{"id":2390,"date":"2018-04-11T23:52:46","date_gmt":"2018-04-12T03:52:46","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/quantum-numbers-for-electrons\/"},"modified":"2019-05-13T15:28:28","modified_gmt":"2019-05-13T19:28:28","slug":"quantum-numbers-for-electrons","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/chapter\/quantum-numbers-for-electrons\/","title":{"raw":"8.2 Quantization of the Energy of Electrons","rendered":"8.2 Quantization of the Energy of Electrons"},"content":{"raw":"<div class=\"section\" id=\"ball-ch08_s02\" lang=\"en\">\r\n<div class=\"learning_objectives editable block\" id=\"ball-ch08_s02_n01\">\r\n<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this module, you will be able to:\r\n<ul>\r\n \t<li>Explain what spectra are.<\/li>\r\n \t<li>Describe Bohr's Model of the hydrogen atom.<\/li>\r\n \t<li>Describe the Electron Shell Model.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<figure id=\"CNX_Chem_06_03_sOrbit\"><figcaption><\/figcaption><\/figure>\r\n<\/div>\r\n<figure id=\"CNX_Chem_06_03_subshells\"><figcaption><\/figcaption><\/figure>\r\n<p id=\"ball-ch08_s02_p01\" class=\"para editable block\">There are two fundamental ways of generating light: either heat an object up so hot it glows or pass an electrical current through a sample of matter (usually a gas). Incandescent lights and fluorescent lights generate light via these two methods, respectively.<\/p>\r\n<p id=\"ball-ch08_s02_p02\" class=\"para editable block\">A hot object gives off a continuum of light. We notice this when the visible portion of the electromagnetic spectrum is passed through a prism: the prism separates light into its constituent colors, and all colors are present in a continuous rainbow (part (a) in <a class=\"xref\" href=\"#ball-ch08_s02_f01\">Figure 1 \"Prisms and Light\"<\/a>). This image is known as a <span class=\"margin_term\"><a class=\"glossterm\">continuous spectrum<\/a><\/span>. However, when electricity is passed through a gas and light is emitted and this light is passed though a prism, we see only certain lines of light in the image (part (b) in <a class=\"xref\" href=\"#ball-ch08_s02_f01\">Figure 1 \"Prisms and Light\"<\/a>). This image is called a <span class=\"margin_term\"><a class=\"glossterm\">line spectrum<\/a><\/span>. It turns out that every element has its own unique, characteristic line spectrum.<\/p>\r\n\r\n<div class=\"figure large editable block\" id=\"ball-ch08_s02_f01\">\r\n\r\n[caption id=\"attachment_4685\" align=\"aligncenter\" width=\"600\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Prisms-and-Light.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Prisms-and-Light-1.png\" alt=\"Prisms and Light\" width=\"600\" height=\"180\" class=\"wp-image-4685 size-full\" \/><\/a> <strong>Figure 1.<\/strong> Prisms and Light \u00a0(a) A glowing object gives off a full rainbow of colors, which are noticed only when light is passed through a prism to make a continuous spectrum. (b) However, when electricity is passed through a gas, only certain colors of light are emitted. Here are the colors of light in the line spectrum of Hg.[\/caption]\r\n\r\nWhy does the light emitted from an electrically excited gas have only certain colors, while light given off by hot objects has a continuous spectrum? For a long time, it was not well explained. Particularly simple was the spectrum of hydrogen gas, which could be described easily by an equation; no other element has a spectrum that is so predictable (<a class=\"xref\" href=\"#ball-ch08_s02_f02\">Figure 2 \"Hydrogen Spectrum\"<\/a>).\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"figure large editable block\" id=\"ball-ch08_s02_f02\">\r\n\r\n[caption id=\"attachment_4687\" align=\"aligncenter\" width=\"600\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Hydrogen-Spectrum.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Hydrogen-Spectrum-1.png\" alt=\"Hydrogen Spectrum\" width=\"600\" height=\"107\" class=\"wp-image-4687 size-full\" \/><\/a> <strong>Figure 2.<\/strong> Hydrogen Spectrum[\/caption]\r\n\r\n&nbsp;\r\n<div class=\"figure large editable block\" id=\"ball-ch08_s02_f01\">\r\n\r\nLate-nineteenth-century scientists found that the positions of the lines obeyed a pattern given by the equation\r\n\r\n<\/div>\r\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/07\/Screen-Shot-2014-07-22-at-8.04.37-PM.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2014-07-22-at-8.04.37-PM-1.png\" alt=\"Screen Shot 2014-07-22 at 8.04.37 PM\" width=\"260\" height=\"64\" class=\"wp-image-3851 aligncenter\" \/><\/a>\r\n<p id=\"ball-ch08_s02_p04\" class=\"para editable block\">where <em class=\"emphasis\">n<\/em> = 3, 4, 5, 6,\u2026, but they could not explain why this was so.\u00a0 The spectrum of hydrogen was particularly simple and could be predicted by a simple mathematical expression.<\/p>\r\n\r\n<\/div>\r\n<p id=\"ball-ch08_s02_p05\" class=\"para editable block\">In 1913, the Danish scientist Niels Bohr suggested a reason why the hydrogen atom spectrum looked this way. He suggested that the electron in a hydrogen atom could not have any random energy, having <em class=\"emphasis\">only<\/em> certain fixed values of energy that were indexed by the number <em class=\"emphasis\">n<\/em> (the same <em class=\"emphasis\">n<\/em> in the equation above and now called a <span class=\"margin_term\"><a class=\"glossterm\">quantum number<\/a><\/span>) (Figure 3). Quantities that have certain specific values are called <span class=\"margin_term\"><a class=\"glossterm\">quantized<\/a><\/span>. Bohr suggested that the energy of the electron in hydrogen was quantized because it was in a specific orbit. Because the energies of the electron can have only certain values, the changes in energies can have only certain values (somewhat similar to a staircase: not only are the stair steps set at specific heights but the height between steps is fixed).