{"id":228,"date":"2019-04-09T01:27:50","date_gmt":"2019-04-09T05:27:50","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/?post_type=chapter&#038;p=228"},"modified":"2019-04-12T19:11:34","modified_gmt":"2019-04-12T23:11:34","slug":"4-4-the-exclusion-principle-and-the-periodic-table","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/bcitphys8400\/chapter\/4-4-the-exclusion-principle-and-the-periodic-table\/","title":{"raw":"4.4 The Exclusion Principle and the Periodic Table","rendered":"4.4 The Exclusion Principle and the Periodic Table"},"content":{"raw":"<div data-type=\"abstract\" id=\"87050\" class=\"ui-has-child-title\"><header>\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Explain the importance of Pauli\u2019s exclusion principle to an understanding of atomic structure and molecular bonding<\/li>\r\n \t<li>Explain the structure of the periodic table in terms of the total energy, orbital angular momentum, and spin of individual electrons in an atom<\/li>\r\n \t<li>Describe the electron configuration of atoms in the periodic table<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<span style=\"font-size: 14pt\">So far, we have studied only hydrogen, the simplest chemical element. We have found that an electron in the hydrogen atom can be completely specified by five quantum numbers:<\/span>\r\n\r\n<\/header><\/div>\r\n<div data-label=\"\" data-type=\"equation\" id=\"fs-id1170903806651\">\r\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-844-Frame\">\r\n<div class=\"textbox\">\r\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-844-Frame\"><span class=\"MathJax_MathContainer\"><span>n: principal quantum number\r\n\r\nl: angular momentum quantum number\r\n\r\nm: angular momentum projection quantum number\r\n\r\ns: spin quantum number\r\n\r\nms: spin projection quantum number\r\n\r\n<\/span><\/span><\/div>\r\n<div class=\"os-equation-number\"><span class=\"os-number\">[4.34]<\/span><\/div>\r\n<\/div>\r\n<span style=\"font-size: 14pt\">To construct the ground state of a neutral multi-electron atom, imagine starting with a nucleus of charge<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Ze<\/em><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">(that is, a nucleus of atomic number<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Z<\/em><span style=\"font-size: 14pt\">) and then adding<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Z<\/em><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">electrons one by one. Assume that each electron moves in a spherically symmetrical electric field produced by the nucleus and all other electrons of the atom. The assumption is valid because the electrons are distributed randomly around the nucleus and produce an average electric field (and potential) that is spherically symmetrical. The electric potential<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">U<\/em><span style=\"font-size: 14pt\">(<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">r<\/em><span style=\"font-size: 14pt\">) for each electron does not follow the simple<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-845-Frame\" style=\"font-size: 14pt\"><span class=\"MathJax_MathContainer\">\u22121\/r<\/span><\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">form because of interactions between electrons, but it turns out that we can still label each individual electron state by quantum numbers,<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-846-Frame\" style=\"font-size: 14pt\"><span class=\"MathJax_MathContainer\">(n,l,m,s,ms)<\/span><\/span><span style=\"font-size: 14pt\">. (The spin quantum number<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">s<\/em><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">is the same for all electrons, so it will not be used in this section.)<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170902772689\">The structure and chemical properties of atoms are explained in part by<span>\u00a0<\/span><span data-type=\"term\" id=\"term350\">Pauli\u2019s exclusion principle<\/span>: No two electrons in an atom can have the same values for all four quantum numbers<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-847-Frame\"><span class=\"MathJax_MathContainer\"><span>(n,l,m,ms).<\/span><\/span><\/span><span>\u00a0<\/span>This principle is related to two properties of electrons: All electrons are identical (\u201cwhen you\u2019ve seen one electron, you\u2019ve seen them all\u201d) and they have half-integral spin<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-848-Frame\"><span class=\"MathJax_MathContainer\"><span>(s=1\/2).<\/span><\/span><\/span><span>\u00a0<\/span>Sample sets of quantum numbers for the electrons in an atom are given in<span>\u00a0<\/span>Table 4.5. Consistent with Pauli\u2019s exclusion principle, no two rows of the table have the exact same set of quantum numbers.<\/p>\r\n\r\n<div class=\"os-table\">\r\n<table id=\"fs-id1170902930686\" summary=\"Table 8.5 Electron States of Atoms Because of Pauli\u2019s exclusion principle, no two electrons in an atom have the same set of four quantum numbers.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\"><em data-effect=\"italics\">n<\/em><\/th>\r\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\"><em data-effect=\"italics\">l<\/em><\/th>\r\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\"><em data-effect=\"italics\">m<\/em><\/th>\r\n<th scope=\"col\" data-align=\"right\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-849-Frame\"><span class=\"MathJax_MathContainer\"><span>ms<\/span><\/span><\/span><\/th>\r\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\">Subshell symbol<\/th>\r\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\">No. of electrons: subshell<\/th>\r\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\">No. of electrons: shell<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">1<em data-effect=\"italics\">s<\/em><\/td>\r\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\r\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<em data-effect=\"italics\">s<\/em><\/td>\r\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\r\n<td rowspan=\"8\" data-align=\"center\" data-valign=\"top\">8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">2<em data-effect=\"italics\">p<\/em><\/td>\r\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">6<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">3<em data-effect=\"italics\">s<\/em><\/td>\r\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\r\n<td rowspan=\"18\" data-align=\"center\" data-valign=\"middle\">18<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">3<em data-effect=\"italics\">p<\/em><\/td>\r\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">6<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20132<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<td rowspan=\"10\" data-align=\"center\" data-valign=\"middle\">3<em data-effect=\"italics\">d<\/em><\/td>\r\n<td rowspan=\"10\" data-align=\"center\" data-valign=\"middle\">10<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20132<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\r\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><em><span class=\"os-title-label\">Table 4<\/span><span class=\"os-number\">.5<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-title\" data-type=\"title\">Electron States of Atoms<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-caption\">Because of Pauli\u2019s exclusion principle, no two electrons in an atom have the same set of four quantum numbers.<\/span><\/em><\/div>\r\n<\/div>\r\n<p id=\"fs-id1170901705116\">Electrons with the same principal quantum number<span>\u00a0<\/span><em data-effect=\"italics\">n<\/em><span>\u00a0<\/span>are said to be in the same<span>\u00a0<\/span><span class=\"no-emphasis\" data-type=\"term\" id=\"term351\">shell<\/span>, and those that have the same value of<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em><span>\u00a0<\/span>are said to occupy the same<span>\u00a0<\/span><span class=\"no-emphasis\" data-type=\"term\" id=\"term352\">subshell<\/span>. An electron in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-850-Frame\"><span class=\"MathJax_MathContainer\"><span>n=1<\/span><\/span><\/span><span>\u00a0<\/span>state of a hydrogen atom is denoted 1<em data-effect=\"italics\">s<\/em>, where the first digit indicates the shell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-851-Frame\"><span class=\"MathJax_MathContainer\"><span>(n=1)<\/span><\/span><\/span><span>\u00a0<\/span>and the letter indicates the subshell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-852-Frame\"><span class=\"MathJax_MathContainer\"><span>(s,p,d,f\u2026correspond to l=0,1,2,3\u2026).