{"id":322,"date":"2017-12-14T21:32:48","date_gmt":"2017-12-14T21:32:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-mcc-introductorychemistry\/chapter\/organization-of-electrons-in-atoms\/"},"modified":"2023-01-07T16:18:31","modified_gmt":"2023-01-07T16:18:31","slug":"organization-of-electrons-in-atoms","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-mcc-introductorychemistry\/chapter\/organization-of-electrons-in-atoms\/","title":{"raw":"4.1 Organization of Electrons in Atoms","rendered":"4.1 Organization of Electrons in Atoms"},"content":{"raw":"<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\r\n<div id=\"ball-ch08_s03_n01\" class=\"learning_objectives editable block\">\r\n<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Learn how electrons are organized in atoms<\/li>\r\n \t<li>Represent the organization of electrons by an electron configuration<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\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 Figure 1). This image is known as a continuous spectrum. 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 Firgure 1). This image is called a line spectrum. It turns out that every element has its own unique, characteristic line spectrum.<\/p>\r\n\r\n<div id=\"ball-ch08_s02_f01\" class=\"figure large editable block\">\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 class=\"wp-image-4685 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213318\/Prisms-and-Light-1.png\" alt=\"Prisms and Light\" width=\"600\" height=\"180\" \/><\/a> Figure 1 (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<p id=\"ball-ch08_s02_p03\" class=\"para editable block\">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 (Figure 2). Late-nineteenth-century scientists found that the positions of the lines obeyed a pattern given by the equation<\/p>\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 class=\"wp-image-3851 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213320\/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\" \/><\/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.<\/p>\r\n\r\n<div id=\"ball-ch08_s02_f02\" class=\"figure large editable block\">\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 class=\"wp-image-4687 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213321\/Hydrogen-Spectrum-1.png\" alt=\"Hydrogen Spectrum\" width=\"600\" height=\"107\" \/><\/a> Figure 2 The spectrum of hydrogen was particularly simple and could be predicted by a simple mathematical expression.[\/caption]\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 <strong>quantum number<\/strong>. Quantities that have certain specific values are called quantized. 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). 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\">[latex]E_{light} =h\\nu = \\Delta E_{electron}[\/latex]<\/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. Figure 3 shows a model of the hydrogen atom based on Bohr\u2019s ideas.<\/p>\r\n\r\n<div id=\"ball-ch08_s02_f03\" class=\"figure large medium-height editable block\">\r\n\r\n[caption id=\"attachment_4688\" align=\"aligncenter\" width=\"600\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Bohrs-Hydrogen-Atom.png\"><img class=\"wp-image-4688 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213324\/Bohrs-Hydrogen-Atom-1.png\" alt=\"Bohr's Hydrogen Atom\" width=\"600\" height=\"510\" \/><\/a> Figure 3 Bohr's Model. Bohr\u2019s description of the hydrogen atom had specific orbits for the electron, which had quantized energies.[\/caption]\r\n\r\n<\/div>\r\n<p id=\"ball-ch08_s02_p07\" class=\"para editable block\">Bohr\u2019s ideas were useful but were applied only to the hydrogen atom. However, later researchers generalized Bohr\u2019s ideas into a new theory called quantum mechanics, which explains the behaviour of electrons as if they were acting as a wave, not as particles. Quantum mechanics predicts two major things: quantized energies for electrons of all atoms (not just hydrogen) and an organization of electrons within atoms. Electrons are no longer thought of as being randomly distributed around a nucleus or restricted to certain orbits (in that regard, Bohr was wrong). Instead, electrons are collected into groups and subgroups that explain much about the chemical behaviour of the atom.<\/p>\r\n<p id=\"ball-ch08_s02_p08\" class=\"para block\">In the quantum-mechanical model of an atom, the state of an electron is described by four quantum numbers, not just the one predicted by Bohr. The first quantum number is called the principle quantum number, r<span class=\"margin_term\"><span class=\"glossdef\">epresented by <span class=\"inlineequation\">n<\/span>.<\/span><\/span> (<em class=\"emphasis\">n<\/em>). The principal quantum number largely determines the energy of an electron. Electrons in the same atom that have the same principal quantum number are said to occupy an electron <strong>shell<\/strong> of the atom. The principal quantum number can be any nonzero positive integer: 1, 2, 3, 4,\u2026.<\/p>\r\n<p id=\"ball-ch08_s02_p09\" class=\"para editable block\">Within a shell, there may be multiple possible values of the next quantum number, the angular momentum quantum number.<span class=\"margin_term\"><span class=\"glossdef\"> Represented by \u2113.<\/span><\/span> (\u2113). The \u2113 quantum number has a minor effect on the energy of the electron but also affects the spatial distribution of the electron in three-dimensional space\u2014that is, the shape of an electron\u2019s distribution in space. The value of the \u2113 quantum number can be any integer between 0 and <em class=\"emphasis\">n<\/em> \u2212 1:<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">\u2113 = 0, 1, 2,\u2026, <em class=\"emphasis\">n<\/em> \u2212 1<\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s02_p10\" class=\"para editable block\">Thus, for a given value of <em class=\"emphasis\">n<\/em>, there are different possible values of \u2113:<\/p>\r\n\r\n<div class=\"informaltable block\">\r\n<table cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>If <em class=\"emphasis\">n<\/em> equals<\/th>\r\n<th>\u2113 can be<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>1<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>0 or 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>0, 1, or 2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>4<\/td>\r\n<td>0, 1, 2, or 3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"ball-ch08_s02_p11\" class=\"para editable block\">and so forth. Electrons within a shell that have the same value of \u2113 are said to occupy a <strong>subshell<\/strong> in the atom. Commonly, instead of referring to the numerical value of \u2113, a letter represents the value of \u2113 (to help distinguish it from the principal quantum number):<\/p>\r\n\r\n<div class=\"informaltable block\">\r\n<table cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>If \u2113 equals<\/th>\r\n<th>The letter is<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>0<\/td>\r\n<td><em class=\"emphasis\">s<\/em><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td><em class=\"emphasis\">p<\/em><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td><em class=\"emphasis\">d<\/em><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td><em class=\"emphasis\">f<\/em><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"ball-ch08_s02_p12\" class=\"para block\">The next quantum number is called the magnetic quantum number re<span class=\"margin_term\"><span class=\"glossdef\">presented by <span class=\"inlineequation\">m\u2113<\/span>.<\/span><\/span> (<em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub>). For any value of \u2113, there are 2\u2113 +\u00a01 possible values of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub>, ranging from \u2212\u2113 to \u2113:<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">\u2212\u2113 \u2264 <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> \u2264 \u2113<\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s02_p13\" class=\"para editable block\" style=\"text-align: center;\">or<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\">|m\u2113| \u2264\u00a0\u2113<\/span><\/p>\r\n<p id=\"ball-ch08_s02_p14\" class=\"para editable block\">The following explicitly lists the possible values of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> for the possible values of \u2113:<\/p>\r\n\r\n<div class=\"informaltable block\">\r\n<table cellpadding=\"0\">\r\n<thead>\r\n<tr>\r\n<th>If \u2113 equals<\/th>\r\n<th>The <span class=\"inlineequation\">m\u2113<\/span> values can be<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>0<\/td>\r\n<td>0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>1<\/td>\r\n<td>\u22121, 0, or 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>2<\/td>\r\n<td>\u22122, \u22121, 0, 1, or 2<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>3<\/td>\r\n<td>\u22123, \u22122, \u22121, 0, 1, 2, or 3<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<p id=\"ball-ch08_s02_p15\" class=\"para editable block\">The particular value of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> dictates the orientation of an electron\u2019s distribution in space. When \u2113 is zero, <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> can be only zero, so there is only one possible orientation. When \u2113 is 1, there are three possible orientations for an electron\u2019s distribution. When \u2113 is 2, there are five possible orientations of electron distribution. This goes on and on for other values of \u2113, but we need not consider any higher values of \u2113 here. Each value of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> designates a certain <strong>orbital<\/strong>. Thus, there is only one orbital when \u2113 is zero, three orbitals when \u2113 is 1, five orbitals when \u2113 is 2, and so forth. The <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> quantum number has no effect on the energy of an electron unless the electrons are subjected to a magnetic field\u2014hence its name.<\/p>\r\n<p id=\"ball-ch08_s02_p16\" class=\"para block\">The \u2113 quantum number dictates the general shape of electron distribution in space (Figure 4). Any <em class=\"emphasis\">s<\/em> orbital is spherically symmetric (part (a) in Figure 4), and there is only one orbital in any <em class=\"emphasis\">s<\/em> subshell. Any <em class=\"emphasis\">p<\/em> orbital has a two-lobed, dumbbell-like shape (part (b) in Figure 4); because there are three of them, we normally represent them as pointing along the <em class=\"emphasis\">x<\/em>-, <em class=\"emphasis\">y<\/em>-, and <em class=\"emphasis\">z<\/em>-axes of Cartesian space. The <em class=\"emphasis\">d<\/em> orbitals are four-lobed rosettes (part (c) in Figure 4); they are oriented differently in space (the one labelled <span class=\"inlineequation\">dz2<\/span> has two lobes and a torus instead of four lobes, but it is equivalent to the other orbitals). When there is more than one possible value of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub>, each orbital is labelled with one of the possible values. It should be noted that the diagrams in Figure 4 are estimates of the electron distribution in space, not surfaces electrons are fixed on.