<\/p>\r\n&nbsp;\r\n\r\n[caption id=\"attachment_4848\" align=\"aligncenter\" width=\"532\"]<a href=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission.png\" alt=\"\" width=\"532\" height=\"743\" class=\"size-full wp-image-4848\" \/><\/a> <strong>Figure 3.<\/strong> Some emission possibilities from the energy levels of an atom.[\/caption]\r\n<p class=\"para editable block\">Finally, Bohr suggested that the energy of light emitted from electrified hydrogen gas was equal to the energy difference of the electron\u2019s energy states:<\/p>\r\n<p style=\"text-align: center\"><span class=\"informalequation block\">E<sub>light<\/sub> = h\u03bd = \u0394E<sub>electron<\/sub><\/span><\/p>\r\n<p id=\"ball-ch08_s02_p06\" class=\"para editable block\">This means that only certain frequencies (and thus, certain wavelengths) of light are emitted. <a class=\"xref\" href=\"#ball-ch08_s02_f03\">Figure 4 \"Bohr\u2019s Model of the Hydrogen Atom\"<\/a> shows a model of the hydrogen atom based on Bohr\u2019s ideas.<\/p>\r\n\r\n<div class=\"figure large medium-height editable block\" id=\"ball-ch08_s02_f03\">\r\n\r\n[caption id=\"attachment_4688\" align=\"aligncenter\" width=\"372\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Bohrs-Hydrogen-Atom.png\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Bohrs-Hydrogen-Atom-1.png\" alt=\"Bohr's Hydrogen Atom\" width=\"372\" height=\"316\" class=\"wp-image-4688\" \/><\/a> <strong>Figure 4.<\/strong>\u00a0Bohr\u2019s Model of the Hydrogen Atom[\/caption]\r\n<p class=\"para\">Bohr\u2019s description of the hydrogen atom had specific orbits for the electron, which had quantized energies.<\/p>\r\n\r\n<div class=\"textbox\">\r\n<p style=\"text-align: left\"><strong>Postulates of the Bohr Model:<\/strong><\/p>\r\n<p style=\"text-align: left\">1)\u00a0 Electrons move in specific circular orbits only.\r\n2)\u00a0 As an atom absorbs energy, the electron jumps to a larger orbit, of higher energy (an excited state).\r\n3)\u00a0 As an atom emits energy, it \u201cfalls\u201d to a smaller, lower energy orbit.<\/p>\r\n\r\n<\/div>\r\nThis model represented a great intellectual achievement by Bohr, as it was the first atom model that invoked quantization of the electron energy in some way. Also his mathematical formula\u00a0 which calculated the energy of the electron in any orbit, matched the real energies observed in experiments with hydrogen. However, the theory had significant limitations.\r\n<div class=\"textbox\">\r\n\r\n<strong>Some Key Problems with the Bohr Model:\u00a0<\/strong>\r\n<ul>\r\n \t<li>It only works for hydrogen (though can be adapted to other one electron ions). If there are 2 or more electrons, the mathematical formula does not match real data.<\/li>\r\n \t<li>It is fundamentally incorrect in that electrons <em>do not\u00a0<\/em>move in fixed orbits!<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>The Electron Shell Model of the Atom<\/h2>\r\nWe can overcome one of the key objections to the Bohr Model by abandoning the concept of electrons moving in fixed diameter orbits. Instead we envision a series of spherical <em>shells\u00a0<\/em>of increasing size surrounding the nucleus in which the electrons reside (Figure 5). The Electron Shell Model does not attempt to describe the movement of the electrons, only that each shell has a different size and energy and the electron moves within that space. The quantum jumps of the electron are thus the electron moving from one <em>shell\u00a0<\/em>to another.\r\n\r\n[caption id=\"attachment_3653\" align=\"aligncenter\" width=\"344\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.06-AM-300x177.png\" alt=\"\" width=\"344\" height=\"203\" class=\"wp-image-3653\" \/> <strong>Figure 5.<\/strong>\u00a0Electron Shell Model of the Atom (showing only the first three shells)[\/caption]\r\n\r\nWe also account for other experimental evidence and specify that the shells can hold a certain maximum number of electrons. Table 1 shows this maximum filling, as well as some other aspects of these shells.\r\n\r\n[caption id=\"attachment_3655\" align=\"aligncenter\" width=\"464\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM-300x139.png\" alt=\"\" width=\"464\" height=\"215\" class=\"wp-image-3655\" \/> <strong>Table 1.<\/strong> Properties of Electron Shells in Atoms[\/caption]\r\n<h2>The Electron Configuration of Atoms using the Shell Model<\/h2>\r\nSo, for a given atom or ion, in which shell(s) do the electrons reside? It turns out the electrons follow a simple principle, namely, they go into the lowest energy shell that is available. If a lower energy shell is full, they go into the next lowest energy shell. A crude analogy is putting water into a pail; the water always fills from the bottom! So to establish this\u00a0<em>electron configuration<\/em>, first determine the number of electrons the atom has, then \u201cput\u201d them into the shells as the above rule dictates. Look at Figure 5 again, which represents an atom with 13 electrons. Notice how the lower energy shells are full, and the last three electrons go into shell 3, which is not full. Additional electrons would continue to go into shell 3 until it is full with 8 electrons, for a total of 18. A 19th electron would be forced to go into shell 4.\r\n<div class=\"textbox shaded\">\r\n<h3>Example 1<\/h3>\r\nDraw an electron shell model of an aluminum atom.\r\n\r\n&nbsp;\r\n\r\n<strong>Solution\u00a0\u00a0<\/strong>\r\n\r\nStep 1: Determine the number of electrons.