<\/span><\/span><\/span><span>\u00a0<\/span>Two electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-853-Frame\"><span class=\"MathJax_MathContainer\"><span>n=1<\/span><\/span><\/span><span>\u00a0<\/span>state are denoted as<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-854-Frame\"><span class=\"MathJax_MathContainer\"><span>1s2,<\/span><\/span><\/span><span>\u00a0<\/span>where the superscript indicates the number of electrons. An electron in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-855-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>state with<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-856-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span><span>\u00a0<\/span>is denoted 2<em data-effect=\"italics\">p<\/em>. The combination of two electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-857-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>and<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-858-Frame\"><span class=\"MathJax_MathContainer\"><span>l=0<\/span><\/span><\/span><span>\u00a0<\/span>state, and three electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-859-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>and<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-860-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span><span>\u00a0<\/span>state is written as<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-861-Frame\"><span class=\"MathJax_MathContainer\"><span>2s22p3,<\/span><\/span><\/span><span>\u00a0<\/span>and so on. This representation of the electron state is called the<span>\u00a0<\/span><span data-type=\"term\" id=\"term353\">electron configuration<\/span><span>\u00a0<\/span>of the atom. The electron configurations for several atoms are given in<span>\u00a0<\/span>Table 4.6. Electrons in the outer shell of an atom are called<span>\u00a0<\/span><span data-type=\"term\" id=\"term354\">valence electron<\/span><strong data-effect=\"bold\">s<\/strong>. Chemical bonding between atoms in a molecule are explained by the transfer and sharing of valence electrons.<\/p>\r\n\r\n<div class=\"os-table\">\r\n<table id=\"fs-id1170902767240\" summary=\"Table 8.6 Electron Configurations of Electrons in an Atom The symbol (\u2191)(\u2191) indicates an unpaired electron in the outer shell, whereas the symbol (\u2191\u2193)(\u2191\u2193) indicates a pair of spin-up and -down electrons in an outer shell.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th scope=\"col\" data-align=\"left\" data-valign=\"top\">Element<\/th>\r\n<th scope=\"col\" data-align=\"left\" data-valign=\"top\">Electron Configuration<\/th>\r\n<th scope=\"col\" data-align=\"left\" data-valign=\"top\">Spin Alignment<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">H<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-862-Frame\"><span class=\"MathJax_MathContainer\"><span>1s1<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-863-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">He<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-864-Frame\"><span class=\"MathJax_MathContainer\"><span>1s2<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-865-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">Li<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-866-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s1<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-867-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">Be<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-868-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s2<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-869-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">B<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-870-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p1<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-871-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">C<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-872-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p2<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-873-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">N<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-874-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p3<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-875-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)(\u2191)(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">O<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-876-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p4<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-877-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191\u2193)(\u2191)(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">F<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-878-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p5<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-879-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191\u2193)(\u2191\u2193)(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">Ne<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-880-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p6<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-881-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191\u2193)(\u2191\u2193)(\u2191\u2193)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">Na<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-882-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p63s1<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-883-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">Mg<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-884-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p63s2<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-885-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\" data-valign=\"top\">Al<\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-886-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p63s23p1<\/span><\/span><\/span><\/td>\r\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-887-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)<\/span><\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"os-caption-container\"><em><span class=\"os-title-label\">Table 4<\/span><span class=\"os-number\">.6<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-title\" data-type=\"title\">Electron Configurations of Electrons in an Atom<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-caption\">The symbol\u00a0<span class=\"MathJax_MathML\" id=\"MathJax-Element-888-Frame\"><span class=\"MathJax_MathContainer\">(\u2191)<\/span><\/span>\u00a0indicates an unpaired electron in the outer shell, whereas the symbol\u00a0<span class=\"MathJax_MathML\" id=\"MathJax-Element-889-Frame\"><span class=\"MathJax_MathContainer\">(\u2191\u2193)<\/span><\/span>\u00a0indicates a pair of spin-up and -down electrons in an outer shell.<\/span><\/em><\/div>\r\n<\/div>\r\n<p id=\"fs-id1170901571182\">The maximum number of electrons in a subshell depends on the value of the angular momentum quantum number,<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em>. For a given a value<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em>, there are<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-890-Frame\"><span class=\"MathJax_MathContainer\"><span>2l+1<\/span><\/span><\/span><span>\u00a0<\/span>orbital angular momentum states. However, each of these states can be filled by two electrons (spin up and down,<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-891-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>). Thus, the maximum number of electrons in a subshell is<\/p>\r\n\r\n<div class=\"textbox\">\r\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-892-Frame\"><span class=\"MathJax_MathContainer\"><span>N=2(2l+1)=4l+2.<\/span><\/span><\/div>\r\n<div class=\"os-equation-number\"><span class=\"os-number\">[4.35]<\/span><\/div>\r\n<\/div>\r\n<p id=\"fs-id1170901705860\">In the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-893-Frame\"><span class=\"MathJax_MathContainer\"><span>(l=0)<\/span><\/span><\/span><span>\u00a0<\/span>subshell, the maximum number of electrons is 2. In the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-894-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) subshell, the maximum number of electrons is 6. Therefore, the total maximum number of electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-895-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>shell (including both the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-896-Frame\"><span class=\"MathJax_MathContainer\"><span>l=0<\/span><\/span><\/span><span>\u00a0<\/span>and 1 subshells) is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-897-Frame\"><span class=\"MathJax_MathContainer\"><span>2+6<\/span><\/span><\/span><span>\u00a0<\/span>or 8. In general, the maximum number of electrons in the<span>\u00a0<\/span><em data-effect=\"italics\">n<\/em>th shell is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-898-Frame\"><span class=\"MathJax_MathContainer\"><span>2n2.<\/span><\/span><\/span><\/p>\r\n\r\n<div data-type=\"example\" id=\"fs-id1170903027803\" class=\"ui-has-child-title\"><header><\/header><section>\r\n<div class=\"textbox shaded\"><header>\r\n<h3 class=\"os-title\"><span class=\"os-title-label\">EXAMPLE<span>\u00a04<\/span><\/span><span class=\"os-number\">.5<\/span><span class=\"os-divider\"><\/span><\/h3>\r\n<\/header><section>\r\n<p id=\"fs-id1170902597970\"><span data-type=\"title\"><strong>Subshells and Totals for\u00a0<\/strong><span class=\"MathJax_MathML\" id=\"MathJax-Element-899-Frame\"><span class=\"MathJax_MathContainer\"><strong>n=3<\/strong><\/span><\/span><\/span><\/p>\r\nHow many subshells are in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-900-Frame\"><span class=\"MathJax_MathContainer\"><span>n=3<\/span><\/span><\/span><span>\u00a0<\/span>shell? Identify each subshell and calculate the maximum number of electrons that will fill each. Show that the maximum number of electrons that fill an atom is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-901-Frame\"><span class=\"MathJax_MathContainer\"><span>2n2<\/span><\/span><\/span>.\r\n\r\n<span data-type=\"title\"><strong>Strategy<\/strong><\/span>\r\n\r\nSubshells are determined by the value of<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em>; thus, we first determine which values of<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em><span>\u00a0<\/span>are allowed, and then we apply the equation \u201cmaximum number of electrons that can be in a subshell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-902-Frame\"><span class=\"MathJax_MathContainer\"><span>=2(2l+1)<\/span><\/span><\/span>\u201d to find the number of electrons in each subshell.