<\/p>\r\n\r\n<div id=\"ball-ch08_s02_f04\" class=\"figure large block\">\r\n\r\n[caption id=\"attachment_4689\" align=\"aligncenter\" width=\"600\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Electron-Orbitals.png\"><img class=\"wp-image-4689 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213327\/Electron-Orbitals-1.png\" alt=\"Electron Orbitals\" width=\"600\" height=\"498\" \/><\/a> Figure 4 Electron Orbitals. (a) The lone s orbital is spherical in distribution. (b) The three p orbitals are shaped like dumbbells, and each one points in a different direction. (c) The five d orbitals are rosette in shape, except for the dz2 orbital, which is a \u201cdumbbell + torus\u201d combination. They are all oriented in different directions.[\/caption]\r\n\r\n<\/div>\r\n<p id=\"ball-ch08_s02_p17\" class=\"para block\">The final quantum number is the spin quantum number<span class=\"margin_term\"><span class=\"glossdef\">. Represented by <span class=\"inlineequation\">ms<\/span>.<\/span><\/span> (<em class=\"emphasis\">m<\/em><sub class=\"subscript\">s<\/sub>). Electrons and other subatomic particles behave as if they are spinning (we cannot tell if they really are, but they behave as if they are). Electrons themselves have two possible spin states, and because of mathematics, they are assigned the quantum numbers +1\/2 and \u22121\/2. These are the only two possible choices for the spin quantum number of an electron.Chemistry Is Everywhere: Neon Lights<\/p>\r\n\r\n<div id=\"ball-ch08_s02_n03\" class=\"callout block\">\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 id=\"ball-ch08_s02_f05\" class=\"informalfigure medium\">\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 class=\"size-full wp-image-3226\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213329\/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.\" width=\"450\" height=\"600\" \/><\/a> Figure 5 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<h2>The Pauli Exclusion Principle<\/h2>\r\nAn electron in an atom is completely described by four quantum numbers: <em>n<\/em>, <em>l<\/em>, <em>m<sub>l<\/sub><\/em>, and <em>m<sub>s<\/sub><\/em>. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The <strong>Pauli exclusion principle<\/strong> can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers <em>n<\/em>, <em>l<\/em>, and <em>m<sub>l<\/sub><\/em>), but only if their spin quantum numbers <em>m<sub>s<\/sub><\/em> have different values. Since the spin quantum number can only have two values [latex]\\left(\\pm \\frac{1}{2}\\right)[\/latex], no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons.\r\n\r\nHaving introduced the basics of atomic structure and quantum mechanics, we can use our understanding of quantum numbers to determine how atomic orbitals relate to one another. This allows us to determine which orbitals are occupied by electrons in each atom. The specific arrangement of electrons in orbitals of an atom determines many of the chemical properties of that atom.\r\n<h2>Orbital Energies and Atomic Structure<\/h2>\r\nThe energy of atomic orbitals increases as the principal quantum number, <em>n<\/em>, increases. In any atom with two or more electrons, the repulsion between the electrons makes energies of subshells with different values of <em>l<\/em> differ so that the energy of the orbitals increases within a shell in the order <em>s<\/em> &lt; <em>p<\/em> &lt; <em>d<\/em> &lt; <em>f.<\/em> Figure 1 depicts how these two trends in increasing energy relate. The 1<em>s<\/em> orbital at the bottom of the diagram is the orbital with electrons of lowest energy. The energy increases as we move up to the 2<em>s<\/em> and then 2<em>p<\/em>, 3<em>s<\/em>, and 3<em>p<\/em> orbitals, showing that the increasing <em>n<\/em> value has more influence on energy than the increasing <em>l<\/em> value for small atoms. However, this pattern does not hold for larger atoms. The 3<em>d<\/em> orbital is higher in energy than the 4<em>s<\/em> orbital. Such overlaps continue to occur frequently as we move up the chart.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"880\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213426\/CNX_Chem_06_04_eLeveldiag.jpg\" alt=\"A table entitled, \u201cSubshell electron capacity,\u201d is shown. Along the left side of the table, an upward pointing arrow labeled, \u201cE,\u201d is drawn. The table includes three columns. The first column is narrow and is labeled, \u201c2.\u201d The second is slightly wider and is labeled, \u201c6.\u201d The third is slightly wider yet and is labeled, \u201c10.\u201d The fourth is the widest and is labeled, \u201c14.\u201d The first column begins at the very bottom with a horizontal line segment labeled \u201c1 s.\u201d Evenly spaced line segments continue up to 7 s near the top of the column. In the second column, a horizontal dashed line segment labeled, \u201c2 p,\u201d appears at a level between the 2 s and 3 s levels. Similarly 3 p appears at a level between 3 s and 4 s, 4 p appears just below 5 s, 5 p appears just below 6 s, and 6 p appears just below 7 s. In the third column, a dashed line labeled, \u201c3 d,\u201d appears just below the level of 4 p. Similarly, 4 d appears just below 5 p and 5 d appears just below 6 p. Six d however appears above the levels of both 6 p and 7 s. The far right column entries begin with a dashed line labeled, \u201c4 f,\u201d positioned at a level just below 5 d. Similarly, a second dashed line segment appears just below the level of 6 d, which is labeled, \u201c5 f.\u201d\" width=\"880\" height=\"451\" \/> Figure 5. Generalized energy-level diagram for atomic orbitals in an atom with two or more electrons (not to scale).[\/caption]\r\n\r\nElectrons in successive atoms on the periodic table tend to fill low-energy orbitals first. Thus, many students find it confusing that, for example, the 5<em>p<\/em> orbitals fill immediately after the 4<em>d<\/em>, and immediately before the 6<em>s<\/em>. The filling order is based on observed experimental results, and has been confirmed by theoretical calculations. As the principal quantum number, <em>n<\/em>, increases, the size of the orbital increases and the electrons spend more time farther from the nucleus. Thus, the attraction to the nucleus is weaker and the energy associated with the orbital is higher (less stabilized). But this is not the only effect we have to take into account. Within each shell, as the value of <em>l<\/em> increases, the electrons are less penetrating (meaning there is less electron density found close to the nucleus), in the order <em>s<\/em> &gt; <em>p<\/em> &gt; <em>d<\/em> &gt; <em>f<\/em>. Electrons that are closer to the nucleus slightly repel electrons that are farther out, offsetting the more dominant electron\u2013nucleus attractions slightly (recall that all electrons have \u22121 charges, but nuclei have +<em>Z<\/em> charges). This phenomenon is called shielding and will be discussed in more detail in the next section. Electrons in orbitals that experience more shielding are less stabilized and thus higher in energy. For small orbitals (1<em>s<\/em> through 3<em>p<\/em>), the increase in energy due to <em>n<\/em> is more significant than the increase due to <em>l<\/em>; however, for larger orbitals the two trends are comparable and cannot be simply predicted. We will discuss methods for remembering the observed order.\r\n\r\nThe arrangement of electrons in the orbitals of an atom is called the <strong>electron configuration<\/strong> of the atom. We describe an electron configuration with a symbol that contains three pieces of information (Figure 6):\r\n<ol>\r\n \t<li>The number of the principal quantum shell, <em>n<\/em>,<\/li>\r\n \t<li>The letter that designates the orbital type (the subshell, <em>l<\/em>), and<\/li>\r\n \t<li>A superscript number that designates the number of electrons in that particular subshell.<\/li>\r\n<\/ol>\r\nFor example, the notation 2<em>p<\/em><sup>4<\/sup> (read \"two\u2013p\u2013four\") indicates four electrons in a <em>p<\/em> subshell (<em>l<\/em> = 1) with a principal quantum number (<em>n<\/em>) of 2. The notation 3<em>d<\/em><sup>8<\/sup> (read \"three\u2013d\u2013eight\") indicates eight electrons in the <em>d<\/em> subshell (i.e., <em>l<\/em> = 2) of the principal shell for which <em>n<\/em> = 3.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"881\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213428\/CNX_Chem_06_04_Econfig.jpg\" alt=\"A light blue hemisphere is labeled H. At a location about midway between the center and outer edge of the hemisphere, a small yellow-orange sphere is shown that is labeled with a negative sign. To the right of this diagram is the electron configuration 1 s superscript 1. The superscript is shown in a small yellow-orange circle. This superscript is labeled, \u201cNumber of electrons in subshell,\u201d and the s is labeled, \u201cSubshell.\u201d\" width=\"881\" height=\"168\" \/> Figure 6. The diagram of an electron configuration specifies the subshell (n and l value, with letter symbol) and superscript number of electrons.[\/caption]\r\n<h2>The Aufbau Principle<\/h2>\r\n[caption id=\"\" align=\"alignright\" width=\"500\"]<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213430\/CNX_Chem_06_04_Efillorder.jpg\" alt=\"This figure includes a chart used to order the filling of electrons into atoms. At the top is a blue circle labeled \u201c1 s.\u201d In a row beneath this circle are 6 additional blue circles labeled \u201c2 s\u201d through \u201c7 s.\u201d A column to the right begins just right of 2 s and contains pink circles labeled 2 p through 7 p. A column to the right begins just right of 3 p and contains yellow circles labeled 3 d through 6 d. No circles are placed to the right of the 7 s and 7 p circles. A final column on the right begins right of 4 d. It includes grey circles labeled, \u201c4 f\u201d and, \u201c5 f.\u201d No circles are placed right of 6 d. Through these circles, arrows are included in the figure pointing down and to the left. The first arrow begins in the upper right and passes through 1 s. The second arrow begins just below and passes through 2 s. The third arrow passes through 2 p and 3 s. The fourth arrow passes through 3 p and 4 s. This pattern of parallel arrows pointing downward to the left continues through all circles completing the pattern 1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p 5 s 4 d 5 p 6 s 4 f 5 d 6 p 7 s 5 f 6 d 7 p.\" width=\"500\" height=\"361\" \/> Figure 7. The arrow leads through each subshell in the appropriate filling order for electron configurations. This chart is straightforward to construct. Simply make a column for all the s orbitals with each n shell on a separate row. Repeat for p, d, and f. Be sure to only include orbitals allowed by the quantum numbers (no 1p or 2d, and so forth). Finally, draw diagonal lines from top to bottom as shown.[\/caption]\r\n\r\nTo determine the electron configuration for any particular atom, we can \u201cbuild\u201d the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements.\r\n\r\nThis procedure is called the <strong>Aufbau principle<\/strong>, from the German word <em>Aufbau<\/em> (\u201cto build up\u201d). Each added electron occupies the subshell of lowest energy available (in the order shown in Figure 7), subject to the limitations imposed by the allowed quantum numbers according to the Pauli exclusion principle. Electrons enter higher-energy subshells only after lower-energy subshells have been filled to capacity.\u00a0Figure 7 illustrates the traditional way to remember the filling order for atomic orbitals.\r\n<h2>Writing Electron Configurations<\/h2>\r\nChemists use an electron configuration<span class=\"margin_term\"><a class=\"glossterm\">, <\/a><\/span>to represent the organization of electrons in shells and subshells in an atom. An electron configuration simply lists the shell and subshell labels, with a right superscript giving the number of electrons in that subshell. The shells and subshells are listed in the order of filling.\r\n<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\r\n<p id=\"ball-ch08_s03_p11\" class=\"para editable block\">For example, an H atom has a single electron in the 1<em class=\"emphasis\">s<\/em> subshell. Its electron configuration is<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]H: 1s^{1}[\/latex]<\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p12\" class=\"para editable block\">He has two electrons in the 1<em class=\"emphasis\">s<\/em> subshell. Its electron configuration is<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]He: 1s^{2}[\/latex]<\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p13\" class=\"para editable block\">The three electrons for Li are arranged in the 1<em class=\"emphasis\">s<\/em> subshell (two electrons) and the 2<em class=\"emphasis\">s<\/em> subshell (one electron). The electron configuration of Li is<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]Li: 1s^{2}2s^{1}[\/latex]<\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p14\" class=\"para editable block\">Be has four electrons, two in the 1<em class=\"emphasis\">s<\/em> subshell and two in the 2<em class=\"emphasis\">s<\/em> subshell. Its electron configuration is<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]Be: 1s^{2}2s^{2}[\/latex]<\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p15\" class=\"para editable block\">Now that the 2<em class=\"emphasis\">s<\/em> subshell is filled, electrons in larger atoms must go into the 2<em class=\"emphasis\">p<\/em> subshell, which can hold a maximum of six electrons. The next six elements progressively fill up the 2<em class=\"emphasis\">p<\/em> subshell:<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]B: 1s^{2}2s^{2}2p^{1}[\/latex]<\/span><\/span>\r\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]C: 1s^{2}2s^{2}2p^{2}[\/latex]<\/span><\/span>\r\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]N: 1s^{2}2s^{2}2p^{3}[\/latex]<\/span><\/span>\r\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]O: 1s^{2}2s^{2}2p^{4}[\/latex]<\/span><\/span>\r\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]F: 1s^{2}2s^{2}2p^{5}[\/latex]<\/span><\/span>\r\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]Ne: 1s^{2}2s^{2}2p^{6}[\/latex]<\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p16\" class=\"para editable block\">Now that the 2<em class=\"emphasis\">p<\/em> subshell is filled (all possible subshells in the <em class=\"emphasis\">n<\/em> = 2 shell), the next electron for the next-larger atom must go into the <em class=\"emphasis\">n<\/em> = 3 shell, <em class=\"emphasis\">s<\/em> subshell.<\/p>\r\n\r\n<div class=\"textbox examples\">\r\n<h3>Example 1: Electron Configuration<\/h3>\r\nWhat is the electron configuration for Na, which has 11 electrons?\r\n\r\n[reveal-answer q=\"177286\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"177286\"]\r\n\r\nThe first two electrons occupy the 1<em class=\"emphasis\">s<\/em> subshell. The next two occupy the 2<em class=\"emphasis\">s<\/em> subshell, while the next six electrons occupy the 2<em class=\"emphasis\">p<\/em> subshell. This gives us 10 electrons so far, with 1 electron left. This last electron goes into the <em class=\"emphasis\">n<\/em> = 3 shell, <em class=\"emphasis\">s<\/em> subshell. Thus, the electron configuration of Na is 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup>.\r\n\r\n[\/hidden-answer]\r\n<h4><strong>Check Your Learning<\/strong><\/h4>\r\nWhat is the electron configuration for Mg, which has 12 electrons?\r\n\r\n[reveal-answer q=\"174864\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"174864\"]1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>[\/hidden-answer]\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example 2: Electron Configuration<\/h3>\r\nWhat is the predicted electron configuration for Sn, which has 50 electrons?\r\n\r\n[reveal-answer q=\"1772861\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"1772861\"]\r\n<p id=\"ball-ch08_s03_p24\" class=\"para\">We will follow the Aufbau diagram until we can accommodate 50 electrons in the subshells in the proper order:<\/p>\r\n<span class=\"informalequation\"><span class=\"mathphrase\">Sn: 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>4<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>5<em class=\"emphasis\">p<\/em><sup class=\"superscript\">2<\/sup><\/span><\/span>\r\n<p id=\"ball-ch08_s03_p25\" class=\"para\">Verify by adding the superscripts, which indicate the number of electrons: 2 +\u00a02 +\u00a06 +\u00a02 +\u00a06 +\u00a02 +\u00a010 +\u00a06 +\u00a02 +\u00a010 +\u00a02 = 50, so we have placed all 50 electrons in subshells in the proper order.<\/p>\r\n[\/hidden-answer]\r\n<h4><strong>Check Your Learning<\/strong><\/h4>\r\nWhat is the electron configuration for Ba, which has 56 electrons?\r\n\r\n[reveal-answer q=\"1748614\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"1748614\"]1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>4<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>5<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>6<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>[\/hidden-answer]\r\n\r\n<\/div>\r\n<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\r\n<h2>Abbreviated Electron Configurations<\/h2>\r\n<p id=\"ball-ch08_s03_p28\" class=\"para editable block\">As the previous example demonstrated, electron configurations can get fairly long. An abbreviated electron configuration, also known as a noble gas abbreviated electron configuration,\u00a0 uses one of the elements from the last column of the periodic table, which contains what are called the <em class=\"emphasis\">noble gases<\/em>, to represent the core of electrons up to that element. Then the remaining electrons are listed explicitly. For example, the abbreviated electron configuration for Li, which has three electrons, would be<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">Li: [He]2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup><\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p29\" class=\"para editable block\">where [He] represents the two-electron core that is equivalent to He\u2019s electron configuration. The square brackets represent the electron configuration of a noble gas. This is not much of an abbreviation. However, consider the abbreviated electron configuration for W, which has 74 electrons:<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">W: [Xe]6<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">f<\/em><sup class=\"superscript\">14<\/sup>5<em class=\"emphasis\">d<\/em><sup class=\"superscript\">4<\/sup><\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p30\" class=\"para editable block\">This is a significant simplification over an explicit listing of all 74 electrons. So for larger elements, the abbreviated electron configuration can be a very useful shorthand.<\/p>\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example 7: Abbreviated Electron Configuration<\/h3>\r\nWhat is the abbreviated electron configuration for P, which has 15 electrons?\r\n\r\n[reveal-answer q=\"17728613\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"17728613\"]\r\n<p id=\"ball-ch08_s03_p32\" class=\"para\">With 15 electrons, the electron configuration of P is<\/p>\r\n<span class=\"informalequation\"><span class=\"mathphrase\">P: 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">3<\/sup><\/span><\/span>\r\n<p id=\"ball-ch08_s03_p33\" class=\"para\">The first immediate noble gas is Ne, which has an electron configuration of 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>. Using the electron configuration of Ne to represent the first 10 electrons, the abbreviated electron configuration of P is<\/p>\r\n<span class=\"informalequation\"><span class=\"mathphrase\">P: [Ne]3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">3<\/sup><\/span><\/span>\r\n\r\n[\/hidden-answer]\r\n<h4><strong>Check Your Learning<\/strong><\/h4>\r\nWhat is the abbreviated electron configuration for Rb, which has 37 electrons?\r\n\r\n[reveal-answer q=\"1748614\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"1748614\"][Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup>[\/hidden-answer]\r\n\r\n<\/div>\r\n<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\r\n<p id=\"ball-ch08_s03_p36\" class=\"para editable block\">There are some exceptions to the rigorous filling of subshells by electrons. In many cases, an electron goes from a higher-numbered shell to a lower-numbered but later-filled subshell to fill the later-filled subshell. One example is Ag. With 47 electrons, its electron configuration is predicted to be<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">Ag: [Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">9<\/sup><\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p37\" class=\"para editable block\">However, experiments have shown that the electron configuration is actually<\/p>\r\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">Ag: [Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup><\/span><\/span><\/p>\r\n<p id=\"ball-ch08_s03_p38\" class=\"para editable block\">This, then, qualifies as an exception to our expectations. At this point, you do not need to worry about the exceptions; we will ignore these exceptions in this course.<\/p>\r\n\r\n<h2>Electron Configuration Energy Diagrams<\/h2>\r\nWe have just seen that electrons fill orbitals in shells and subshells in a regular pattern, but why does it follow this pattern? There are three principles which should be followed to properly fill electron orbital energy diagrams:\r\n<ol>\r\n \t<li>The <b>Aufbau principle<\/b><\/li>\r\n \t<li>The <b>Pauli exclusion principle<\/b><\/li>\r\n \t<li><b>Hund\u2019s rule<\/b><\/li>\r\n<\/ol>\r\nThe overall pattern of the electron shell filling order emerges from the <b>Aufbau principle <\/b>(German for \u201cbuilding up\u201d): \u00a0electrons fill the lowest energy orbitals first. Increasing the principle quantum number, <i>n<\/i>, increases orbital energy levels, as the electron density becomes more spread out away from the nucleus. In many-electron atoms (all atoms except hydrogen), the energy levels of subshells varies due to electron-electron repulsions. The trend that emerges is that energy levels increase with value of the angular momentum quantum number, <i>l<\/i>, for orbitals sharing the same principle quantum number, <i>n<\/i>. This is demonstrated in Figure 7, where each line represents an orbital, and each set of lines at the same energy represents a subshell of orbitals.