\r\n\r\nSince it is not specified that the atom is charged, we presume it is neutral. Aluminum has 13 protons, so neutral aluminum would have 13 electrons.\r\n\r\nStep 2: Determine the electron configuration.\r\n\r\nPut 2 electrons in shell 1 which fills it, next put 8 electrons in shell 2 which fills it, and the last three electrons go into shell 3.\r\n\r\nStep 3: Draw the image.\r\n\r\n<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.15-AM-300x256.png\" alt=\"\" width=\"218\" height=\"186\" class=\" wp-image-3664 aligncenter\" \/>\r\n\r\n<em><strong>Test Yourself<\/strong><\/em>\r\n\r\nDraw an electron shell model of a calcium atom.\r\n\r\n&nbsp;\r\n\r\n<em><strong>Answer<\/strong><\/em>\r\n\r\n<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.28.14-AM-300x284.png\" alt=\"\" width=\"200\" height=\"189\" class=\" wp-image-3656 aligncenter\" \/>\r\n\r\n<\/div>\r\n<h2>Electron Configurations and the Periodic Table<\/h2>\r\nLook at the number of elements in each row of the periodic table. Rows 1 through 4 contain 2, 8, 8, and 18 elements respectively. Now look at Table 1. Is this a coincidence? No! In fact this shows that the patterns of elemental properties that the periodic table reflects have their <em>basis in electron configurations<\/em>. Consider Figure 6 which shows the electron shell models of hydrogen, lithium, sodium, and potassium.\r\n\r\n[caption id=\"attachment_3657\" align=\"aligncenter\" width=\"528\"]<img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.36-AM-300x112.png\" alt=\"\" width=\"528\" height=\"197\" class=\"wp-image-3657\" \/> <strong>Figure 6.<\/strong>\u00a0Electron shell models of hydrogen, lithium, sodium, and potassium[\/caption]\r\n\r\nSee how each has <em>one\u00a0<\/em>electron in its highest energy shell. Now find these elements on the periodic table. They are all in the first column of the periodic table. Consider the elements of the last column of the periodic table (draw them out for yourself). They all have <em>full\u00a0<\/em>outer shells. A general relationship begins to emerge:\u00a0<em>elements in the same column on the periodic table have similar electron configurations<\/em>.\r\n\r\nOriginally, the periodic table was constructed based on observable chemical and physical properties. Elements that behaved similarly were placed in the same column; however the chemists had no explanation of <em>why\u00a0<\/em>they were similar. Now with the electron shell model we have a theory that helps us understand the <em>reasons\u00a0<\/em>for these similarities.\r\n<div class=\"textbox shaded\">\r\n<div class=\"figure large medium-height editable block\" id=\"ball-ch08_s02_f03\">\r\n<h3>Chemistry Is Everywhere: Neon Lights<\/h3>\r\n<\/div>\r\n<div class=\"section\" id=\"ball-ch08_s02\" lang=\"en\">\r\n<div class=\"callout block\" id=\"ball-ch08_s02_n03\">\r\n<p id=\"ball-ch08_s02_p20\" class=\"para\">A neon light is basically an electrified tube with a small amount of gas in it. Electricity excites electrons in the gas atoms, which then give off light as the electrons go back into a lower energy state. However, many so-called \u201cneon\u201d lights don\u2019t contain neon!<\/p>\r\n<p id=\"ball-ch08_s02_p21\" class=\"para\">Although we know now that a gas discharge gives off only certain colors of light, without a prism or other component to separate the individual light colors, we see a composite of all the colors emitted. It is not unusual for a certain color to predominate. True neon lights, with neon gas in them, have a reddish-orange light due to the large amount of red-, orange-, and yellow-colored light emitted. However, if you use krypton instead of neon, you get a whitish light, while using argon yields a blue-purple light. A light filled with nitrogen gas glows purple, as does a helium lamp. Other gases\u2014and mixtures of gases\u2014emit other colors of light. Ironically, despite its importance in the development of modern electronic theory, hydrogen lamps emit little visible light and are rarely used for illumination purposes.<\/p>\r\n\r\n<div class=\"informalfigure medium\" id=\"ball-ch08_s02_f05\">\r\n\r\n[caption id=\"attachment_3226\" align=\"alignnone\" width=\"450\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/07\/450px-Neon_Internet_Cafe_open_24_hours.jpg\"><img src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/450px-Neon_Internet_Cafe_open_24_hours-1.jpg\" alt=\"The different colors of these \u201cneon\u201d lights are caused by gases other than neon in the discharge tubes. Source: \u201cNeon Internet Cafe open 24 hours\u201d by JustinC is licensed under the Creative Commons Attribution- Share Alike 2.0 Generic license.\" class=\"size-full wp-image-3226\" height=\"600\" width=\"450\" \/><\/a> The different colors of these \u201cneon\u201d lights are caused by gases other than neon in the discharge tubes. Source: \u201cNeon Internet Cafe open 24 hours\u201d by JustinC is licensed under the Creative Commons Attribution- Share Alike 2.0 Generic license.[\/caption]\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"section\" id=\"ball-ch08_s02\" lang=\"en\">\r\n<div class=\"callout block\" id=\"ball-ch08_s02_n03\">\r\n<div class=\"informalfigure medium\" id=\"ball-ch08_s02_f05\"><section id=\"fs-idp4059248\" class=\"summary\">\r\n<h2>Key Concepts and Summary<\/h2>\r\n<p id=\"fs-idp119487440\">Bohr incorporated Planck\u2019s and Einstein\u2019s quantization ideas into a model of the hydrogen atom that resolved the paradox of atom stability and discrete spectra. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. He postulated that the electron was restricted to certain orbits characterized by discrete energies. Transitions between these allowed orbits result in the absorption or emission of photons. When an electron moves from a higher-energy orbit to a more stable one, energy is emitted in the form of a photon. To move an electron from a stable orbit to a more excited one, a photon of energy must be absorbed. Using the Bohr model, we can calculate the energy of an electron and the radius of its orbit in any one-electron system.<\/p>\r\n\r\n<\/section><section id=\"fs-idp212850576\" class=\"key-equations\"><\/section><\/div>\r\n<\/div>\r\n<div class=\"key_takeaways editable block\" id=\"ball-ch08_s02_n04\"><section id=\"fs-idp53264832\" class=\"exercises\">\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Exercises<\/h3>\r\n1. What does it mean to say that the energy of the electrons in an atom is quantized?\r\n\r\n2. How are the Bohr model and the Rutherford model of the atom similar? How are they different?\r\n\r\n3.\u00a0Differentiate between a continuous spectrum and a line spectrum.\r\n\r\n&nbsp;\r\n\r\n<strong>Answers<\/strong>\r\n\r\n1. Quantized energy means that the electrons can possess only certain discrete energy values; values between those quantized values are not permitted.\r\n\r\n2. Both involve a relatively heavy nucleus with electrons moving around it, although strictly speaking, the Bohr model works only for one-electron atoms or ions. According to classical mechanics, the Rutherford model predicts a miniature \u201csolar system\u201d with electrons moving about the nucleus in circular or elliptical orbits that are confined to planes. If the requirements of classical electromagnetic theory that electrons in such orbits would emit electromagnetic radiation are ignored, such atoms would be stable, having constant energy and angular momentum, but would not emit any visible light (contrary to observation). If classical electromagnetic theory is applied, then the Rutherford atom would emit electromagnetic radiation of continually increasing frequency (contrary to the observed discrete spectra), thereby losing energy until the atom collapsed in an absurdly short time (contrary to the observed long-term stability of atoms). The Bohr model retains the classical mechanics view of circular orbits confined to planes having constant energy and angular momentum, but restricts these to quantized values dependent on a single quantum number, <em>n<\/em>. The orbiting electron in Bohr\u2019s model is assumed not to emit any electromagnetic radiation while moving about the nucleus in its stationary orbits, but the atom can emit or absorb electromagnetic radiation when the electron changes from one orbit to another. Because of the quantized orbits, such \u201cquantum jumps\u201d will produce discrete spectra, in agreement with observations.\r\n\r\n3. A continuous spectrum is a range of light frequencies or wavelengths; a line spectrum shows only certain frequencies or wavelengths.\r\n\r\n<\/div>\r\n<\/section>\r\n<div>\r\n<h2>Glossary<\/h2>\r\n<strong>Bohr\u2019s model of the hydrogen atom:\u00a0<\/strong>structural model in which an electron moves around the nucleus only in circular orbits, each with a specific allowed radius; the orbiting electron does not normally emit electromagnetic radiation, but does so when changing from one orbit to another.\r\n\r\n<strong>excited state:\u00a0<\/strong>state having an energy greater than the ground-state energy\r\n\r\n<strong>ground state:\u00a0<\/strong>state in which the electrons in an atom, ion, or molecule have the lowest energy possible\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"section\" id=\"ball-ch08_s02\" lang=\"en\">\n<div class=\"learning_objectives editable block\" id=\"ball-ch08_s02_n01\">\n<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this module, you will be able to:<\/p>\n<ul>\n<li>Explain what spectra are.<\/li>\n<li>Describe Bohr&#8217;s Model of the hydrogen atom.<\/li>\n<li>Describe the Electron Shell Model.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<figure id=\"CNX_Chem_06_03_sOrbit\"><figcaption><\/figcaption><\/figure>\n<\/div>\n<figure id=\"CNX_Chem_06_03_subshells\"><figcaption><\/figcaption><\/figure>\n<p id=\"ball-ch08_s02_p01\" class=\"para editable block\">There are two fundamental ways of generating light: either heat an object up so hot it glows or pass an electrical current through a sample of matter (usually a gas). Incandescent lights and fluorescent lights generate light via these two methods, respectively.<\/p>\n<p id=\"ball-ch08_s02_p02\" class=\"para editable block\">A hot object gives off a continuum of light. We notice this when the visible portion of the electromagnetic spectrum is passed through a prism: the prism separates light into its constituent colors, and all colors are present in a continuous rainbow (part (a) in <a class=\"xref\" href=\"#ball-ch08_s02_f01\">Figure 1 &#8220;Prisms and Light&#8221;<\/a>). This image is known as a <span class=\"margin_term\"><a class=\"glossterm\">continuous spectrum<\/a><\/span>. However, when electricity is passed through a gas and light is emitted and this light is passed though a prism, we see only certain lines of light in the image (part (b) in <a class=\"xref\" href=\"#ball-ch08_s02_f01\">Figure 1 &#8220;Prisms and Light&#8221;<\/a>). This image is called a <span class=\"margin_term\"><a class=\"glossterm\">line spectrum<\/a><\/span>. It turns out that every element has its own unique, characteristic line spectrum.<\/p>\n<div class=\"figure large editable block\" id=\"ball-ch08_s02_f01\">\n<figure id=\"attachment_4685\" aria-describedby=\"caption-attachment-4685\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Prisms-and-Light.