\r\n\r\n<span data-type=\"title\"><strong>Solution<\/strong><\/span>\r\n\r\nBecause<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-903-Frame\"><span class=\"MathJax_MathContainer\"><span>n=3,<\/span><\/span><\/span><span>\u00a0<\/span>we know that<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em><span>\u00a0<\/span>can be 0, 1, or 2; thus, there are three possible subshells. In standard notation, they are labeled the 3<em data-effect=\"italics\">s<\/em>, 3<em data-effect=\"italics\">p<\/em>, and 3<em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>subshells. We have already seen that two electrons can be in an<span>\u00a0<\/span><em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>state, and six in a<span>\u00a0<\/span><em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>state, but let us use the equation \u201cmaximum number of electrons that can be in a subshell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-904-Frame\"><span class=\"MathJax_MathContainer\"><span>=2(2l+1)<\/span><\/span><\/span>\u201d to calculate the maximum number in each:\r\n<div class=\"unnumbered\" data-label=\"\" data-type=\"equation\" id=\"fs-id1170901594429\">\r\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-905-Frame\">\r\n\r\n<span class=\"MathJax_MathContainer\"><span>3shasl=0;thus,2(2l+1)=2(0+1)=23phasl=1;thus,2(2l+1)=2(2+1)=63dhasl=2;thus,2(2l+1)=2(4+1)=10Total=18(inthen=3shell).<\/span><\/span>\r\n\r\n<span style=\"text-indent: 1em;font-size: 1rem\">The equation \u201cmaximum number of electrons that can be in a shell<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-906-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">=2n2<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u201d gives the maximum number in the<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-907-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=3<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell to be<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"unnumbered\" data-label=\"\" data-type=\"equation\" id=\"fs-id1170902734856\">\r\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-908-Frame\">\r\n\r\n<span class=\"MathJax_MathContainer\"><span>Maximum number of electrons=2n2=2(3)2=2(9)=18.<\/span><\/span>\r\n\r\n<span data-type=\"title\" style=\"text-indent: 1em;font-size: 1rem\"><strong>Significance<\/strong><\/span>\r\n\r\n<span style=\"text-indent: 1em;font-size: 1rem\">The total number of electrons in the three possible subshells is thus the same as the formula<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-909-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">2n2<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">. In standard (spectroscopic) notation, a filled<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-910-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=3<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell is denoted as<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-911-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">3s23p63d10<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">. Shells do not fill in a simple manner. Before the<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-912-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=3\u00a0<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell is completely filled, for example, we begin to find electrons in the<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-913-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=4<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell.<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section><\/div>\r\n<span style=\"font-size: 14pt\">The structure of the<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span class=\"no-emphasis\" data-type=\"term\" id=\"term355\" style=\"font-size: 14pt\">periodic table<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">(<\/span>Figure 4.17<span style=\"font-size: 14pt\">) can be understood in terms of shells and subshells, and, ultimately, the total energy, orbital angular momentum, and spin of the electrons in the atom. A detailed discussion of the periodic table is left to a chemistry course\u2014we sketch only its basic features here. In this discussion, we assume that the atoms are electrically neutral; that is, they have the same number of electrons and protons. (Recall that the total number of protons in an atomic nucleus is called the atomic number,<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Z<\/em><span style=\"font-size: 14pt\">.)<\/span>\r\n\r\n<\/section><\/div>\r\n<p id=\"fs-id1170902872614\">First, the periodic table is arranged into columns and rows. The table is read left to right and top to bottom in the order of increasing atomic number<span>\u00a0<\/span><em data-effect=\"italics\">Z<\/em>. Atoms that belong to the same column or<span>\u00a0<\/span><span data-type=\"term\" id=\"term356\">chemical group<\/span><span>\u00a0<\/span>share many of the same chemical properties. For example, the Li and Na atoms (in the first column) bond to other atoms in a similar way. The first row of the table corresponds to the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-914-Frame\"><span class=\"MathJax_MathContainer\"><span>l=0<\/span><\/span><\/span>) shell of an atom.<\/p>\r\n<p id=\"fs-id1170901609017\">Consider the hypothetical procedure of adding electrons, one by one, to an atom. For hydrogen (H) (upper left), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with either a spin up or down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-915-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191or\u2193<\/span><\/span><\/span>). This lone electron is easily shared with other atoms, so hydrogen is chemically active. For helium (He) (upper right), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with both a spin up and a spin down (<span class=\"MathJax_MathML\" id=\"MathJax-Element-916-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>) electron. This \u201cfills\u201d the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell, so a helium atom tends not to share electrons with other atoms. The helium atom is said to be chemically inactive, inert, or noble; likewise, helium gas is said to be an inert gas or noble gas.<\/p>\r\n\r\n<div class=\"media-2 ui-has-child-title\" data-type=\"note\" id=\"fs-id1170901570549\"><header>\r\n<h3 class=\"os-title\" data-type=\"title\"><span class=\"os-title-label\">INTERACTIVE<\/span><\/h3>\r\n<\/header><section>\r\n<div class=\"os-note-body\">\r\n<p id=\"fs-id1170901570553\">Build an atom by adding and subtracting protons, neutrons, and electrons. How does the element, charge, and mass change? Visit<span>\u00a0<\/span><a href=\"https:\/\/openstax.org\/l\/21buildanatom\" rel=\"nofollow\">PhET Explorations: Build an Atom<\/a><span>\u00a0<\/span>to explore the answers to these questions.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"os-figure\">\r\n<figure id=\"CNX_UPhysics_41_04_PeriodTab\">\r\n\r\n[caption id=\"\" align=\"alignnone\" width=\"978\"]<img alt=\"The Periodic Table of Elements, showing the structure of shells and subshells, is shown. The 18 columns are numbered labeled \u201cGroup\u201d and the 7 rows are numbered and labeled \u201cPeriod.\u201d Groups 1 and 2 are shaded purple. Groups 3 through 12 are shaded yellow. Groups 13 through 18, are shaded red, with the exception of period 1, group 18, which is purple. The period 6 and 7, group 3 boxes are outlined and an arrow points from them to an additional section of two rows and 14 columns that is shaded green. The period 6 group 3 box has an asterisk, which also appears to the left of the first row of the additional section. The period 7 group 3 box has two asterisks, which also appear to the left of the second row of the additional section. Below the table to the left is an enlarged picture of the upper-left most box on the table. The letter \u201cH\u201d is in its upper-left hand corner and is labeled \u201cSymbol.\u201d The number 1 is in its upper-right hand corner and is labeled \u201cElectrons.\u201d In its center the entry \u201c1 s\u201d is labeled \u201csubshell.\u201d The box is shaded purple. Every element has its symbol and electrons indicated in the box. The subshells are indicated as a group for contiguous sections of a row. Beginning at the top left of the table, period 1, group 1, is shaded purple and contains symbol H, electrons 1, subshell 1 s. The only other element box in period 1 is in the last column, group 18, which is shaded purple and contains \u201cH e, 1, 1 s\u201d. Period 2, group 1 contains \u201cL i, 1\u201d Group 2 contains \u201cB e, 2.\u201d Period 2 groups 1 and 2 both have subshell 2 s. Groups 3 through 12 are skipped. Group 13 contains \u201cB, 1.\u201d Group 14 contains \u201cC, 2.\u201d Group 15 contains \u201cN, 3.\u201d Group 16 contains \u201cO, 4.\u201d Group 17 contains \u201cF, 5.\u201d Group 18 contains \u201cN e, 6.\u201d Period 2 group 13 through 18 have subshell 2 p. Period 3, group 1 contains \u201cN a,1.\u201d Group 2 contains \u201cM g, 2.\u201d These two have subshell 3 s. Groups 3 through 12 are skipped again in period 3 and group 13 contains \u201cA l, 1.\u201d Group 14 contains \u201cS I, 2.\u201d Group 15 contains \u201cP, 3.\u201d Group 16 contains \u201cS, 4.\u201d Group 17 contains \u201cC l, 5.\u201d Group 18 contains \u201cA r, 6.\u201d These 6 have subshell 3 p. Period 4, group 1 contains \u201cK, 1.