\r\n\r\n[caption id=\"attachment_2448\" align=\"alignnone\" width=\"429\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/generic-energy-diagram-of-orbitals-in-multi-electron-atom.jpg\"><img class=\"size-full wp-image-2448\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213236\/generic-energy-diagram-of-orbitals-in-multi-electron-atom-1.jpg\" alt=\"Figure 8.# Generic energy diagram of orbitals in a multi-electron atom.\" width=\"429\" height=\"387\" \/><\/a> Figure 7. Generic energy diagram of orbitals in a multi-electron atom.[\/caption]\r\n\r\nAs previously discussed, the <b>Pauli exclusion principle <\/b>states that we can only fill each orbital with a maximum of two electrons of opposite spin. But how should we fill multiple orbitals of the same energy level within a subshell (eg. The three orbitals in the 2<i>p<\/i> subshell)? Orbitals of the same energy level are known as degenerate orbitals, and we fill them using <b>Hund\u2019s rule<\/b>: place one electron into each degenerate orbital first, before pairing them in the same orbital.\r\n\r\nLet\u2019s examine a few examples to demonstrate the use of the three principles.\r\n\r\nBoron is atomic number 5, and therefore has 5 electrons. First fill the lowest energy 1<i>s<\/i> orbital with two electrons of opposite spin, then the 2<i>s <\/i>orbital with 2 electrons of opposite spin and finally place the last electron into any of the three degenerate 2<i>p<\/i> orbitals (Figure 8).\r\n\r\n[caption id=\"attachment_2449\" align=\"alignnone\" width=\"593\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/Boron_electron_configuration_energy_diagram.png\"><img class=\"size-full wp-image-2449\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213238\/Boron_electron_configuration_energy_diagram-1.png\" alt=\"Figure 8.#. Boron electron configuration energy diagram\" width=\"593\" height=\"527\" \/><\/a> Figure 8. Boron electron configuration energy diagram[\/caption]\r\n\r\nMoving across the periodic table, we follow Hund\u2019s rule and add an additional electron to each degenerate 2<i>p<\/i> orbital for each subsequent element (Figure 9). At oxygen we can finally pair up and fill one of the degenerate 2<i>p<\/i> orbitals.\r\n\r\n[caption id=\"attachment_2450\" align=\"alignnone\" width=\"600\"]<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/Electron-configuration-energy-diagrams-for-carbon-nitrogen-and-oxygen.jpg\"><img class=\"wp-image-2450 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213240\/Electron-configuration-energy-diagrams-for-carbon-nitrogen-and-oxygen-e1411755889659-1.jpg\" alt=\"Figure 8.#. Electron configuration energy diagrams for carbon, nitrogen and oxygen.\" width=\"600\" height=\"173\" \/><\/a> Figure 9. Electron configuration energy diagrams for carbon, nitrogen and oxygen.[\/caption]\r\n\r\n<div id=\"ball-ch08_s03_n06\" class=\"key_takeaways editable block\">\r\n<div class=\"bcc-box bcc-success\">\r\n<h3>Key Takeaways<\/h3>\r\n<ul>\r\n \t<li>The Pauli exclusion principle limits the number of electrons in the subshells and shells.<\/li>\r\n \t<li>Electrons in larger atoms fill shells and subshells in a regular pattern that we can follow.<\/li>\r\n \t<li>Electron configurations are a shorthand method of indicating what subshells electrons occupy in atoms.<\/li>\r\n \t<li>Abbreviated electron configurations are a simpler way of representing electron configurations for larger atoms.<\/li>\r\n \t<li>Exceptions to the strict filling of subshells with electrons occur.<\/li>\r\n \t<li>Electron configurations are assigned from lowest to highest energy following the Aufbau principle<\/li>\r\n \t<li>One electron is placed in each degenerate orbital before pairing electrons following Hund's rule.<\/li>\r\n \t<li>Electron configuration energy diagrams follow three principles: the Aufbau principle, the Pauli exclusion principle and Hund's rule.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div id=\"ball-ch08_s03_qs01\" class=\"qandaset block\">\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Exercises<\/h3>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p1\" class=\"para\">1. How many subshells are completely filled with electrons for Na? How many subshells are unfilled?<\/p>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p7\" class=\"para\">2. How many subshells are completely filled with electrons for Mg? How many subshells are unfilled?<\/p>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p9\" class=\"para\">3. What is the maximum number of electrons in the entire <em class=\"emphasis\">n<\/em> = 2 shell?<\/p>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p11\" class=\"para\">4. What is the maximum number of electrons in the entire <em class=\"emphasis\">n<\/em> = 4 shell?<\/p>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p13\" class=\"para\">5. Write the complete electron configuration for each atom.<\/p>\r\n\r\n<\/div>\r\n<p style=\"padding-left: 30px;\">a) \u00a0Si, 14 electrons<\/p>\r\n<p style=\"padding-left: 30px;\">b) \u00a0Sc, 21 electrons<\/p>\r\n\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p14\" class=\"para\">6.\u00a0 Write the complete electron configuration for each atom.<\/p>\r\n<p style=\"padding-left: 30px;\">a) \u00a0Br, 35 electrons<\/p>\r\n<p style=\"padding-left: 30px;\">b) \u00a0Be, 4 electrons<\/p>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p15\" class=\"para\">7.\u00a0 Write the complete electron configuration for each atom.<\/p>\r\n<p style=\"padding-left: 30px;\">a) \u00a0Cd, 48 electrons<\/p>\r\n<p style=\"padding-left: 30px;\">b) \u00a0Mg, 12 electrons<\/p>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p16\" class=\"para\">8.\u00a0 Write the complete electron configuration for each atom.<\/p>\r\n<p style=\"padding-left: 30px;\">a) \u00a0Cs, 55 electrons<\/p>\r\n<p style=\"padding-left: 30px;\">b) \u00a0Ar, 18 electrons<\/p>\r\n9. \u00a0Write the abbreviated electron configuration for each atom in Exercise 7.\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p18\" class=\"para\">10. \u00a0Write the abbreviated electron configuration for each atom in Exercise 8.<\/p>\r\n\r\n<\/div>\r\n<div class=\"question\">\r\n<p id=\"ball-ch08_s03_qs01_qd01_p19\" class=\"para\">11. \u00a0Write the abbreviated electron configuration for each atom in Exercise 9.<\/p>\r\n\r\n<\/div>\r\n<p id=\"ball-ch08_s03_qs01_qd01_p20\" class=\"para\" style=\"line-height: 1.5em;\">12. \u00a0Write the abbreviated electron configuration for each atom in Exercise 10.<\/p>\r\n<p class=\"para\" style=\"line-height: 1.5em;\">13. \u00a0 Draw electron configuration energy diagrams for potassium, and bromine.<\/p>\r\n&nbsp;\r\n\r\n[reveal-answer q=\"367563\"]Show Answer to Select Questions[\/reveal-answer]\r\n[hidden-answer a=\"367563\"]\r\n\r\n1. Three subshells (1<em class=\"emphasis\">s<\/em>, 2<em class=\"emphasis\">s<\/em>, 2<em class=\"emphasis\">p<\/em>) are completely filled, and one shell (3<em class=\"emphasis\">s<\/em>) is partially filled.\r\n\r\n3. 8 electrons\r\n\r\n5. a) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">2 <\/sup>,b) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">1<\/sup>\r\n\r\n7. a) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>4<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10 <\/sup>,b) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>\r\n\r\n9. a) \u00a0[Ne]3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">2 <\/sup>,b) \u00a0[Ar]4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">1<\/sup>\r\n\r\n11. a) \u00a0[Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10 <\/sup>,b) \u00a0[Ne]3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>\r\n\r\n13.\r\n\r\n<a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/Electron_configuration_potassium.svg_.png\"><img class=\"alignnone wp-image-2454\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213243\/Electron_configuration_potassium.svg_-1.png\" alt=\"Electron_configuration_potassium.svg\" width=\"600\" height=\"843\" \/><\/a>\r\n\r\n[footnote]Orbital representation diagram for potassium, depicting each orbital as a line. Adrignola\\Public domain[\/footnote]\r\n\r\n<img class=\"alignnone wp-image-2455\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213247\/1000px-Electron_configuration_bromine.svg_-1.png\" alt=\"1000px-Electron_configuration_bromine.svg\" width=\"600\" height=\"474\" \/>\r\n<ol>\r\n \t<li>[footnote]Orbital representation diagram for bromine, depicting each orbital as a line. Adrignola\\Public domain[\/footnote]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<strong>Aufbau principle: <\/strong>procedure in which the electron configuration of the elements is determined by \u201cbuilding\u201d them in order of atomic numbers, adding one proton to the nucleus and one electron to the proper subshell at a time\r\n\r\n<strong>core electron: <\/strong>electron in an atom that occupies the orbitals of the inner shells\r\n\r\n<strong>electron configuration: <\/strong>electronic structure of an atom in its ground state given as a listing of the orbitals occupied by the electrons\r\n\r\n<strong>Hund\u2019s rule: <\/strong>every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin\r\n\r\n<strong>orbital diagram: <\/strong>pictorial representation of the electron configuration showing each orbital as a box and each electron as an arrow\r\n\r\n<strong>valence electrons: <\/strong>electrons in the outermost or valence shell (highest value of <em>n<\/em>) of a ground-state atom; determine how an element reacts\r\n\r\n<strong>valence shell: <\/strong>outermost shell of electrons in a ground-state atom; for main group elements, the orbitals with the highest <em>n<\/em> level (<em>s<\/em> and <em>p<\/em> subshells) are in the valence shell, while for transition metals, the highest energy <em>s<\/em> and <em>d<\/em> subshells make up the valence shell and for inner transition elements, the highest <em>s<\/em>, <em>d,<\/em> and <em>f<\/em> subshells are included\r\n\r\n<\/div>\r\n<\/div>","rendered":"<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\n<div id=\"ball-ch08_s03_n01\" class=\"learning_objectives editable block\">\n<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Learn how electrons are organized in atoms<\/li>\n<li>Represent the organization of electrons by an electron configuration<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\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 Figure 1). This image is known as a continuous spectrum. 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 Firgure 1). This image is called a line spectrum. It turns out that every element has its own unique, characteristic line spectrum.<\/p>\n<div id=\"ball-ch08_s02_f01\" class=\"figure large editable block\">\n<div id=\"attachment_4685\" style=\"width: 610px\" 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\" aria-describedby=\"caption-attachment-4685\" class=\"wp-image-4685 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213318\/Prisms-and-Light-1.png\" alt=\"Prisms and Light\" width=\"600\" height=\"180\" \/><\/a><\/p>\n<p id=\"caption-attachment-4685\" class=\"wp-caption-text\">Figure 1 (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.