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Prisms-and-Light-1.png\" alt=\"Prisms and Light\" width=\"600\" height=\"180\" class=\"wp-image-4685 size-full\" \/><\/a><figcaption id=\"caption-attachment-4685\" class=\"wp-caption-text\"><strong>Figure 1.<\/strong> Prisms and Light \u00a0(a) A glowing object gives off a full rainbow of colors, which are noticed only when light is passed through a prism to make a continuous spectrum. (b) However, when electricity is passed through a gas, only certain colors of light are emitted. Here are the colors of light in the line spectrum of Hg.<\/figcaption><\/figure>\n<p>Why does the light emitted from an electrically excited gas have only certain colors, while light given off by hot objects has a continuous spectrum? For a long time, it was not well explained. Particularly simple was the spectrum of hydrogen gas, which could be described easily by an equation; no other element has a spectrum that is so predictable (<a class=\"xref\" href=\"#ball-ch08_s02_f02\">Figure 2 &#8220;Hydrogen Spectrum&#8221;<\/a>).<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"figure large editable block\" id=\"ball-ch08_s02_f02\">\n<figure id=\"attachment_4687\" aria-describedby=\"caption-attachment-4687\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Hydrogen-Spectrum.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Hydrogen-Spectrum-1.png\" alt=\"Hydrogen Spectrum\" width=\"600\" height=\"107\" class=\"wp-image-4687 size-full\" \/><\/a><figcaption id=\"caption-attachment-4687\" class=\"wp-caption-text\"><strong>Figure 2.<\/strong> Hydrogen Spectrum<\/figcaption><\/figure>\n<p>&nbsp;<\/p>\n<div class=\"figure large editable block\" id=\"ball-ch08_s02_f01\">\n<p>Late-nineteenth-century scientists found that the positions of the lines obeyed a pattern given by the equation<\/p>\n<\/div>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/07\/Screen-Shot-2014-07-22-at-8.04.37-PM.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2014-07-22-at-8.04.37-PM-1.png\" alt=\"Screen Shot 2014-07-22 at 8.04.37 PM\" width=\"260\" height=\"64\" class=\"wp-image-3851 aligncenter\" \/><\/a><\/p>\n<p id=\"ball-ch08_s02_p04\" class=\"para editable block\">where <em class=\"emphasis\">n<\/em> = 3, 4, 5, 6,\u2026, but they could not explain why this was so.\u00a0 The spectrum of hydrogen was particularly simple and could be predicted by a simple mathematical expression.<\/p>\n<\/div>\n<p id=\"ball-ch08_s02_p05\" class=\"para editable block\">In 1913, the Danish scientist Niels Bohr suggested a reason why the hydrogen atom spectrum looked this way. He suggested that the electron in a hydrogen atom could not have any random energy, having <em class=\"emphasis\">only<\/em> certain fixed values of energy that were indexed by the number <em class=\"emphasis\">n<\/em> (the same <em class=\"emphasis\">n<\/em> in the equation above and now called a <span class=\"margin_term\"><a class=\"glossterm\">quantum number<\/a><\/span>) (Figure 3). Quantities that have certain specific values are called <span class=\"margin_term\"><a class=\"glossterm\">quantized<\/a><\/span>. Bohr suggested that the energy of the electron in hydrogen was quantized because it was in a specific orbit. Because the energies of the electron can have only certain values, the changes in energies can have only certain values (somewhat similar to a staircase: not only are the stair steps set at specific heights but the height between steps is fixed).<\/p>\n<p>&nbsp;<\/p>\n<figure id=\"attachment_4848\" aria-describedby=\"caption-attachment-4848\" style=\"width: 532px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission.png\" alt=\"\" width=\"532\" height=\"743\" class=\"size-full wp-image-4848\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission.png 532w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission-215x300.png 215w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission-65x91.png 65w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission-225x314.png 225w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Emission-350x489.png 350w\" sizes=\"auto, (max-width: 532px) 100vw, 532px\" \/><\/a><figcaption id=\"caption-attachment-4848\" class=\"wp-caption-text\"><strong>Figure 3.<\/strong> Some emission possibilities from the energy levels of an atom.<\/figcaption><\/figure>\n<p class=\"para editable block\">Finally, Bohr suggested that the energy of light emitted from electrified hydrogen gas was equal to the energy difference of the electron\u2019s energy states:<\/p>\n<p style=\"text-align: center\"><span class=\"informalequation block\">E<sub>light<\/sub> = h\u03bd = \u0394E<sub>electron<\/sub><\/span><\/p>\n<p id=\"ball-ch08_s02_p06\" class=\"para editable block\">This means that only certain frequencies (and thus, certain wavelengths) of light are emitted. <a class=\"xref\" href=\"#ball-ch08_s02_f03\">Figure 4 &#8220;Bohr\u2019s Model of the Hydrogen Atom&#8221;<\/a> shows a model of the hydrogen atom based on Bohr\u2019s ideas.<\/p>\n<div class=\"figure large medium-height editable block\" id=\"ball-ch08_s02_f03\">\n<figure id=\"attachment_4688\" aria-describedby=\"caption-attachment-4688\" style=\"width: 372px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Bohrs-Hydrogen-Atom.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Bohrs-Hydrogen-Atom-1.png\" alt=\"Bohr's Hydrogen Atom\" width=\"372\" height=\"316\" class=\"wp-image-4688\" \/><\/a><figcaption id=\"caption-attachment-4688\" class=\"wp-caption-text\"><strong>Figure 4.<\/strong>\u00a0Bohr\u2019s Model of the Hydrogen Atom<\/figcaption><\/figure>\n<p class=\"para\">Bohr\u2019s description of the hydrogen atom had specific orbits for the electron, which had quantized energies.