\u201d Group 2 contains \u201cC a, 2.\u201d These two have subshell 4 s. Group 3 contains \u201cS, 1.\u201d Group 4 contains \u201cT i, 2.\u201d Group 5 contains \u201cV, 3.\u201d Group 6 contains \u201cC r, 4.\u201d Group 7 contains \u201cM n, 5.\u201d Group 8 contains \u201cF e, 6.\u201d Group 9 contains \u201cC o, 7.\u201d Group 10 contains \u201cN i, 8.\u201d Group 11 contains \u201cC u, 9.\u201d Group 12 contains \u201cZ n, 10.\u201d These 10 have subshell 3 d. Group 13 contains \u201cG a, 1.\u201d Group 14 contains \u201cG e, 2.\u201d Group 15 contains \u201cA s, 3.\u201d Group 16 contains \u201cS e, 4.\u201d Group 17 contains \u201cB r, 5.\u201d Group 18 contains \u201cK r, 6.\u201d These six have subshell 4 p. Period 5, group 1 contains \u201cR b, 1.\u201d Group 2 contains \u201cS r, 2.\u201d These 2 have subshell 5 s. Group 3 contains \u201cY, 1.\u201d Group 4 contains \u201cZ r, 2.\u201d Group 5 contains \u201cN b, 3.\u201d Group 6 contains \u201cM o, 4.\u201d Group 7 contains \u201cT c, 5 \u201cR u, 6.\u201d Group 9 contains \u201cR h, 7.\u201d Group 10 contains \u201cP d, 8.\u201d Group 11 contains \u201cA g, 9.\u201d Group 12 contains \u201cC d, 10.\u201d These ten have subshell 4 d. Group 13 contains \u201cI n, 1.\u201d Group 14 contains \u201cS n, 2.\u201d Group 15 contains \u201cS b, 3.\u201d Group 16 contains \u201cT e, 4.\u201d Group 17 contains \u201cI, 5.\u201d Group 18 contains \u201cX e, 6.\u201d These six have subshell 5 p. Period 6, group 1 contains \u201cC s, 1.\u201d Group 2 contains \u201cB a, 2.\u201d These two have subshell 6 s. Group 3 contains \u201cL a, 1,\u201d and has an additional asterisk. Group 4 contains \u201cH f, 2.\u201d Group 5 contains \u201cT a, 3.\u201d Group 6 contains \u201cW, 4.\u201d Group 7 contains \u201cR e, 5.\u201d Group 8 contains \u201cO s, 6.\u201d Group 9 contains \u201cI r, 7.\u201d Group 10 contains \u201cP t, 8.\u201d Group 11 contains \u201cA u, 9.\u201d Group 12 contains \u201cH g, 10.\u201d These 10 have subshell 5 d. Group 13 contains \u201cT l, 1.\u201d Group 14 contains \u201cP b, 2.\u201d Group 15 contains \u201cB i, 3.\u201d Group 16 contains \u201cP o, 4.\u201d Group 17 contains \u201cA t, 5.\u201d Group 18 contains \u201cR n, 6.\u201d These six have subshell 6 p. Period 7, group 1 contains \u201cF r, 1.\u201d Group 2 contains \u201cR a, 2.\u201d These two have subshell 7 s. Group 3 contains \u201cA c, 1,\u201d and has an additional double asterisk. Group 4 contains \u201cR f, 2.\u201d Group 5 contains \u201cD b, 3.\u201d Group 6 contains \u201cS g, 4.\u201d Group 7 contains \u201cB h, 5.\u201d Group 8 contains \u201cH s, 6.\u201d Group 9 contains \u201cM t, 7.\u201d Group 10 contains \u201cD s, 8.\u201d Group 11 contains \u201cR g, 9.\u201d Group 12 contains \u201cC n, 10.\u201d These 10 have subshell 6 d. Group 13 contains \u201cU u t, 1.\u201d Group 14 contains \u201cF l, 2.\u201d Group 15 contains \u201cU u p, 3.\u201d Group 16 contains \u201cL v, 4.\u201d Group 17 is missing. Group 18 contains \u201cU u o, 6.\u201d These five have subshell 7 p. An arrow links the period 6 and 7, group 3 to an additional section with two rows, each with 14 columns. The columns are not numbered. The first row is labeled with an asterisk and all the elements in it have subshell 4 f. The boxes in this row contain, in order: C e, 1, P r, 2, N d, 3, P m, 4, S m, 5, E u, 6, G d, 7, T b, 8, D y, 9, H o, 10, E r, 11, T m, 12, Y b, 13, L u, 14. The second row is labeled with a double asterisk and all the elements in it have subshell 5 f. The boxes in this row contain, in order: T h 1, P a, 2, U, 3, N p, 4, P u, 5, A m, 6, C m, 7, B k, 8, C f, 9, E s, 10, F m, 11, M d, 12, N o, 13, L r, 14.\" data-media-type=\"image\/jpeg\" id=\"62224\" src=\"https:\/\/cnx.org\/resources\/ef6cb1cbf8af0bacd78121bb76b57801b80ea520\" width=\"978\" height=\"760\" \/> Figure 4.17 The periodic table of elements, showing the structure of shells and subshells.[\/caption]<\/figure>\r\n<div class=\"os-caption-container\"><em><span class=\"os-title-label\"><\/span><span class=\"os-caption\">\r\n<\/span><\/em><\/div>\r\n<\/div>\r\n<p id=\"fs-id1170902956107\">The second row corresponds to the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>and 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>subshells. For lithium (Li) (upper left), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with a spin-up<span>\u00a0<\/span><em data-effect=\"italics\">and<\/em><span>\u00a0<\/span>spin-down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-917-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>) and the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with either a spin-up or -down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-918-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191or\u2193<\/span><\/span><\/span>). Its electron configuration is therefore<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-919-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s1<\/span><\/span><\/span><span>\u00a0<\/span>or [He]2<em data-effect=\"italics\">s<\/em>, where [He] indicates a helium core. Like hydrogen, the lone electron in the outermost shell is easily shared with other atoms. For beryllium (Be), the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with a spin-up and -down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-920-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>), and has the electron configuration [He]<span class=\"MathJax_MathML\" id=\"MathJax-Element-921-Frame\"><span class=\"MathJax_MathContainer\"><span>2s2<\/span><\/span><\/span>.<\/p>\r\n<p id=\"fs-id1170901921894\">Next, we look at the right side of the table. For boron (B), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>and 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shells are filled and the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-922-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) shell contains either a spin up or down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-923-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191or\u2193<\/span><\/span><\/span>). From carbon (C) to neon (N), we the fill the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>shell. The maximum number of electrons in the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>shells is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-924-Frame\"><span class=\"MathJax_MathContainer\"><span>4l+2=4(2)+2=6<\/span><\/span><\/span>. For neon (Ne), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with a spin-up and spin-down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-925-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>), and the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>shell is filled with six electrons (<span class=\"MathJax_MathML\" id=\"MathJax-Element-926-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193\u2191\u2193\u2191\u2193)<\/span><\/span><\/span>. This \u201cfills\u201d the 1<em data-effect=\"italics\">s<\/em>, 2<em data-effect=\"italics\">s<\/em>, and 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>subshells, so like helium, the neon atom tends not to share electrons with other atoms.<\/p>\r\n<p id=\"fs-id1170901571607\">The process of electron filling repeats in the third row. However, beginning in the fourth row, the pattern is broken. The actual order of order of electron filling is given by<\/p>\r\n<p id=\"fs-id1170901571612\">1<em data-effect=\"italics\">s<\/em>, 2<em data-effect=\"italics\">s<\/em>, 2<em data-effect=\"italics\">p<\/em>, 3<em data-effect=\"italics\">s<\/em>, 3<em data-effect=\"italics\">p<\/em>, 4<em data-effect=\"italics\">s<\/em>,<span>\u00a0<\/span><strong data-effect=\"bold\">3<em data-effect=\"italics\">d<\/em><\/strong>, 4<em data-effect=\"italics\">p<\/em>, 5<em data-effect=\"italics\">s<\/em>,<span>\u00a0<\/span><strong data-effect=\"bold\">4<em data-effect=\"italics\">d<\/em><\/strong>, 5<em data-effect=\"italics\">p<\/em>, 6<em data-effect=\"italics\">s<\/em>,<span>\u00a0<\/span><strong data-effect=\"bold\">4<em data-effect=\"italics\">f<\/em>, 5<em data-effect=\"italics\">d<\/em><\/strong>, 6<em data-effect=\"italics\">p<\/em>, 7<em data-effect=\"italics\">s<\/em>,...<\/p>\r\n<p id=\"fs-id1170902703517\">Notice that the 3<em data-effect=\"italics\">d<\/em>, 4<em data-effect=\"italics\">d<\/em>, 4<em data-effect=\"italics\">f<\/em>, and 5<em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>subshells (in bold) are filled out of order; this occurs because of interactions between electrons in the atom, which so far we have neglected. The<span>\u00a0<\/span><span data-type=\"term\" id=\"term357\">transition metal<\/span><strong data-effect=\"bold\">s<\/strong><span>\u00a0<\/span>are elements in the gap between the first two columns and the last six columns that contain electrons that fill the<span>\u00a0<\/span><em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-927-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) subshell. As expected, these atoms are arranged in<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-928-Frame\"><span class=\"MathJax_MathContainer\"><span>4l+2=4(2)+2=10\u00a0<\/span><\/span><\/span>columns. The structure of the periodic table can be understood in terms of the quantization of the total energy (<em data-effect=\"italics\">n<\/em>), orbital angular momentum (<em data-effect=\"italics\">l<\/em>), and spin (<em data-effect=\"italics\">s<\/em>). The first two columns correspond to the<span>\u00a0<\/span><em data-effect=\"italics\">s<\/em><span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-929-Frame\"><span class=\"MathJax_MathContainer\"><span>(l=0<\/span><\/span><\/span>) subshell, the next six columns correspond to the<span>\u00a0<\/span><em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-930-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) subshell, and the gap between these columns corresponds to the<span>\u00a0<\/span><em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-931-Frame\"><span class=\"MathJax_MathContainer\"><span>l=2<\/span><\/span><\/span>) subshell.