<\/p>\n<\/div>\n<p id=\"ball-ch08_s02_p03\" class=\"para editable block\">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 (Figure 2). 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\" class=\"wp-image-3851 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213320\/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\" \/><\/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.<\/p>\n<div id=\"ball-ch08_s02_f02\" class=\"figure large editable block\">\n<div id=\"attachment_4687\" style=\"width: 610px\" 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\" aria-describedby=\"caption-attachment-4687\" class=\"wp-image-4687 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213321\/Hydrogen-Spectrum-1.png\" alt=\"Hydrogen Spectrum\" width=\"600\" height=\"107\" \/><\/a><\/p>\n<p id=\"caption-attachment-4687\" class=\"wp-caption-text\">Figure 2 The spectrum of hydrogen was particularly simple and could be predicted by a simple mathematical expression.<\/p>\n<\/div>\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 <strong>quantum number<\/strong>. Quantities that have certain specific values are called quantized. 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). 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\">[latex]E_{light} =h\\nu = \\Delta E_{electron}[\/latex]<\/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. Figure 3 shows a model of the hydrogen atom based on Bohr\u2019s ideas.<\/p>\n<div id=\"ball-ch08_s02_f03\" class=\"figure large medium-height editable block\">\n<div id=\"attachment_4688\" style=\"width: 610px\" 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\" aria-describedby=\"caption-attachment-4688\" class=\"wp-image-4688 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213324\/Bohrs-Hydrogen-Atom-1.png\" alt=\"Bohr's Hydrogen Atom\" width=\"600\" height=\"510\" \/><\/a><\/p>\n<p id=\"caption-attachment-4688\" class=\"wp-caption-text\">Figure 3 Bohr&#8217;s Model. Bohr\u2019s description of the hydrogen atom had specific orbits for the electron, which had quantized energies.<\/p>\n<\/div>\n<\/div>\n<p id=\"ball-ch08_s02_p07\" class=\"para editable block\">Bohr\u2019s ideas were useful but were applied only to the hydrogen atom. However, later researchers generalized Bohr\u2019s ideas into a new theory called quantum mechanics, which explains the behaviour of electrons as if they were acting as a wave, not as particles. Quantum mechanics predicts two major things: quantized energies for electrons of all atoms (not just hydrogen) and an organization of electrons within atoms. Electrons are no longer thought of as being randomly distributed around a nucleus or restricted to certain orbits (in that regard, Bohr was wrong). Instead, electrons are collected into groups and subgroups that explain much about the chemical behaviour of the atom.<\/p>\n<p id=\"ball-ch08_s02_p08\" class=\"para block\">In the quantum-mechanical model of an atom, the state of an electron is described by four quantum numbers, not just the one predicted by Bohr. The first quantum number is called the principle quantum number, r<span class=\"margin_term\"><span class=\"glossdef\">epresented by <span class=\"inlineequation\">n<\/span>.<\/span><\/span> (<em class=\"emphasis\">n<\/em>). The principal quantum number largely determines the energy of an electron. Electrons in the same atom that have the same principal quantum number are said to occupy an electron <strong>shell<\/strong> of the atom. The principal quantum number can be any nonzero positive integer: 1, 2, 3, 4,\u2026.<\/p>\n<p id=\"ball-ch08_s02_p09\" class=\"para editable block\">Within a shell, there may be multiple possible values of the next quantum number, the angular momentum quantum number.<span class=\"margin_term\"><span class=\"glossdef\"> Represented by \u2113.<\/span><\/span> (\u2113). The \u2113 quantum number has a minor effect on the energy of the electron but also affects the spatial distribution of the electron in three-dimensional space\u2014that is, the shape of an electron\u2019s distribution in space. The value of the \u2113 quantum number can be any integer between 0 and <em class=\"emphasis\">n<\/em> \u2212 1:<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">\u2113 = 0, 1, 2,\u2026, <em class=\"emphasis\">n<\/em> \u2212 1<\/span><\/span><\/p>\n<p id=\"ball-ch08_s02_p10\" class=\"para editable block\">Thus, for a given value of <em class=\"emphasis\">n<\/em>, there are different possible values of \u2113:<\/p>\n<div class=\"informaltable block\">\n<table cellpadding=\"0\">\n<thead>\n<tr>\n<th>If <em class=\"emphasis\">n<\/em> equals<\/th>\n<th>\u2113 can be<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>0 or 1<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>0, 1, or 2<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>0, 1, 2, or 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"ball-ch08_s02_p11\" class=\"para editable block\">and so forth. Electrons within a shell that have the same value of \u2113 are said to occupy a <strong>subshell<\/strong> in the atom. Commonly, instead of referring to the numerical value of \u2113, a letter represents the value of \u2113 (to help distinguish it from the principal quantum number):<\/p>\n<div class=\"informaltable block\">\n<table cellpadding=\"0\">\n<thead>\n<tr>\n<th>If \u2113 equals<\/th>\n<th>The letter is<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td><em class=\"emphasis\">s<\/em><\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td><em class=\"emphasis\">p<\/em><\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td><em class=\"emphasis\">d<\/em><\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td><em class=\"emphasis\">f<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"ball-ch08_s02_p12\" class=\"para block\">The next quantum number is called the magnetic quantum number re<span class=\"margin_term\"><span class=\"glossdef\">presented by <span class=\"inlineequation\">m\u2113<\/span>.<\/span><\/span> (<em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub>). For any value of \u2113, there are 2\u2113 +\u00a01 possible values of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub>, ranging from \u2212\u2113 to \u2113:<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">\u2212\u2113 \u2264 <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> \u2264 \u2113<\/span><\/span><\/p>\n<p id=\"ball-ch08_s02_p13\" class=\"para editable block\" style=\"text-align: center;\">or<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\">|m\u2113| \u2264\u00a0\u2113<\/span><\/p>\n<p id=\"ball-ch08_s02_p14\" class=\"para editable block\">The following explicitly lists the possible values of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> for the possible values of \u2113:<\/p>\n<div class=\"informaltable block\">\n<table cellpadding=\"0\">\n<thead>\n<tr>\n<th>If \u2113 equals<\/th>\n<th>The <span class=\"inlineequation\">m\u2113<\/span> values can be<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>0<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>\u22121, 0, or 1<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>\u22122, \u22121, 0, 1, or 2<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>\u22123, \u22122, \u22121, 0, 1, 2, or 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p id=\"ball-ch08_s02_p15\" class=\"para editable block\">The particular value of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> dictates the orientation of an electron\u2019s distribution in space. When \u2113 is zero, <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> can be only zero, so there is only one possible orientation. When \u2113 is 1, there are three possible orientations for an electron\u2019s distribution. When \u2113 is 2, there are five possible orientations of electron distribution. This goes on and on for other values of \u2113, but we need not consider any higher values of \u2113 here. Each value of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> designates a certain <strong>orbital<\/strong>. Thus, there is only one orbital when \u2113 is zero, three orbitals when \u2113 is 1, five orbitals when \u2113 is 2, and so forth. The <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub> quantum number has no effect on the energy of an electron unless the electrons are subjected to a magnetic field\u2014hence its name.<\/p>\n<p id=\"ball-ch08_s02_p16\" class=\"para block\">The \u2113 quantum number dictates the general shape of electron distribution in space (Figure 4). Any <em class=\"emphasis\">s<\/em> orbital is spherically symmetric (part (a) in Figure 4), and there is only one orbital in any <em class=\"emphasis\">s<\/em> subshell. Any <em class=\"emphasis\">p<\/em> orbital has a two-lobed, dumbbell-like shape (part (b) in Figure 4); because there are three of them, we normally represent them as pointing along the <em class=\"emphasis\">x<\/em>-, <em class=\"emphasis\">y<\/em>-, and <em class=\"emphasis\">z<\/em>-axes of Cartesian space. The <em class=\"emphasis\">d<\/em> orbitals are four-lobed rosettes (part (c) in Figure 4); they are oriented differently in space (the one labelled <span class=\"inlineequation\">dz2<\/span> has two lobes and a torus instead of four lobes, but it is equivalent to the other orbitals). When there is more than one possible value of <em class=\"emphasis\">m<\/em><sub class=\"subscript\">\u2113<\/sub>, each orbital is labelled with one of the possible values. It should be noted that the diagrams in Figure 4 are estimates of the electron distribution in space, not surfaces electrons are fixed on.<\/p>\n<div id=\"ball-ch08_s02_f04\" class=\"figure large block\">\n<div id=\"attachment_4689\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/09\/Electron-Orbitals.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4689\" class=\"wp-image-4689 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213327\/Electron-Orbitals-1.png\" alt=\"Electron Orbitals\" width=\"600\" height=\"498\" \/><\/a><\/p>\n<p id=\"caption-attachment-4689\" class=\"wp-caption-text\">Figure 4 Electron Orbitals. (a) The lone s orbital is spherical in distribution. (b) The three p orbitals are shaped like dumbbells, and each one points in a different direction. (c) The five d orbitals are rosette in shape, except for the dz2 orbital, which is a \u201cdumbbell + torus\u201d combination. They are all oriented in different directions.<\/p>\n<\/div>\n<\/div>\n<p id=\"ball-ch08_s02_p17\" class=\"para block\">The final quantum number is the spin quantum number<span class=\"margin_term\"><span class=\"glossdef\">. Represented by <span class=\"inlineequation\">ms<\/span>.<\/span><\/span> (<em class=\"emphasis\">m<\/em><sub class=\"subscript\">s<\/sub>). Electrons and other subatomic particles behave as if they are spinning (we cannot tell if they really are, but they behave as if they are). Electrons themselves have two possible spin states, and because of mathematics, they are assigned the quantum numbers +1\/2 and \u22121\/2. These are the only two possible choices for the spin quantum number of an electron.Chemistry Is Everywhere: Neon Lights<\/p>\n<div id=\"ball-ch08_s02_n03\" class=\"callout block\">\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 id=\"ball-ch08_s02_f05\" class=\"informalfigure medium\">\n<div id=\"attachment_3226\" style=\"width: 460px\" 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\" aria-describedby=\"caption-attachment-3226\" class=\"size-full wp-image-3226\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213329\/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.