<\/p>\n<div class=\"textbox\">\n<p style=\"text-align: left\"><strong>Postulates of the Bohr Model:<\/strong><\/p>\n<p style=\"text-align: left\">1)\u00a0 Electrons move in specific circular orbits only.<br \/>\n2)\u00a0 As an atom absorbs energy, the electron jumps to a larger orbit, of higher energy (an excited state).<br \/>\n3)\u00a0 As an atom emits energy, it \u201cfalls\u201d to a smaller, lower energy orbit.<\/p>\n<\/div>\n<p>This model represented a great intellectual achievement by Bohr, as it was the first atom model that invoked quantization of the electron energy in some way. Also his mathematical formula\u00a0 which calculated the energy of the electron in any orbit, matched the real energies observed in experiments with hydrogen. However, the theory had significant limitations.<\/p>\n<div class=\"textbox\">\n<p><strong>Some Key Problems with the Bohr Model:\u00a0<\/strong><\/p>\n<ul>\n<li>It only works for hydrogen (though can be adapted to other one electron ions). If there are 2 or more electrons, the mathematical formula does not match real data.<\/li>\n<li>It is fundamentally incorrect in that electrons <em>do not\u00a0<\/em>move in fixed orbits!<\/li>\n<\/ul>\n<\/div>\n<h2>The Electron Shell Model of the Atom<\/h2>\n<p>We can overcome one of the key objections to the Bohr Model by abandoning the concept of electrons moving in fixed diameter orbits. Instead we envision a series of spherical <em>shells\u00a0<\/em>of increasing size surrounding the nucleus in which the electrons reside (Figure 5). The Electron Shell Model does not attempt to describe the movement of the electrons, only that each shell has a different size and energy and the electron moves within that space. The quantum jumps of the electron are thus the electron moving from one <em>shell\u00a0<\/em>to another.<\/p>\n<figure id=\"attachment_3653\" aria-describedby=\"caption-attachment-3653\" style=\"width: 344px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.06-AM-300x177.png\" alt=\"\" width=\"344\" height=\"203\" class=\"wp-image-3653\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.06-AM-300x177.png 300w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.06-AM-65x38.png 65w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.06-AM-225x133.png 225w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.06-AM-350x207.png 350w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.06-AM.png 681w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><figcaption id=\"caption-attachment-3653\" class=\"wp-caption-text\"><strong>Figure 5.<\/strong>\u00a0Electron Shell Model of the Atom (showing only the first three shells)<\/figcaption><\/figure>\n<p>We also account for other experimental evidence and specify that the shells can hold a certain maximum number of electrons. Table 1 shows this maximum filling, as well as some other aspects of these shells.<\/p>\n<figure id=\"attachment_3655\" aria-describedby=\"caption-attachment-3655\" style=\"width: 464px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM-300x139.png\" alt=\"\" width=\"464\" height=\"215\" class=\"wp-image-3655\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM-300x139.png 300w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM-768x355.png 768w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM-65x30.png 65w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM-225x104.png 225w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM-350x162.png 350w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.17.42-AM.png 987w\" sizes=\"auto, (max-width: 464px) 100vw, 464px\" \/><figcaption id=\"caption-attachment-3655\" class=\"wp-caption-text\"><strong>Table 1.<\/strong> Properties of Electron Shells in Atoms<\/figcaption><\/figure>\n<h2>The Electron Configuration of Atoms using the Shell Model<\/h2>\n<p>So, for a given atom or ion, in which shell(s) do the electrons reside? It turns out the electrons follow a simple principle, namely, they go into the lowest energy shell that is available. If a lower energy shell is full, they go into the next lowest energy shell. A crude analogy is putting water into a pail; the water always fills from the bottom! So to establish this\u00a0<em>electron configuration<\/em>, first determine the number of electrons the atom has, then \u201cput\u201d them into the shells as the above rule dictates. Look at Figure 5 again, which represents an atom with 13 electrons. Notice how the lower energy shells are full, and the last three electrons go into shell 3, which is not full. Additional electrons would continue to go into shell 3 until it is full with 8 electrons, for a total of 18. A 19th electron would be forced to go into shell 4.<\/p>\n<div class=\"textbox shaded\">\n<h3>Example 1<\/h3>\n<p>Draw an electron shell model of an aluminum atom.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Solution\u00a0\u00a0<\/strong><\/p>\n<p>Step 1: Determine the number of electrons.<\/p>\n<p>Since it is not specified that the atom is charged, we presume it is neutral. Aluminum has 13 protons, so neutral aluminum would have 13 electrons.<\/p>\n<p>Step 2: Determine the electron configuration.<\/p>\n<p>Put 2 electrons in shell 1 which fills it, next put 8 electrons in shell 2 which fills it, and the last three electrons go into shell 3.<\/p>\n<p>Step 3: Draw the image.