<\/p>\r\n<p id=\"fs-id1170903064608\">The periodic table also gives information on molecular bonding. To see this, consider atoms in the left-most column (the so-called alkali metals including: Li, Na, and K). These atoms contain a single electron in the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>subshell, which is easily donated to other atoms. In contrast, atoms in the second-to-right column (the halogens: for example, Cl, F, and Br) are relatively stingy in sharing electrons. These atoms would much rather accept an electron, because they are just one electron shy of a filled shell (\u201cof being noble\u201d).<\/p>\r\n<p id=\"fs-id1170902690725\">Therefore, if a Na atom is placed in close proximity to a Cl atom, the Na atom freely donates its 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>electron and the Cl atom eagerly accepts it. In the process, the Na atom (originally a neutral charge) becomes positively charged and the Cl (originally a neutral charge) becomes negatively charged. Charged atoms are called ions. In this case, the ions are<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-932-Frame\"><span class=\"MathJax_MathContainer\"><span>Na+<\/span><\/span><\/span><span>\u00a0<\/span>and<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-933-Frame\"><span class=\"MathJax_MathContainer\"><span>Cl\u2212<\/span><\/span><\/span>, where the superscript indicates charge of the ion. The electric (Coulomb) attraction between these atoms forms a NaCl (salt) molecule. A chemical bond between two ions is called an<span>\u00a0<\/span><span data-type=\"term\" id=\"term358\">ionic bond<\/span>. There are many kinds of chemical bonds. For example, in an oxygen molecule<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-934-Frame\"><span class=\"MathJax_MathContainer\"><span>O2\u00a0<\/span><\/span><\/span>electrons are equally shared between the atoms. The bonding of oxygen atoms is an example of a<span>\u00a0<\/span><span data-type=\"term\" id=\"term359\">covalent bond<\/span>.<\/p>\r\n&nbsp;\r\n<div class=\"textbox\"><em>Download for free at http:\/\/cnx.org\/contents\/af275420-6050-4707-995c-57b9cc13c358@11.1<\/em><\/div>","rendered":"<div data-type=\"abstract\" id=\"87050\" class=\"ui-has-child-title\">\n<header>\n<div class=\"textbox textbox--learning-objectives\"><\/div>\n<\/header>\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Explain the importance of Pauli\u2019s exclusion principle to an understanding of atomic structure and molecular bonding<\/li>\n<li>Explain the structure of the periodic table in terms of the total energy, orbital angular momentum, and spin of individual electrons in an atom<\/li>\n<li>Describe the electron configuration of atoms in the periodic table<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p><span style=\"font-size: 14pt\">So far, we have studied only hydrogen, the simplest chemical element. We have found that an electron in the hydrogen atom can be completely specified by five quantum numbers:<\/span><\/p>\n<div data-label=\"\" data-type=\"equation\" id=\"fs-id1170903806651\">\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-844-Frame\">\n<div class=\"textbox\">\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-844-Frame\"><span class=\"MathJax_MathContainer\"><span>n: principal quantum number<\/p>\n<p>l: angular momentum quantum number<\/p>\n<p>m: angular momentum projection quantum number<\/p>\n<p>s: spin quantum number<\/p>\n<p>ms: spin projection quantum number<\/p>\n<p><\/span><\/span><\/div>\n<div class=\"os-equation-number\"><span class=\"os-number\">[4.34]<\/span><\/div>\n<\/div>\n<p><span style=\"font-size: 14pt\">To construct the ground state of a neutral multi-electron atom, imagine starting with a nucleus of charge<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Ze<\/em><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">(that is, a nucleus of atomic number<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Z<\/em><span style=\"font-size: 14pt\">) and then adding<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Z<\/em><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">electrons one by one. Assume that each electron moves in a spherically symmetrical electric field produced by the nucleus and all other electrons of the atom. The assumption is valid because the electrons are distributed randomly around the nucleus and produce an average electric field (and potential) that is spherically symmetrical. The electric potential<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">U<\/em><span style=\"font-size: 14pt\">(<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">r<\/em><span style=\"font-size: 14pt\">) for each electron does not follow the simple<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-845-Frame\" style=\"font-size: 14pt\"><span class=\"MathJax_MathContainer\">\u22121\/r<\/span><\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">form because of interactions between electrons, but it turns out that we can still label each individual electron state by quantum numbers,<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-846-Frame\" style=\"font-size: 14pt\"><span class=\"MathJax_MathContainer\">(n,l,m,s,ms)<\/span><\/span><span style=\"font-size: 14pt\">. (The spin quantum number<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">s<\/em><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">is the same for all electrons, so it will not be used in this section.)<\/span><\/p>\n<\/div>\n<\/div>\n<p id=\"fs-id1170902772689\">The structure and chemical properties of atoms are explained in part by<span>\u00a0<\/span><span data-type=\"term\" id=\"term350\">Pauli\u2019s exclusion principle<\/span>: No two electrons in an atom can have the same values for all four quantum numbers<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-847-Frame\"><span class=\"MathJax_MathContainer\"><span>(n,l,m,ms).<\/span><\/span><\/span><span>\u00a0<\/span>This principle is related to two properties of electrons: All electrons are identical (\u201cwhen you\u2019ve seen one electron, you\u2019ve seen them all\u201d) and they have half-integral spin<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-848-Frame\"><span class=\"MathJax_MathContainer\"><span>(s=1\/2).<\/span><\/span><\/span><span>\u00a0<\/span>Sample sets of quantum numbers for the electrons in an atom are given in<span>\u00a0<\/span>Table 4.5. Consistent with Pauli\u2019s exclusion principle, no two rows of the table have the exact same set of quantum numbers.<\/p>\n<div class=\"os-table\">\n<table id=\"fs-id1170902930686\" summary=\"Table 8.5 Electron States of Atoms Because of Pauli\u2019s exclusion principle, no two electrons in an atom have the same set of four quantum numbers.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\"><em data-effect=\"italics\">n<\/em><\/th>\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\"><em data-effect=\"italics\">l<\/em><\/th>\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\"><em data-effect=\"italics\">m<\/em><\/th>\n<th scope=\"col\" data-align=\"right\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-849-Frame\"><span class=\"MathJax_MathContainer\"><span>ms<\/span><\/span><\/span><\/th>\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\">Subshell symbol<\/th>\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\">No. of electrons: subshell<\/th>\n<th scope=\"col\" data-align=\"center\" data-valign=\"top\">No. of electrons: shell<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">1<em data-effect=\"italics\">s<\/em><\/td>\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<em data-effect=\"italics\">s<\/em><\/td>\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\n<td rowspan=\"8\" data-align=\"center\" data-valign=\"top\">8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">2<em data-effect=\"italics\">p<\/em><\/td>\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">6<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">3<em data-effect=\"italics\">s<\/em><\/td>\n<td rowspan=\"2\" data-align=\"center\" data-valign=\"middle\">2<\/td>\n<td rowspan=\"18\" data-align=\"center\" data-valign=\"middle\">18<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">3<em data-effect=\"italics\">p<\/em><\/td>\n<td rowspan=\"6\" data-align=\"center\" data-valign=\"middle\">6<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20132<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<td rowspan=\"10\" data-align=\"center\" data-valign=\"middle\">3<em data-effect=\"italics\">d<\/em><\/td>\n<td rowspan=\"10\" data-align=\"center\" data-valign=\"middle\">10<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20132<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">\u20131<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">0<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">1<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u00bd<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"center\" data-valign=\"top\">3<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"center\" data-valign=\"top\">2<\/td>\n<td data-align=\"right\" data-valign=\"top\">\u2013\u00bd<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><em><span class=\"os-title-label\">Table 4<\/span><span class=\"os-number\">.5<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-title\" data-type=\"title\">Electron States of Atoms<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-caption\">Because of Pauli\u2019s exclusion principle, no two electrons in an atom have the same set of four quantum numbers.