\" width=\"450\" height=\"600\" \/><\/a><\/p>\n<p id=\"caption-attachment-3226\" class=\"wp-caption-text\">Figure 5 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.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2>The Pauli Exclusion Principle<\/h2>\n<p>An electron in an atom is completely described by four quantum numbers: <em>n<\/em>, <em>l<\/em>, <em>m<sub>l<\/sub><\/em>, and <em>m<sub>s<\/sub><\/em>. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The <strong>Pauli exclusion principle<\/strong> can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers <em>n<\/em>, <em>l<\/em>, and <em>m<sub>l<\/sub><\/em>), but only if their spin quantum numbers <em>m<sub>s<\/sub><\/em> have different values. Since the spin quantum number can only have two values [latex]\\left(\\pm \\frac{1}{2}\\right)[\/latex], no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons.<\/p>\n<p>Having introduced the basics of atomic structure and quantum mechanics, we can use our understanding of quantum numbers to determine how atomic orbitals relate to one another. This allows us to determine which orbitals are occupied by electrons in each atom. The specific arrangement of electrons in orbitals of an atom determines many of the chemical properties of that atom.<\/p>\n<h2>Orbital Energies and Atomic Structure<\/h2>\n<p>The energy of atomic orbitals increases as the principal quantum number, <em>n<\/em>, increases. In any atom with two or more electrons, the repulsion between the electrons makes energies of subshells with different values of <em>l<\/em> differ so that the energy of the orbitals increases within a shell in the order <em>s<\/em> &lt; <em>p<\/em> &lt; <em>d<\/em> &lt; <em>f.<\/em> Figure 1 depicts how these two trends in increasing energy relate. The 1<em>s<\/em> orbital at the bottom of the diagram is the orbital with electrons of lowest energy. The energy increases as we move up to the 2<em>s<\/em> and then 2<em>p<\/em>, 3<em>s<\/em>, and 3<em>p<\/em> orbitals, showing that the increasing <em>n<\/em> value has more influence on energy than the increasing <em>l<\/em> value for small atoms. However, this pattern does not hold for larger atoms. The 3<em>d<\/em> orbital is higher in energy than the 4<em>s<\/em> orbital. Such overlaps continue to occur frequently as we move up the chart.<\/p>\n<div style=\"width: 890px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213426\/CNX_Chem_06_04_eLeveldiag.jpg\" alt=\"A table entitled, \u201cSubshell electron capacity,\u201d is shown. Along the left side of the table, an upward pointing arrow labeled, \u201cE,\u201d is drawn. The table includes three columns. The first column is narrow and is labeled, \u201c2.\u201d The second is slightly wider and is labeled, \u201c6.\u201d The third is slightly wider yet and is labeled, \u201c10.\u201d The fourth is the widest and is labeled, \u201c14.\u201d The first column begins at the very bottom with a horizontal line segment labeled \u201c1 s.\u201d Evenly spaced line segments continue up to 7 s near the top of the column. In the second column, a horizontal dashed line segment labeled, \u201c2 p,\u201d appears at a level between the 2 s and 3 s levels. Similarly 3 p appears at a level between 3 s and 4 s, 4 p appears just below 5 s, 5 p appears just below 6 s, and 6 p appears just below 7 s. In the third column, a dashed line labeled, \u201c3 d,\u201d appears just below the level of 4 p. Similarly, 4 d appears just below 5 p and 5 d appears just below 6 p. Six d however appears above the levels of both 6 p and 7 s. The far right column entries begin with a dashed line labeled, \u201c4 f,\u201d positioned at a level just below 5 d. Similarly, a second dashed line segment appears just below the level of 6 d, which is labeled, \u201c5 f.\u201d\" width=\"880\" height=\"451\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 5. Generalized energy-level diagram for atomic orbitals in an atom with two or more electrons (not to scale).<\/p>\n<\/div>\n<p>Electrons in successive atoms on the periodic table tend to fill low-energy orbitals first. Thus, many students find it confusing that, for example, the 5<em>p<\/em> orbitals fill immediately after the 4<em>d<\/em>, and immediately before the 6<em>s<\/em>. The filling order is based on observed experimental results, and has been confirmed by theoretical calculations. As the principal quantum number, <em>n<\/em>, increases, the size of the orbital increases and the electrons spend more time farther from the nucleus. Thus, the attraction to the nucleus is weaker and the energy associated with the orbital is higher (less stabilized). But this is not the only effect we have to take into account. Within each shell, as the value of <em>l<\/em> increases, the electrons are less penetrating (meaning there is less electron density found close to the nucleus), in the order <em>s<\/em> &gt; <em>p<\/em> &gt; <em>d<\/em> &gt; <em>f<\/em>. Electrons that are closer to the nucleus slightly repel electrons that are farther out, offsetting the more dominant electron\u2013nucleus attractions slightly (recall that all electrons have \u22121 charges, but nuclei have +<em>Z<\/em> charges). This phenomenon is called shielding and will be discussed in more detail in the next section. Electrons in orbitals that experience more shielding are less stabilized and thus higher in energy. For small orbitals (1<em>s<\/em> through 3<em>p<\/em>), the increase in energy due to <em>n<\/em> is more significant than the increase due to <em>l<\/em>; however, for larger orbitals the two trends are comparable and cannot be simply predicted. We will discuss methods for remembering the observed order.<\/p>\n<p>The arrangement of electrons in the orbitals of an atom is called the <strong>electron configuration<\/strong> of the atom. We describe an electron configuration with a symbol that contains three pieces of information (Figure 6):<\/p>\n<ol>\n<li>The number of the principal quantum shell, <em>n<\/em>,<\/li>\n<li>The letter that designates the orbital type (the subshell, <em>l<\/em>), and<\/li>\n<li>A superscript number that designates the number of electrons in that particular subshell.<\/li>\n<\/ol>\n<p>For example, the notation 2<em>p<\/em><sup>4<\/sup> (read &#8220;two\u2013p\u2013four&#8221;) indicates four electrons in a <em>p<\/em> subshell (<em>l<\/em> = 1) with a principal quantum number (<em>n<\/em>) of 2. The notation 3<em>d<\/em><sup>8<\/sup> (read &#8220;three\u2013d\u2013eight&#8221;) indicates eight electrons in the <em>d<\/em> subshell (i.e., <em>l<\/em> = 2) of the principal shell for which <em>n<\/em> = 3.<\/p>\n<div style=\"width: 891px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213428\/CNX_Chem_06_04_Econfig.jpg\" alt=\"A light blue hemisphere is labeled H. At a location about midway between the center and outer edge of the hemisphere, a small yellow-orange sphere is shown that is labeled with a negative sign. To the right of this diagram is the electron configuration 1 s superscript 1. The superscript is shown in a small yellow-orange circle. This superscript is labeled, \u201cNumber of electrons in subshell,\u201d and the s is labeled, \u201cSubshell.\u201d\" width=\"881\" height=\"168\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 6. The diagram of an electron configuration specifies the subshell (n and l value, with letter symbol) and superscript number of electrons.<\/p>\n<\/div>\n<h2>The Aufbau Principle<\/h2>\n<div style=\"width: 510px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213430\/CNX_Chem_06_04_Efillorder.jpg\" alt=\"This figure includes a chart used to order the filling of electrons into atoms. At the top is a blue circle labeled \u201c1 s.\u201d In a row beneath this circle are 6 additional blue circles labeled \u201c2 s\u201d through \u201c7 s.\u201d A column to the right begins just right of 2 s and contains pink circles labeled 2 p through 7 p. A column to the right begins just right of 3 p and contains yellow circles labeled 3 d through 6 d. No circles are placed to the right of the 7 s and 7 p circles. A final column on the right begins right of 4 d. It includes grey circles labeled, \u201c4 f\u201d and, \u201c5 f.\u201d No circles are placed right of 6 d. Through these circles, arrows are included in the figure pointing down and to the left. The first arrow begins in the upper right and passes through 1 s. The second arrow begins just below and passes through 2 s. The third arrow passes through 2 p and 3 s. The fourth arrow passes through 3 p and 4 s. This pattern of parallel arrows pointing downward to the left continues through all circles completing the pattern 1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p 5 s 4 d 5 p 6 s 4 f 5 d 6 p 7 s 5 f 6 d 7 p.\" width=\"500\" height=\"361\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 7. The arrow leads through each subshell in the appropriate filling order for electron configurations. This chart is straightforward to construct. Simply make a column for all the s orbitals with each n shell on a separate row. Repeat for p, d, and f. Be sure to only include orbitals allowed by the quantum numbers (no 1p or 2d, and so forth). Finally, draw diagonal lines from top to bottom as shown.<\/p>\n<\/div>\n<p>To determine the electron configuration for any particular atom, we can \u201cbuild\u201d the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements.<\/p>\n<p>This procedure is called the <strong>Aufbau principle<\/strong>, from the German word <em>Aufbau<\/em> (\u201cto build up\u201d). Each added electron occupies the subshell of lowest energy available (in the order shown in Figure 7), subject to the limitations imposed by the allowed quantum numbers according to the Pauli exclusion principle. Electrons enter higher-energy subshells only after lower-energy subshells have been filled to capacity.\u00a0Figure 7 illustrates the traditional way to remember the filling order for atomic orbitals.<\/p>\n<h2>Writing Electron Configurations<\/h2>\n<p>Chemists use an electron configuration<span class=\"margin_term\"><a class=\"glossterm\">, <\/a><\/span>to represent the organization of electrons in shells and subshells in an atom. An electron configuration simply lists the shell and subshell labels, with a right superscript giving the number of electrons in that subshell. The shells and subshells are listed in the order of filling.