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.15-AM-300x256.png\" alt=\"\" width=\"218\" height=\"186\" class=\"wp-image-3664 aligncenter\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.15-AM-300x256.png 300w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.15-AM-65x55.png 65w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.15-AM-225x192.png 225w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.15-AM-350x298.png 350w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.15-AM.png 372w\" sizes=\"auto, (max-width: 218px) 100vw, 218px\" \/><\/p>\n<p><em><strong>Test Yourself<\/strong><\/em><\/p>\n<p>Draw an electron shell model of a calcium atom.<\/p>\n<p>&nbsp;<\/p>\n<p><em><strong>Answer<\/strong><\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.28.14-AM-300x284.png\" alt=\"\" width=\"200\" height=\"189\" class=\"wp-image-3656 aligncenter\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.28.14-AM-300x284.png 300w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.28.14-AM-65x62.png 65w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.28.14-AM-225x213.png 225w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.28.14-AM.png 324w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/p>\n<\/div>\n<h2>Electron Configurations and the Periodic Table<\/h2>\n<p>Look at the number of elements in each row of the periodic table. Rows 1 through 4 contain 2, 8, 8, and 18 elements respectively. Now look at Table 1. Is this a coincidence? No! In fact this shows that the patterns of elemental properties that the periodic table reflects have their <em>basis in electron configurations<\/em>. Consider Figure 6 which shows the electron shell models of hydrogen, lithium, sodium, and potassium.<\/p>\n<figure id=\"attachment_3657\" aria-describedby=\"caption-attachment-3657\" style=\"width: 528px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.36-AM-300x112.png\" alt=\"\" width=\"528\" height=\"197\" class=\"wp-image-3657\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.36-AM-300x112.png 300w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.36-AM-65x24.png 65w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.36-AM-225x84.png 225w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.36-AM-350x130.png 350w, https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/Screen-Shot-2018-05-18-at-11.18.36-AM.png 736w\" sizes=\"auto, (max-width: 528px) 100vw, 528px\" \/><figcaption id=\"caption-attachment-3657\" class=\"wp-caption-text\"><strong>Figure 6.<\/strong>\u00a0Electron shell models of hydrogen, lithium, sodium, and potassium<\/figcaption><\/figure>\n<p>See how each has <em>one\u00a0<\/em>electron in its highest energy shell. Now find these elements on the periodic table. They are all in the first column of the periodic table. Consider the elements of the last column of the periodic table (draw them out for yourself). They all have <em>full\u00a0<\/em>outer shells. A general relationship begins to emerge:\u00a0<em>elements in the same column on the periodic table have similar electron configurations<\/em>.<\/p>\n<p>Originally, the periodic table was constructed based on observable chemical and physical properties. Elements that behaved similarly were placed in the same column; however the chemists had no explanation of <em>why\u00a0<\/em>they were similar. Now with the electron shell model we have a theory that helps us understand the <em>reasons\u00a0<\/em>for these similarities.<\/p>\n<div class=\"textbox shaded\">\n<div class=\"figure large medium-height editable block\" id=\"ball-ch08_s02_f03\">\n<h3>Chemistry Is Everywhere: Neon Lights<\/h3>\n<\/div>\n<div class=\"section\" id=\"ball-ch08_s02\" lang=\"en\">\n<div class=\"callout block\" id=\"ball-ch08_s02_n03\">\n<p id=\"ball-ch08_s02_p20\" class=\"para\">A neon light is basically an electrified tube with a small amount of gas in it. Electricity excites electrons in the gas atoms, which then give off light as the electrons go back into a lower energy state. However, many so-called \u201cneon\u201d lights don\u2019t contain neon!<\/p>\n<p id=\"ball-ch08_s02_p21\" class=\"para\">Although we know now that a gas discharge gives off only certain colors of light, without a prism or other component to separate the individual light colors, we see a composite of all the colors emitted. It is not unusual for a certain color to predominate. True neon lights, with neon gas in them, have a reddish-orange light due to the large amount of red-, orange-, and yellow-colored light emitted. However, if you use krypton instead of neon, you get a whitish light, while using argon yields a blue-purple light. A light filled with nitrogen gas glows purple, as does a helium lamp. Other gases\u2014and mixtures of gases\u2014emit other colors of light. Ironically, despite its importance in the development of modern electronic theory, hydrogen lamps emit little visible light and are rarely used for illumination purposes.<\/p>\n<div class=\"informalfigure medium\" id=\"ball-ch08_s02_f05\">\n<figure id=\"attachment_3226\" aria-describedby=\"caption-attachment-3226\" style=\"width: 450px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/07\/450px-Neon_Internet_Cafe_open_24_hours.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-content\/uploads\/sites\/387\/2018\/04\/450px-Neon_Internet_Cafe_open_24_hours-1.jpg\" alt=\"The different colors of these \u201cneon\u201d lights are caused by gases other than neon in the discharge tubes. Source: \u201cNeon Internet Cafe open 24 hours\u201d by JustinC is licensed under the Creative Commons Attribution- Share Alike 2.0 Generic license.\" class=\"size-full wp-image-3226\" height=\"600\" width=\"450\" \/><\/a><figcaption id=\"caption-attachment-3226\" class=\"wp-caption-text\">The different colors of these \u201cneon\u201d lights are caused by gases other than neon in the discharge tubes. Source: \u201cNeon Internet Cafe open 24 hours\u201d by JustinC is licensed under the Creative Commons Attribution- Share Alike 2.0 Generic license.