters per second, so the energy released by the conversion of just 1 kilogram of hydrogen into helium is:<\/p>\n<div id=\"fs-id1170325354129\" class=\"equation unnumbered\">$\\begin{array}{}\\\\ \\\\ E=m{c}^{2}\\hfill \\\\ E=0.0071\\phantom{\\rule{0.2em}{0ex}}\\text{kg}\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}{\\left(3\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}{10}^{8}\\text{m\/s}\\right)}^{2}=6.4\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}\u00d7\\phantom{\\rule{0.2em}{0ex}}\\phantom{\\rule{0.2em}{0ex}}{10}^{14}\\phantom{\\rule{0.2em}{0ex}}\\text{J}\\hfill \\end{array}$<\/div>\n<p id=\"fs-id1170325078026\">This amount, the energy released when a single kilogram (2.2 pounds) of hydrogen undergoes fusion, would supply all of the electricity used in the United States for about 2 weeks.<\/p>\n<p id=\"fs-id1170325240627\">To produce the Sun\u2019s luminosity of 4 \u00d7 10<sup>26<\/sup> watts, some 600 million tons of hydrogen must be converted into helium <em>each second<\/em>, of which about 4 million tons are converted from matter into energy. As large as these numbers are, the store of hydrogen (and thus of nuclear energy) in the Sun is still <em>more<\/em> enormous, and can last a long time\u2014billions of years, in fact.<\/p>\n<p id=\"fs-id1170325210554\">At the temperatures inside the stars with masses smaller than about 1.2 times the mass of our Sun (a category that includes the Sun itself), most of the energy is produced by the reactions we have just described, and this set of reactions is called the <span>proton-proton chain<\/span> (or sometimes, the p-p chain). In the proton-proton chain, protons collide directly with other protons to form helium nuclei.<\/p>\n<p id=\"fs-id1170325195013\">In hotter stars, another set of reactions, called the carbon-nitrogen-oxygen (CNO) cycle, accomplishes the same net result. In the <span class=\"no-emphasis\">CNO cycle<\/span>, carbon and hydrogen nuclei collide to initiate a series of reactions that form nitrogen, oxygen, and ultimately, helium. The nitrogen and oxygen nuclei do not survive but interact to form carbon again. Therefore, the outcome is the same as in the proton-proton chain: four hydrogen atoms disappear, and in their place, a single helium atom is created. The CNO cycle plays only a minor role in the Sun but is the main source of energy for stars with masses greater than about the mass of the Sun.<\/p>\n<p id=\"fs-id1170325206822\">So you can see that we have solved the puzzle that so worried scientists at the end of the nineteenth century. The Sun can maintain its high temperature and energy output for billions of years through the fusion of the simplest element in the universe, hydrogen. Because most of the Sun (and the other stars) is made of hydrogen, it is an ideal \u201cfuel\u201d for powering a star. As will be discussed in the following chapters, we can define a star as a ball of gas capable of getting its core hot enough to initiate the fusion of hydrogen. There are balls of gas that lack the mass required to do this (Jupiter is a local example); like so many hopefuls in Hollywood, they will never be stars.<\/p>\n<div id=\"fs-id1170325047754\" class=\"note astronomy making-connections\">\n<div class=\"textbox shaded\">\n<div class=\"title\"><strong>Fusion on Earth<\/strong><\/div>\n<p id=\"fs-id1170324943586\">Wouldn\u2019t it be wonderful if we could duplicate the Sun\u2019s energy mechanism in a controlled way on Earth? (We have already duplicated it in an uncontrolled way in hydrogen bombs, but we hope our storehouses of these will never be used.) Fusion energy would have many advantages: it would use hydrogen (or deuterium, which is heavy hydrogen) as fuel, and there is abundant hydrogen in Earth\u2019s lakes and oceans. Water is much more evenly distributed around the world than oil or uranium, meaning that a few countries would no longer hold an energy advantage over the others. And unlike fission, which leaves dangerous byproducts, the nuclei that result from fusion are perfectly safe.<\/p>\n<p id=\"fs-id1170325091806\">The problem is that, as we saw, it takes extremely high temperatures for nuclei to overcome their electrical repulsion and undergo fusion. When the first hydrogen bombs were exploded in tests in the 1950s, the \u201cfuses\u201d to get them hot enough were fission bombs. Interactions at such temperatures are difficult to sustain and control. To make fusion power on Earth, after all, we have to do what the Sun does: produce temperatures and pressures high enough to get hydrogen nuclei on intimate terms with one another.<\/p>\n<p id=\"fs-id1170325206600\">The European Union, the United States, South Korea, Japan, China, Russia, Switzerland, and India are collaborating on the <span class=\"no-emphasis\">International Thermonuclear Experimental Reactor (ITER)<\/span>, a project to demonstrate the feasibility of controlled fusion (<a href=\"#OSC_Astro_16_02_ITER\" class=\"autogenerated-content\">[link]<\/a>). The facility is being built in France. Construction will require over 10,000,000 components and 2000 workers for assembly. The date for the start of operations is yet to be determined.