<\/span><\/em><\/div>\n<\/div>\n<p id=\"fs-id1170901705116\">Electrons with the same principal quantum number<span>\u00a0<\/span><em data-effect=\"italics\">n<\/em><span>\u00a0<\/span>are said to be in the same<span>\u00a0<\/span><span class=\"no-emphasis\" data-type=\"term\" id=\"term351\">shell<\/span>, and those that have the same value of<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em><span>\u00a0<\/span>are said to occupy the same<span>\u00a0<\/span><span class=\"no-emphasis\" data-type=\"term\" id=\"term352\">subshell<\/span>. An electron in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-850-Frame\"><span class=\"MathJax_MathContainer\"><span>n=1<\/span><\/span><\/span><span>\u00a0<\/span>state of a hydrogen atom is denoted 1<em data-effect=\"italics\">s<\/em>, where the first digit indicates the shell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-851-Frame\"><span class=\"MathJax_MathContainer\"><span>(n=1)<\/span><\/span><\/span><span>\u00a0<\/span>and the letter indicates the subshell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-852-Frame\"><span class=\"MathJax_MathContainer\"><span>(s,p,d,f\u2026correspond to l=0,1,2,3\u2026).<\/span><\/span><\/span><span>\u00a0<\/span>Two electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-853-Frame\"><span class=\"MathJax_MathContainer\"><span>n=1<\/span><\/span><\/span><span>\u00a0<\/span>state are denoted as<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-854-Frame\"><span class=\"MathJax_MathContainer\"><span>1s2,<\/span><\/span><\/span><span>\u00a0<\/span>where the superscript indicates the number of electrons. An electron in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-855-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>state with<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-856-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span><span>\u00a0<\/span>is denoted 2<em data-effect=\"italics\">p<\/em>. The combination of two electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-857-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>and<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-858-Frame\"><span class=\"MathJax_MathContainer\"><span>l=0<\/span><\/span><\/span><span>\u00a0<\/span>state, and three electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-859-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>and<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-860-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span><span>\u00a0<\/span>state is written as<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-861-Frame\"><span class=\"MathJax_MathContainer\"><span>2s22p3,<\/span><\/span><\/span><span>\u00a0<\/span>and so on. This representation of the electron state is called the<span>\u00a0<\/span><span data-type=\"term\" id=\"term353\">electron configuration<\/span><span>\u00a0<\/span>of the atom. The electron configurations for several atoms are given in<span>\u00a0<\/span>Table 4.6. Electrons in the outer shell of an atom are called<span>\u00a0<\/span><span data-type=\"term\" id=\"term354\">valence electron<\/span><strong data-effect=\"bold\">s<\/strong>. Chemical bonding between atoms in a molecule are explained by the transfer and sharing of valence electrons.<\/p>\n<div class=\"os-table\">\n<table id=\"fs-id1170902767240\" summary=\"Table 8.6 Electron Configurations of Electrons in an Atom The symbol (\u2191)(\u2191) indicates an unpaired electron in the outer shell, whereas the symbol (\u2191\u2193)(\u2191\u2193) indicates a pair of spin-up and -down electrons in an outer shell.\">\n<thead>\n<tr valign=\"top\">\n<th scope=\"col\" data-align=\"left\" data-valign=\"top\">Element<\/th>\n<th scope=\"col\" data-align=\"left\" data-valign=\"top\">Electron Configuration<\/th>\n<th scope=\"col\" data-align=\"left\" data-valign=\"top\">Spin Alignment<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">H<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-862-Frame\"><span class=\"MathJax_MathContainer\"><span>1s1<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-863-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">He<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-864-Frame\"><span class=\"MathJax_MathContainer\"><span>1s2<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-865-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Li<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-866-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s1<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-867-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Be<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-868-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s2<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-869-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">B<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-870-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p1<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-871-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">C<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-872-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p2<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-873-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">N<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-874-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p3<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-875-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)(\u2191)(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">O<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-876-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p4<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-877-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191\u2193)(\u2191)(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">F<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-878-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p5<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-879-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191\u2193)(\u2191\u2193)(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Ne<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-880-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p6<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-881-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191\u2193)(\u2191\u2193)(\u2191\u2193)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Na<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-882-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p63s1<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-883-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Mg<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-884-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p63s2<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-885-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)<\/span><\/span><\/span><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td data-align=\"left\" data-valign=\"top\">Al<\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-886-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s22p63s23p1<\/span><\/span><\/span><\/td>\n<td data-align=\"left\" data-valign=\"top\"><span class=\"MathJax_MathML\" id=\"MathJax-Element-887-Frame\"><span class=\"MathJax_MathContainer\"><span>(\u2191\u2193)(\u2191)<\/span><\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"os-caption-container\"><em><span class=\"os-title-label\">Table 4<\/span><span class=\"os-number\">.6<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-title\" data-type=\"title\">Electron Configurations of Electrons in an Atom<\/span><span class=\"os-divider\">\u00a0<\/span><span class=\"os-caption\">The symbol\u00a0<span class=\"MathJax_MathML\" id=\"MathJax-Element-888-Frame\"><span class=\"MathJax_MathContainer\">(\u2191)<\/span><\/span>\u00a0indicates an unpaired electron in the outer shell, whereas the symbol\u00a0<span class=\"MathJax_MathML\" id=\"MathJax-Element-889-Frame\"><span class=\"MathJax_MathContainer\">(\u2191\u2193)<\/span><\/span>\u00a0indicates a pair of spin-up and -down electrons in an outer shell.<\/span><\/em><\/div>\n<\/div>\n<p id=\"fs-id1170901571182\">The maximum number of electrons in a subshell depends on the value of the angular momentum quantum number,<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em>. For a given a value<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em>, there are<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-890-Frame\"><span class=\"MathJax_MathContainer\"><span>2l+1<\/span><\/span><\/span><span>\u00a0<\/span>orbital angular momentum states. However, each of these states can be filled by two electrons (spin up and down,<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-891-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>). Thus, the maximum number of electrons in a subshell is<\/p>\n<div class=\"textbox\">\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-892-Frame\"><span class=\"MathJax_MathContainer\"><span>N=2(2l+1)=4l+2.