<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"section\" id=\"ball-ch08_s02\" lang=\"en\">\n<div class=\"callout block\" id=\"ball-ch08_s02_n03\">\n<div class=\"informalfigure medium\" id=\"ball-ch08_s02_f05\">\n<section id=\"fs-idp4059248\" class=\"summary\">\n<h2>Key Concepts and Summary<\/h2>\n<p id=\"fs-idp119487440\">Bohr incorporated Planck\u2019s and Einstein\u2019s quantization ideas into a model of the hydrogen atom that resolved the paradox of atom stability and discrete spectra. The Bohr model of the hydrogen atom explains the connection between the quantization of photons and the quantized emission from atoms. Bohr described the hydrogen atom in terms of an electron moving in a circular orbit about a nucleus. He postulated that the electron was restricted to certain orbits characterized by discrete energies. Transitions between these allowed orbits result in the absorption or emission of photons. When an electron moves from a higher-energy orbit to a more stable one, energy is emitted in the form of a photon. To move an electron from a stable orbit to a more excited one, a photon of energy must be absorbed. Using the Bohr model, we can calculate the energy of an electron and the radius of its orbit in any one-electron system.<\/p>\n<\/section>\n<section id=\"fs-idp212850576\" class=\"key-equations\"><\/section>\n<\/div>\n<\/div>\n<div class=\"key_takeaways editable block\" id=\"ball-ch08_s02_n04\">\n<section id=\"fs-idp53264832\" class=\"exercises\">\n<div class=\"bcc-box bcc-info\">\n<h3>Exercises<\/h3>\n<p>1. What does it mean to say that the energy of the electrons in an atom is quantized?<\/p>\n<p>2. How are the Bohr model and the Rutherford model of the atom similar? How are they different?<\/p>\n<p>3.\u00a0Differentiate between a continuous spectrum and a line spectrum.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Answers<\/strong><\/p>\n<p>1. Quantized energy means that the electrons can possess only certain discrete energy values; values between those quantized values are not permitted.<\/p>\n<p>2. Both involve a relatively heavy nucleus with electrons moving around it, although strictly speaking, the Bohr model works only for one-electron atoms or ions. According to classical mechanics, the Rutherford model predicts a miniature \u201csolar system\u201d with electrons moving about the nucleus in circular or elliptical orbits that are confined to planes. If the requirements of classical electromagnetic theory that electrons in such orbits would emit electromagnetic radiation are ignored, such atoms would be stable, having constant energy and angular momentum, but would not emit any visible light (contrary to observation). If classical electromagnetic theory is applied, then the Rutherford atom would emit electromagnetic radiation of continually increasing frequency (contrary to the observed discrete spectra), thereby losing energy until the atom collapsed in an absurdly short time (contrary to the observed long-term stability of atoms). The Bohr model retains the classical mechanics view of circular orbits confined to planes having constant energy and angular momentum, but restricts these to quantized values dependent on a single quantum number, <em>n<\/em>. The orbiting electron in Bohr\u2019s model is assumed not to emit any electromagnetic radiation while moving about the nucleus in its stationary orbits, but the atom can emit or absorb electromagnetic radiation when the electron changes from one orbit to another. Because of the quantized orbits, such \u201cquantum jumps\u201d will produce discrete spectra, in agreement with observations.<\/p>\n<p>3. A continuous spectrum is a range of light frequencies or wavelengths; a line spectrum shows only certain frequencies or wavelengths.<\/p>\n<\/div>\n<\/section>\n<div>\n<h2>Glossary<\/h2>\n<p><strong>Bohr\u2019s model of the hydrogen atom:\u00a0<\/strong>structural model in which an electron moves around the nucleus only in circular orbits, each with a specific allowed radius; the orbiting electron does not normally emit electromagnetic radiation, but does so when changing from one orbit to another.<\/p>\n<p><strong>excited state:\u00a0<\/strong>state having an energy greater than the ground-state energy<\/p>\n<p><strong>ground state:\u00a0<\/strong>state in which the electrons in an atom, ion, or molecule have the lowest energy possible<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":330,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"8.2 Quantization of the Energy of Electrons","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"chapter-type":[],"contributor":[],"license":[54],"class_list":["post-2390","chapter","type-chapter","status-publish","hentry","license-cc-by-nc-sa"],"part":2362,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2390","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/users\/330"}],"version-history":[{"count":22,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2390\/revisions"}],"predecessor-version":[{"id":4849,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2390\/revisions\/4849"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/parts\/2362"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapters\/2390\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/media?parent=2390"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/pressbooks\/v2\/chapter-type?post=2390"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/contributor?post=2390"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chem1114langaracollege\/wp-json\/wp\/v2\/license?post=2390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}