<\/p>\n<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\n<p id=\"ball-ch08_s03_p11\" class=\"para editable block\">For example, an H atom has a single electron in the 1<em class=\"emphasis\">s<\/em> subshell. Its electron configuration is<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]H: 1s^{1}[\/latex]<\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p12\" class=\"para editable block\">He has two electrons in the 1<em class=\"emphasis\">s<\/em> subshell. Its electron configuration is<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]He: 1s^{2}[\/latex]<\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p13\" class=\"para editable block\">The three electrons for Li are arranged in the 1<em class=\"emphasis\">s<\/em> subshell (two electrons) and the 2<em class=\"emphasis\">s<\/em> subshell (one electron). The electron configuration of Li is<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]Li: 1s^{2}2s^{1}[\/latex]<\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p14\" class=\"para editable block\">Be has four electrons, two in the 1<em class=\"emphasis\">s<\/em> subshell and two in the 2<em class=\"emphasis\">s<\/em> subshell. Its electron configuration is<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]Be: 1s^{2}2s^{2}[\/latex]<\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p15\" class=\"para editable block\">Now that the 2<em class=\"emphasis\">s<\/em> subshell is filled, electrons in larger atoms must go into the 2<em class=\"emphasis\">p<\/em> subshell, which can hold a maximum of six electrons. The next six elements progressively fill up the 2<em class=\"emphasis\">p<\/em> subshell:<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">[latex]B: 1s^{2}2s^{2}2p^{1}[\/latex]<\/span><\/span><br \/>\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]C: 1s^{2}2s^{2}2p^{2}[\/latex]<\/span><\/span><br \/>\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]N: 1s^{2}2s^{2}2p^{3}[\/latex]<\/span><\/span><br \/>\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]O: 1s^{2}2s^{2}2p^{4}[\/latex]<\/span><\/span><br \/>\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]F: 1s^{2}2s^{2}2p^{5}[\/latex]<\/span><\/span><br \/>\n<span class=\"informalequation block\"><span class=\"mathphrase\">[latex]Ne: 1s^{2}2s^{2}2p^{6}[\/latex]<\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p16\" class=\"para editable block\">Now that the 2<em class=\"emphasis\">p<\/em> subshell is filled (all possible subshells in the <em class=\"emphasis\">n<\/em> = 2 shell), the next electron for the next-larger atom must go into the <em class=\"emphasis\">n<\/em> = 3 shell, <em class=\"emphasis\">s<\/em> subshell.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 1: Electron Configuration<\/h3>\n<p>What is the electron configuration for Na, which has 11 electrons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q177286\">Show Answer<\/span><\/p>\n<div id=\"q177286\" class=\"hidden-answer\" style=\"display: none\">\n<p>The first two electrons occupy the 1<em class=\"emphasis\">s<\/em> subshell. The next two occupy the 2<em class=\"emphasis\">s<\/em> subshell, while the next six electrons occupy the 2<em class=\"emphasis\">p<\/em> subshell. This gives us 10 electrons so far, with 1 electron left. This last electron goes into the <em class=\"emphasis\">n<\/em> = 3 shell, <em class=\"emphasis\">s<\/em> subshell. Thus, the electron configuration of Na is 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup>.<\/p>\n<\/div>\n<\/div>\n<h4><strong>Check Your Learning<\/strong><\/h4>\n<p>What is the electron configuration for Mg, which has 12 electrons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q174864\">Show Answer<\/span><\/p>\n<div id=\"q174864\" class=\"hidden-answer\" style=\"display: none\">1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example 2: Electron Configuration<\/h3>\n<p>What is the predicted electron configuration for Sn, which has 50 electrons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q1772861\">Show Answer<\/span><\/p>\n<div id=\"q1772861\" class=\"hidden-answer\" style=\"display: none\">\n<p id=\"ball-ch08_s03_p24\" class=\"para\">We will follow the Aufbau diagram until we can accommodate 50 electrons in the subshells in the proper order:<\/p>\n<p><span class=\"informalequation\"><span class=\"mathphrase\">Sn: 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>4<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>5<em class=\"emphasis\">p<\/em><sup class=\"superscript\">2<\/sup><\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p25\" class=\"para\">Verify by adding the superscripts, which indicate the number of electrons: 2 +\u00a02 +\u00a06 +\u00a02 +\u00a06 +\u00a02 +\u00a010 +\u00a06 +\u00a02 +\u00a010 +\u00a02 = 50, so we have placed all 50 electrons in subshells in the proper order.<\/p>\n<\/div>\n<\/div>\n<h4><strong>Check Your Learning<\/strong><\/h4>\n<p>What is the electron configuration for Ba, which has 56 electrons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q1748614\">Show Answer<\/span><\/p>\n<div id=\"q1748614\" class=\"hidden-answer\" style=\"display: none\">1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>4<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>5<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>6<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup><\/div>\n<\/div>\n<\/div>\n<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\n<h2>Abbreviated Electron Configurations<\/h2>\n<p id=\"ball-ch08_s03_p28\" class=\"para editable block\">As the previous example demonstrated, electron configurations can get fairly long. An abbreviated electron configuration, also known as a noble gas abbreviated electron configuration,\u00a0 uses one of the elements from the last column of the periodic table, which contains what are called the <em class=\"emphasis\">noble gases<\/em>, to represent the core of electrons up to that element. Then the remaining electrons are listed explicitly. For example, the abbreviated electron configuration for Li, which has three electrons, would be<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">Li: [He]2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup><\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p29\" class=\"para editable block\">where [He] represents the two-electron core that is equivalent to He\u2019s electron configuration. The square brackets represent the electron configuration of a noble gas. This is not much of an abbreviation. However, consider the abbreviated electron configuration for W, which has 74 electrons:<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">W: [Xe]6<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">f<\/em><sup class=\"superscript\">14<\/sup>5<em class=\"emphasis\">d<\/em><sup class=\"superscript\">4<\/sup><\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p30\" class=\"para editable block\">This is a significant simplification over an explicit listing of all 74 electrons. So for larger elements, the abbreviated electron configuration can be a very useful shorthand.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example 7: Abbreviated Electron Configuration<\/h3>\n<p>What is the abbreviated electron configuration for P, which has 15 electrons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q17728613\">Show Answer<\/span><\/p>\n<div id=\"q17728613\" class=\"hidden-answer\" style=\"display: none\">\n<p id=\"ball-ch08_s03_p32\" class=\"para\">With 15 electrons, the electron configuration of P is<\/p>\n<p><span class=\"informalequation\"><span class=\"mathphrase\">P: 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">3<\/sup><\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p33\" class=\"para\">The first immediate noble gas is Ne, which has an electron configuration of 1<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>. Using the electron configuration of Ne to represent the first 10 electrons, the abbreviated electron configuration of P is<\/p>\n<p><span class=\"informalequation\"><span class=\"mathphrase\">P: [Ne]3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">3<\/sup><\/span><\/span><\/p>\n<\/div>\n<\/div>\n<h4><strong>Check Your Learning<\/strong><\/h4>\n<p>What is the abbreviated electron configuration for Rb, which has 37 electrons?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q1748614\">Show Answer<\/span><\/p>\n<div id=\"q1748614\" class=\"hidden-answer\" style=\"display: none\">[Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup><\/div>\n<\/div>\n<\/div>\n<div id=\"ball-ch08_s03\" class=\"section\" lang=\"en\">\n<p id=\"ball-ch08_s03_p36\" class=\"para editable block\">There are some exceptions to the rigorous filling of subshells by electrons. In many cases, an electron goes from a higher-numbered shell to a lower-numbered but later-filled subshell to fill the later-filled subshell. One example is Ag. With 47 electrons, its electron configuration is predicted to be<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">Ag: [Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">9<\/sup><\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p37\" class=\"para editable block\">However, experiments have shown that the electron configuration is actually<\/p>\n<p style=\"text-align: center;\"><span class=\"informalequation block\"><span class=\"mathphrase\">Ag: [Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">1<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup><\/span><\/span><\/p>\n<p id=\"ball-ch08_s03_p38\" class=\"para editable block\">This, then, qualifies as an exception to our expectations. At this point, you do not need to worry about the exceptions; we will ignore these exceptions in this course.<\/p>\n<h2>Electron Configuration Energy Diagrams<\/h2>\n<p>We have just seen that electrons fill orbitals in shells and subshells in a regular pattern, but why does it follow this pattern? There are three principles which should be followed to properly fill electron orbital energy diagrams:<\/p>\n<ol>\n<li>The <b>Aufbau principle<\/b><\/li>\n<li>The <b>Pauli exclusion principle<\/b><\/li>\n<li><b>Hund\u2019s rule<\/b><\/li>\n<\/ol>\n<p>The overall pattern of the electron shell filling order emerges from the <b>Aufbau principle <\/b>(German for \u201cbuilding up\u201d): \u00a0electrons fill the lowest energy orbitals first. Increasing the principle quantum number, <i>n<\/i>, increases orbital energy levels, as the electron density becomes more spread out away from the nucleus. In many-electron atoms (all atoms except hydrogen), the energy levels of subshells varies due to electron-electron repulsions. The trend that emerges is that energy levels increase with value of the angular momentum quantum number, <i>l<\/i>, for orbitals sharing the same principle quantum number, <i>n<\/i>. This is demonstrated in Figure 7, where each line represents an orbital, and each set of lines at the same energy represents a subshell of orbitals.<\/p>\n<div id=\"attachment_2448\" style=\"width: 439px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/generic-energy-diagram-of-orbitals-in-multi-electron-atom.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2448\" class=\"size-full wp-image-2448\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213236\/generic-energy-diagram-of-orbitals-in-multi-electron-atom-1.jpg\" alt=\"Figure 8.# Generic energy diagram of orbitals in a multi-electron atom.\" width=\"429\" height=\"387\" \/><\/a><\/p>\n<p id=\"caption-attachment-2448\" class=\"wp-caption-text\">Figure 7. Generic energy diagram of orbitals in a multi-electron atom.<\/p>\n<\/div>\n<p>As previously discussed, the <b>Pauli exclusion principle <\/b>states that we can only fill each orbital with a maximum of two electrons of opposite spin. But how should we fill multiple orbitals of the same energy level within a subshell (eg. The three orbitals in the 2<i>p<\/i> subshell)? Orbitals of the same energy level are known as degenerate orbitals, and we fill them using <b>Hund\u2019s rule<\/b>: place one electron into each degenerate orbital first, before pairing them in the same orbital.