<\/span><\/span><\/div>\n<div class=\"os-equation-number\"><span class=\"os-number\">[4.35]<\/span><\/div>\n<\/div>\n<p id=\"fs-id1170901705860\">In the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-893-Frame\"><span class=\"MathJax_MathContainer\"><span>(l=0)<\/span><\/span><\/span><span>\u00a0<\/span>subshell, the maximum number of electrons is 2. In the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-894-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) subshell, the maximum number of electrons is 6. Therefore, the total maximum number of electrons in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-895-Frame\"><span class=\"MathJax_MathContainer\"><span>n=2<\/span><\/span><\/span><span>\u00a0<\/span>shell (including both the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-896-Frame\"><span class=\"MathJax_MathContainer\"><span>l=0<\/span><\/span><\/span><span>\u00a0<\/span>and 1 subshells) is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-897-Frame\"><span class=\"MathJax_MathContainer\"><span>2+6<\/span><\/span><\/span><span>\u00a0<\/span>or 8. In general, the maximum number of electrons in the<span>\u00a0<\/span><em data-effect=\"italics\">n<\/em>th shell is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-898-Frame\"><span class=\"MathJax_MathContainer\"><span>2n2.<\/span><\/span><\/span><\/p>\n<div data-type=\"example\" id=\"fs-id1170903027803\" class=\"ui-has-child-title\">\n<header><\/header>\n<section>\n<div class=\"textbox shaded\">\n<header>\n<h3 class=\"os-title\"><span class=\"os-title-label\">EXAMPLE<span>\u00a04<\/span><\/span><span class=\"os-number\">.5<\/span><span class=\"os-divider\"><\/span><\/h3>\n<\/header>\n<section>\n<p id=\"fs-id1170902597970\"><span data-type=\"title\"><strong>Subshells and Totals for\u00a0<\/strong><span class=\"MathJax_MathML\" id=\"MathJax-Element-899-Frame\"><span class=\"MathJax_MathContainer\"><strong>n=3<\/strong><\/span><\/span><\/span><\/p>\n<p>How many subshells are in the<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-900-Frame\"><span class=\"MathJax_MathContainer\"><span>n=3<\/span><\/span><\/span><span>\u00a0<\/span>shell? Identify each subshell and calculate the maximum number of electrons that will fill each. Show that the maximum number of electrons that fill an atom is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-901-Frame\"><span class=\"MathJax_MathContainer\"><span>2n2<\/span><\/span><\/span>.<\/p>\n<p><span data-type=\"title\"><strong>Strategy<\/strong><\/span><\/p>\n<p>Subshells are determined by the value of<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em>; thus, we first determine which values of<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em><span>\u00a0<\/span>are allowed, and then we apply the equation \u201cmaximum number of electrons that can be in a subshell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-902-Frame\"><span class=\"MathJax_MathContainer\"><span>=2(2l+1)<\/span><\/span><\/span>\u201d to find the number of electrons in each subshell.<\/p>\n<p><span data-type=\"title\"><strong>Solution<\/strong><\/span><\/p>\n<p>Because<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-903-Frame\"><span class=\"MathJax_MathContainer\"><span>n=3,<\/span><\/span><\/span><span>\u00a0<\/span>we know that<span>\u00a0<\/span><em data-effect=\"italics\">l<\/em><span>\u00a0<\/span>can be 0, 1, or 2; thus, there are three possible subshells. In standard notation, they are labeled the 3<em data-effect=\"italics\">s<\/em>, 3<em data-effect=\"italics\">p<\/em>, and 3<em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>subshells. We have already seen that two electrons can be in an<span>\u00a0<\/span><em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>state, and six in a<span>\u00a0<\/span><em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>state, but let us use the equation \u201cmaximum number of electrons that can be in a subshell<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-904-Frame\"><span class=\"MathJax_MathContainer\"><span>=2(2l+1)<\/span><\/span><\/span>\u201d to calculate the maximum number in each:<\/p>\n<div class=\"unnumbered\" data-label=\"\" data-type=\"equation\" id=\"fs-id1170901594429\">\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-905-Frame\">\n<p><span class=\"MathJax_MathContainer\"><span>3shasl=0;thus,2(2l+1)=2(0+1)=23phasl=1;thus,2(2l+1)=2(2+1)=63dhasl=2;thus,2(2l+1)=2(4+1)=10Total=18(inthen=3shell).<\/span><\/span><\/p>\n<p><span style=\"text-indent: 1em;font-size: 1rem\">The equation \u201cmaximum number of electrons that can be in a shell<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-906-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">=2n2<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u201d gives the maximum number in the<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-907-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=3<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell to be<\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"unnumbered\" data-label=\"\" data-type=\"equation\" id=\"fs-id1170902734856\">\n<div class=\"MathJax_MathML\" id=\"MathJax-Element-908-Frame\">\n<p><span class=\"MathJax_MathContainer\"><span>Maximum number of electrons=2n2=2(3)2=2(9)=18.<\/span><\/span><\/p>\n<p><span data-type=\"title\" style=\"text-indent: 1em;font-size: 1rem\"><strong>Significance<\/strong><\/span><\/p>\n<p><span style=\"text-indent: 1em;font-size: 1rem\">The total number of electrons in the three possible subshells is thus the same as the formula<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-909-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">2n2<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">. In standard (spectroscopic) notation, a filled<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-910-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=3<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell is denoted as<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-911-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">3s23p63d10<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">. Shells do not fill in a simple manner. Before the<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-912-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=3\u00a0<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell is completely filled, for example, we begin to find electrons in the<\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-913-Frame\" style=\"text-indent: 1em;font-size: 1rem\"><span class=\"MathJax_MathContainer\">n=4<\/span><\/span><span style=\"text-indent: 1em;font-size: 1rem\">\u00a0<\/span><span style=\"text-indent: 1em;font-size: 1rem\">shell.<\/span><\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<p><span style=\"font-size: 14pt\">The structure of the<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span class=\"no-emphasis\" data-type=\"term\" id=\"term355\" style=\"font-size: 14pt\">periodic table<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><span style=\"font-size: 14pt\">(<\/span>Figure 4.17<span style=\"font-size: 14pt\">) can be understood in terms of shells and subshells, and, ultimately, the total energy, orbital angular momentum, and spin of the electrons in the atom. A detailed discussion of the periodic table is left to a chemistry course\u2014we sketch only its basic features here. In this discussion, we assume that the atoms are electrically neutral; that is, they have the same number of electrons and protons. (Recall that the total number of protons in an atomic nucleus is called the atomic number,<\/span><span style=\"font-size: 14pt\">\u00a0<\/span><em style=\"font-size: 14pt\" data-effect=\"italics\">Z<\/em><span style=\"font-size: 14pt\">.)<\/span><\/p>\n<\/section>\n<\/div>\n<p id=\"fs-id1170902872614\">First, the periodic table is arranged into columns and rows. The table is read left to right and top to bottom in the order of increasing atomic number<span>\u00a0<\/span><em data-effect=\"italics\">Z<\/em>. Atoms that belong to the same column or<span>\u00a0<\/span><span data-type=\"term\" id=\"term356\">chemical group<\/span><span>\u00a0<\/span>share many of the same chemical properties. For example, the Li and Na atoms (in the first column) bond to other atoms in a similar way. The first row of the table corresponds to the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-914-Frame\"><span class=\"MathJax_MathContainer\"><span>l=0<\/span><\/span><\/span>) shell of an atom.<\/p>\n<p id=\"fs-id1170901609017\">Consider the hypothetical procedure of adding electrons, one by one, to an atom. For hydrogen (H) (upper left), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with either a spin up or down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-915-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191or\u2193<\/span><\/span><\/span>). This lone electron is easily shared with other atoms, so hydrogen is chemically active. For helium (He) (upper right), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with both a spin up and a spin down (<span class=\"MathJax_MathML\" id=\"MathJax-Element-916-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>) electron. This \u201cfills\u201d the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell, so a helium atom tends not to share electrons with other atoms. The helium atom is said to be chemically inactive, inert, or noble; likewise, helium gas is said to be an inert gas or noble gas.<\/p>\n<div class=\"media-2 ui-has-child-title\" data-type=\"note\" id=\"fs-id1170901570549\">\n<header>\n<h3 class=\"os-title\" data-type=\"title\"><span class=\"os-title-label\">INTERACTIVE<\/span><\/h3>\n<\/header>\n<section>\n<div class=\"os-note-body\">\n<p id=\"fs-id1170901570553\">Build an atom by adding and subtracting protons, neutrons, and electrons. How does the element, charge, and mass change? Visit<span>\u00a0<\/span><a href=\"https:\/\/openstax.org\/l\/21buildanatom\" rel=\"nofollow\">PhET Explorations: Build an Atom<\/a><span>\u00a0<\/span>to explore the answers to these questions.