<\/p>\n<p id=\"fs-id1170325062203\">ITER is based on the Tokamak design, in which a large doughnut-shaped container is surrounded by superconducting magnets to confine and control the hydrogen nuclei in a strong magnetic field. Previous fusion experiments have produced about 15 million watts of energy, but only for a second or two, and they have required 100 million watts to produce the conditions necessary to achieve fusion. The goal of ITER is to build the first fusion device capable of producing 500 million watts of fusion energy for up to 1000 seconds. The challenge is keeping the deuterium and tritium\u2014which will participate in fusion reactions\u2014hot enough and dense enough, for a long enough time to produce energy.<\/p>\n<figure id=\"OSC_Astro_16_02_ITER\">\n<div class=\"title\" style=\"text-align: center\"><strong>ITER Design.<\/strong><\/div>\n<figure style=\"width: 487px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/astrojbrewer\/wp-content\/uploads\/sites\/468\/2017\/09\/OSC_Astro_16_02_ITER-1.jpg\" alt=\"Cutaway Model of the ITER Design. In the center of this model are two pink kidney shaped areas that represents the hollow chamber wherein the particles will travel. The bright yellow areas surrounding the chamber are the superconducting magnets. Surrounding these two structures are a myriad of pipes, wires, conduits and other components of this highly complex machine.\" width=\"487\" height=\"541\" \/><figcaption class=\"wp-caption-text\"><strong>Figure 7.<\/strong> The bright yellow areas in this model show where the superconducting magnets will circle the chamber within which fusion will take place. A huge magnet will keep the charged nuclei of heavy hydrogen confined. The goal is to produce 500 megawatts of energy. (credit: modification of work by Stephan Mosel)<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/section>\n<section id=\"fs-id1170325048064\" class=\"summary\">\n<h1>Key Concepts and Summary<\/h1>\n<p id=\"fs-id1170325447484\">Solar energy is produced by interactions of particles\u2014that is, protons, neutrons, electrons, positrons, and neutrinos. Specifically, the source of the Sun\u2019s energy is the fusion of hydrogen to form helium. The series of reactions required to convert hydrogen to helium is called the proton-proton chain. A helium atom is about 0.71% less massive than the four hydrogen atoms that combine to form it, and that lost mass is converted to energy (with the amount of energy given by the formula <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>).<\/p>\n<\/section>\n<div>\n<h2>Glossary<\/h2>\n<dl id=\"fs-id1170325276212\" class=\"definition\">\n<dt>fission<\/dt>\n<dd id=\"fs-id1170325265957\">breaking up of heavier atomic nuclei into lighter ones<\/dd>\n<\/dl>\n<dl id=\"fs-id1170325016080\" class=\"definition\">\n<dt>fusion<\/dt>\n<dd id=\"fs-id1170325182961\">building up of heavier atomic nuclei from lighter ones<\/dd>\n<\/dl>\n<dl id=\"fs-id1170325187140\" class=\"definition\">\n<dt>neutrino<\/dt>\n<dd id=\"fs-id1170322673782\">fundamental particle that has no charge and a mass that is tiny relative to an electron; it rarely interacts with ordinary matter and comes in three different types<\/dd>\n<\/dl>\n<dl id=\"fs-id1170325200011\" class=\"definition\">\n<dt>positron<\/dt>\n<dd id=\"fs-id1170325159136\">particle with the same mass as an electron, but positively charged<\/dd>\n<\/dl>\n<dl id=\"fs-id1170325181179\" class=\"definition\">\n<dt>proton-proton chain<\/dt>\n<dd id=\"fs-id1170325250566\">series of thermonuclear reactions by which nuclei of hydrogen are built up into nuclei of helium<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":395,"menu_order":1,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-623","chapter","type-chapter","status-publish","hentry"],"part":609,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/pressbooks\/v2\/chapters\/623","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/wp\/v2\/users\/395"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/pressbooks\/v2\/chapters\/623\/revisions"}],"predecessor-version":[{"id":624,"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/pressbooks\/v2\/chapters\/623\/revisions\/624"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/pressbooks\/v2\/parts\/609"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/pressbooks\/v2\/chapters\/623\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/wp\/v2\/media?parent=623"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/pressbooks\/v2\/chapter-type?post=623"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/wp\/v2\/contributor?post=623"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/a7000y2018\/wp-json\/wp\/v2\/license?post=623"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}