<\/p>\n<p>Let\u2019s examine a few examples to demonstrate the use of the three principles.<\/p>\n<p>Boron is atomic number 5, and therefore has 5 electrons. First fill the lowest energy 1<i>s<\/i> orbital with two electrons of opposite spin, then the 2<i>s <\/i>orbital with 2 electrons of opposite spin and finally place the last electron into any of the three degenerate 2<i>p<\/i> orbitals (Figure 8).<\/p>\n<div id=\"attachment_2449\" style=\"width: 603px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/Boron_electron_configuration_energy_diagram.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2449\" class=\"size-full wp-image-2449\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213238\/Boron_electron_configuration_energy_diagram-1.png\" alt=\"Figure 8.#. Boron electron configuration energy diagram\" width=\"593\" height=\"527\" \/><\/a><\/p>\n<p id=\"caption-attachment-2449\" class=\"wp-caption-text\">Figure 8. Boron electron configuration energy diagram<\/p>\n<\/div>\n<p>Moving across the periodic table, we follow Hund\u2019s rule and add an additional electron to each degenerate 2<i>p<\/i> orbital for each subsequent element (Figure 9). At oxygen we can finally pair up and fill one of the degenerate 2<i>p<\/i> orbitals.<\/p>\n<div id=\"attachment_2450\" style=\"width: 610px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/Electron-configuration-energy-diagrams-for-carbon-nitrogen-and-oxygen.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-2450\" class=\"wp-image-2450 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213240\/Electron-configuration-energy-diagrams-for-carbon-nitrogen-and-oxygen-e1411755889659-1.jpg\" alt=\"Figure 8.#. Electron configuration energy diagrams for carbon, nitrogen and oxygen.\" width=\"600\" height=\"173\" \/><\/a><\/p>\n<p id=\"caption-attachment-2450\" class=\"wp-caption-text\">Figure 9. Electron configuration energy diagrams for carbon, nitrogen and oxygen.<\/p>\n<\/div>\n<div id=\"ball-ch08_s03_n06\" class=\"key_takeaways editable block\">\n<div class=\"bcc-box bcc-success\">\n<h3>Key Takeaways<\/h3>\n<ul>\n<li>The Pauli exclusion principle limits the number of electrons in the subshells and shells.<\/li>\n<li>Electrons in larger atoms fill shells and subshells in a regular pattern that we can follow.<\/li>\n<li>Electron configurations are a shorthand method of indicating what subshells electrons occupy in atoms.<\/li>\n<li>Abbreviated electron configurations are a simpler way of representing electron configurations for larger atoms.<\/li>\n<li>Exceptions to the strict filling of subshells with electrons occur.<\/li>\n<li>Electron configurations are assigned from lowest to highest energy following the Aufbau principle<\/li>\n<li>One electron is placed in each degenerate orbital before pairing electrons following Hund&#8217;s rule.<\/li>\n<li>Electron configuration energy diagrams follow three principles: the Aufbau principle, the Pauli exclusion principle and Hund&#8217;s rule.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div id=\"ball-ch08_s03_qs01\" class=\"qandaset block\">\n<div class=\"bcc-box bcc-info\">\n<h3>Exercises<\/h3>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p1\" class=\"para\">1. How many subshells are completely filled with electrons for Na? How many subshells are unfilled?<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p7\" class=\"para\">2. How many subshells are completely filled with electrons for Mg? How many subshells are unfilled?<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p9\" class=\"para\">3. What is the maximum number of electrons in the entire <em class=\"emphasis\">n<\/em> = 2 shell?<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p11\" class=\"para\">4. What is the maximum number of electrons in the entire <em class=\"emphasis\">n<\/em> = 4 shell?<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p13\" class=\"para\">5. Write the complete electron configuration for each atom.<\/p>\n<\/div>\n<p style=\"padding-left: 30px;\">a) \u00a0Si, 14 electrons<\/p>\n<p style=\"padding-left: 30px;\">b) \u00a0Sc, 21 electrons<\/p>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p14\" class=\"para\">6.\u00a0 Write the complete electron configuration for each atom.<\/p>\n<p style=\"padding-left: 30px;\">a) \u00a0Br, 35 electrons<\/p>\n<p style=\"padding-left: 30px;\">b) \u00a0Be, 4 electrons<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p15\" class=\"para\">7.\u00a0 Write the complete electron configuration for each atom.<\/p>\n<p style=\"padding-left: 30px;\">a) \u00a0Cd, 48 electrons<\/p>\n<p style=\"padding-left: 30px;\">b) \u00a0Mg, 12 electrons<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p16\" class=\"para\">8.\u00a0 Write the complete electron configuration for each atom.<\/p>\n<p style=\"padding-left: 30px;\">a) \u00a0Cs, 55 electrons<\/p>\n<p style=\"padding-left: 30px;\">b) \u00a0Ar, 18 electrons<\/p>\n<p>9. \u00a0Write the abbreviated electron configuration for each atom in Exercise 7.<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p18\" class=\"para\">10. \u00a0Write the abbreviated electron configuration for each atom in Exercise 8.<\/p>\n<\/div>\n<div class=\"question\">\n<p id=\"ball-ch08_s03_qs01_qd01_p19\" class=\"para\">11. \u00a0Write the abbreviated electron configuration for each atom in Exercise 9.<\/p>\n<\/div>\n<p id=\"ball-ch08_s03_qs01_qd01_p20\" class=\"para\" style=\"line-height: 1.5em;\">12. \u00a0Write the abbreviated electron configuration for each atom in Exercise 10.<\/p>\n<p class=\"para\" style=\"line-height: 1.5em;\">13. \u00a0 Draw electron configuration energy diagrams for potassium, and bromine.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q367563\">Show Answer to Select Questions<\/span><\/p>\n<div id=\"q367563\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. Three subshells (1<em class=\"emphasis\">s<\/em>, 2<em class=\"emphasis\">s<\/em>, 2<em class=\"emphasis\">p<\/em>) are completely filled, and one shell (3<em class=\"emphasis\">s<\/em>) is partially filled.<\/p>\n<p>3. 8 electrons<\/p>\n<p>5. a) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">2 <\/sup>,b) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">1<\/sup><\/p>\n<p>7. a) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10<\/sup>4<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10 <\/sup>,b) \u00a01<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>2<em class=\"emphasis\">p<\/em><sup class=\"superscript\">6<\/sup>3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup><\/p>\n<p>9. a) \u00a0[Ne]3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">p<\/em><sup class=\"superscript\">2 <\/sup>,b) \u00a0[Ar]4<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>3<em class=\"emphasis\">d<\/em><sup class=\"superscript\">1<\/sup><\/p>\n<p>11. a) \u00a0[Kr]5<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup>4<em class=\"emphasis\">d<\/em><sup class=\"superscript\">10 <\/sup>,b) \u00a0[Ne]3<em class=\"emphasis\">s<\/em><sup class=\"superscript\">2<\/sup><\/p>\n<p>13.<\/p>\n<p><a href=\"http:\/\/opentextbc.ca\/introductorychemistry\/wp-content\/uploads\/sites\/17\/2014\/05\/Electron_configuration_potassium.svg_.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2454\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213243\/Electron_configuration_potassium.svg_-1.png\" alt=\"Electron_configuration_potassium.svg\" width=\"600\" height=\"843\" \/><\/a><\/p>\n<p><a class=\"footnote\" title=\"Orbital representation diagram for potassium, depicting each orbital as a line. Adrignola\\Public domain\" id=\"return-footnote-322-1\" href=\"#footnote-322-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2455\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2835\/2017\/12\/14213247\/1000px-Electron_configuration_bromine.svg_-1.png\" alt=\"1000px-Electron_configuration_bromine.svg\" width=\"600\" height=\"474\" \/><\/p>\n<ol>\n<li><a class=\"footnote\" title=\"Orbital representation diagram for bromine, depicting each orbital as a line. Adrignola\\Public domain\" id=\"return-footnote-322-2\" href=\"#footnote-322-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<h2>Glossary<\/h2>\n<p><strong>Aufbau principle: <\/strong>procedure in which the electron configuration of the elements is determined by \u201cbuilding\u201d them in order of atomic numbers, adding one proton to the nucleus and one electron to the proper subshell at a time<\/p>\n<p><strong>core electron: <\/strong>electron in an atom that occupies the orbitals of the inner shells<\/p>\n<p><strong>electron configuration: <\/strong>electronic structure of an atom in its ground state given as a listing of the orbitals occupied by the electrons<\/p>\n<p><strong>Hund\u2019s rule: <\/strong>every orbital in a subshell is singly occupied with one electron before any one orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin<\/p>\n<p><strong>orbital diagram: <\/strong>pictorial representation of the electron configuration showing each orbital as a box and each electron as an arrow<\/p>\n<p><strong>valence electrons: <\/strong>electrons in the outermost or valence shell (highest value of <em>n<\/em>) of a ground-state atom; determine how an element reacts<\/p>\n<p><strong>valence shell: <\/strong>outermost shell of electrons in a ground-state atom; for main group elements, the orbitals with the highest <em>n<\/em> level (<em>s<\/em> and <em>p<\/em> subshells) are in the valence shell, while for transition metals, the highest energy <em>s<\/em> and <em>d<\/em> subshells make up the valence shell and for inner transition elements, the highest <em>s<\/em>, <em>d,<\/em> and <em>f<\/em> subshells are included<\/p>\n<\/div>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-322\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Introductory Chemistry- 1st Canadian Edition . <strong>Authored by<\/strong>: Jessie A. Key and David W. Ball. <strong>Provided by<\/strong>: BCCampus. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/opentextbc.ca\/introductorychemistry\/\">https:\/\/opentextbc.ca\/introductorychemistry\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. <strong>License Terms<\/strong>: Download this book for free at http:\/\/open.bccampus.ca<\/li><li>Chemistry. <strong>Provided by<\/strong>: OpenStax College. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/openstaxcollege.org\">http:\/\/openstaxcollege.org<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-322-1\">Orbital representation diagram for potassium, depicting each orbital as a line. Adrignola\\Public domain <a href=\"#return-footnote-322-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-322-2\">Orbital representation diagram for bromine, depicting each orbital as a line. Adrignola\\Public domain <a href=\"#return-footnote-322-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":23485,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Introductory Chemistry- 1st Canadian Edition \",\"author\":\"Jessie A. Key and David W. 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