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"os-figure\">\n<figure id=\"CNX_UPhysics_41_04_PeriodTab\">\n<figure style=\"width: 978px\" class=\"wp-caption alignnone\"><img loading=\"lazy\" decoding=\"async\" alt=\"The Periodic Table of Elements, showing the structure of shells and subshells, is shown. The 18 columns are numbered labeled \u201cGroup\u201d and the 7 rows are numbered and labeled \u201cPeriod.\u201d Groups 1 and 2 are shaded purple. Groups 3 through 12 are shaded yellow. Groups 13 through 18, are shaded red, with the exception of period 1, group 18, which is purple. The period 6 and 7, group 3 boxes are outlined and an arrow points from them to an additional section of two rows and 14 columns that is shaded green. The period 6 group 3 box has an asterisk, which also appears to the left of the first row of the additional section. The period 7 group 3 box has two asterisks, which also appear to the left of the second row of the additional section. Below the table to the left is an enlarged picture of the upper-left most box on the table. The letter \u201cH\u201d is in its upper-left hand corner and is labeled \u201cSymbol.\u201d The number 1 is in its upper-right hand corner and is labeled \u201cElectrons.\u201d In its center the entry \u201c1 s\u201d is labeled \u201csubshell.\u201d The box is shaded purple. Every element has its symbol and electrons indicated in the box. The subshells are indicated as a group for contiguous sections of a row. Beginning at the top left of the table, period 1, group 1, is shaded purple and contains symbol H, electrons 1, subshell 1 s. The only other element box in period 1 is in the last column, group 18, which is shaded purple and contains \u201cH e, 1, 1 s\u201d. Period 2, group 1 contains \u201cL i, 1\u201d Group 2 contains \u201cB e, 2.\u201d Period 2 groups 1 and 2 both have subshell 2 s. Groups 3 through 12 are skipped. Group 13 contains \u201cB, 1.\u201d Group 14 contains \u201cC, 2.\u201d Group 15 contains \u201cN, 3.\u201d Group 16 contains \u201cO, 4.\u201d Group 17 contains \u201cF, 5.\u201d Group 18 contains \u201cN e, 6.\u201d Period 2 group 13 through 18 have subshell 2 p. Period 3, group 1 contains \u201cN a,1.\u201d Group 2 contains \u201cM g, 2.\u201d These two have subshell 3 s. Groups 3 through 12 are skipped again in period 3 and group 13 contains \u201cA l, 1.\u201d Group 14 contains \u201cS I, 2.\u201d Group 15 contains \u201cP, 3.\u201d Group 16 contains \u201cS, 4.\u201d Group 17 contains \u201cC l, 5.\u201d Group 18 contains \u201cA r, 6.\u201d These 6 have subshell 3 p. Period 4, group 1 contains \u201cK, 1.\u201d Group 2 contains \u201cC a, 2.\u201d These two have subshell 4 s. Group 3 contains \u201cS, 1.\u201d Group 4 contains \u201cT i, 2.\u201d Group 5 contains \u201cV, 3.\u201d Group 6 contains \u201cC r, 4.\u201d Group 7 contains \u201cM n, 5.\u201d Group 8 contains \u201cF e, 6.\u201d Group 9 contains \u201cC o, 7.\u201d Group 10 contains \u201cN i, 8.\u201d Group 11 contains \u201cC u, 9.\u201d Group 12 contains \u201cZ n, 10.\u201d These 10 have subshell 3 d. Group 13 contains \u201cG a, 1.\u201d Group 14 contains \u201cG e, 2.\u201d Group 15 contains \u201cA s, 3.\u201d Group 16 contains \u201cS e, 4.\u201d Group 17 contains \u201cB r, 5.\u201d Group 18 contains \u201cK r, 6.\u201d These six have subshell 4 p. Period 5, group 1 contains \u201cR b, 1.\u201d Group 2 contains \u201cS r, 2.\u201d These 2 have subshell 5 s. Group 3 contains \u201cY, 1.\u201d Group 4 contains \u201cZ r, 2.\u201d Group 5 contains \u201cN b, 3.\u201d Group 6 contains \u201cM o, 4.\u201d Group 7 contains \u201cT c, 5 \u201cR u, 6.\u201d Group 9 contains \u201cR h, 7.\u201d Group 10 contains \u201cP d, 8.\u201d Group 11 contains \u201cA g, 9.\u201d Group 12 contains \u201cC d, 10.\u201d These ten have subshell 4 d. Group 13 contains \u201cI n, 1.\u201d Group 14 contains \u201cS n, 2.\u201d Group 15 contains \u201cS b, 3.\u201d Group 16 contains \u201cT e, 4.\u201d Group 17 contains \u201cI, 5.\u201d Group 18 contains \u201cX e, 6.\u201d These six have subshell 5 p. Period 6, group 1 contains \u201cC s, 1.\u201d Group 2 contains \u201cB a, 2.\u201d These two have subshell 6 s. Group 3 contains \u201cL a, 1,\u201d and has an additional asterisk. Group 4 contains \u201cH f, 2.\u201d Group 5 contains \u201cT a, 3.\u201d Group 6 contains \u201cW, 4.\u201d Group 7 contains \u201cR e, 5.\u201d Group 8 contains \u201cO s, 6.\u201d Group 9 contains \u201cI r, 7.\u201d Group 10 contains \u201cP t, 8.\u201d Group 11 contains \u201cA u, 9.\u201d Group 12 contains \u201cH g, 10.\u201d These 10 have subshell 5 d. Group 13 contains \u201cT l, 1.\u201d Group 14 contains \u201cP b, 2.\u201d Group 15 contains \u201cB i, 3.\u201d Group 16 contains \u201cP o, 4.\u201d Group 17 contains \u201cA t, 5.\u201d Group 18 contains \u201cR n, 6.\u201d These six have subshell 6 p. Period 7, group 1 contains \u201cF r, 1.\u201d Group 2 contains \u201cR a, 2.\u201d These two have subshell 7 s. Group 3 contains \u201cA c, 1,\u201d and has an additional double asterisk. Group 4 contains \u201cR f, 2.\u201d Group 5 contains \u201cD b, 3.\u201d Group 6 contains \u201cS g, 4.\u201d Group 7 contains \u201cB h, 5.\u201d Group 8 contains \u201cH s, 6.\u201d Group 9 contains \u201cM t, 7.\u201d Group 10 contains \u201cD s, 8.\u201d Group 11 contains \u201cR g, 9.\u201d Group 12 contains \u201cC n, 10.\u201d These 10 have subshell 6 d. Group 13 contains \u201cU u t, 1.\u201d Group 14 contains \u201cF l, 2.\u201d Group 15 contains \u201cU u p, 3.\u201d Group 16 contains \u201cL v, 4.\u201d Group 17 is missing. Group 18 contains \u201cU u o, 6.\u201d These five have subshell 7 p. An arrow links the period 6 and 7, group 3 to an additional section with two rows, each with 14 columns. The columns are not numbered. The first row is labeled with an asterisk and all the elements in it have subshell 4 f. The boxes in this row contain, in order: C e, 1, P r, 2, N d, 3, P m, 4, S m, 5, E u, 6, G d, 7, T b, 8, D y, 9, H o, 10, E r, 11, T m, 12, Y b, 13, L u, 14. The second row is labeled with a double asterisk and all the elements in it have subshell 5 f. The boxes in this row contain, in order: T h 1, P a, 2, U, 3, N p, 4, P u, 5, A m, 6, C m, 7, B k, 8, C f, 9, E s, 10, F m, 11, M d, 12, N o, 13, L r, 14.\" data-media-type=\"image\/jpeg\" id=\"62224\" src=\"https:\/\/cnx.org\/resources\/ef6cb1cbf8af0bacd78121bb76b57801b80ea520\" width=\"978\" height=\"760\" \/><figcaption class=\"wp-caption-text\">Figure 4.17 The periodic table of elements, showing the structure of shells and subshells.<\/figcaption><\/figure>\n<\/figure>\n<div class=\"os-caption-container\"><em><span class=\"os-title-label\"><\/span><span class=\"os-caption\"><br \/>\n<\/span><\/em><\/div>\n<\/div>\n<p id=\"fs-id1170902956107\">The second row corresponds to the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>and 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>subshells. For lithium (Li) (upper left), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with a spin-up<span>\u00a0<\/span><em data-effect=\"italics\">and<\/em><span>\u00a0<\/span>spin-down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-917-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>) and the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with either a spin-up or -down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-918-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191or\u2193<\/span><\/span><\/span>). Its electron configuration is therefore<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-919-Frame\"><span class=\"MathJax_MathContainer\"><span>1s22s1<\/span><\/span><\/span><span>\u00a0<\/span>or [He]2<em data-effect=\"italics\">s<\/em>, where [He] indicates a helium core. Like hydrogen, the lone electron in the outermost shell is easily shared with other atoms. For beryllium (Be), the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with a spin-up and -down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-920-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>), and has the electron configuration [He]<span class=\"MathJax_MathML\" id=\"MathJax-Element-921-Frame\"><span class=\"MathJax_MathContainer\"><span>2s2<\/span><\/span><\/span>.<\/p>\n<p id=\"fs-id1170901921894\">Next, we look at the right side of the table. For boron (B), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>and 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shells are filled and the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-922-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) shell contains either a spin up or down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-923-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191or\u2193<\/span><\/span><\/span>). From carbon (C) to neon (N), we the fill the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>shell. The maximum number of electrons in the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>shells is<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-924-Frame\"><span class=\"MathJax_MathContainer\"><span>4l+2=4(2)+2=6<\/span><\/span><\/span>. For neon (Ne), the 1<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>shell is filled with a spin-up and spin-down electron (<span class=\"MathJax_MathML\" id=\"MathJax-Element-925-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193<\/span><\/span><\/span>), and the 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>shell is filled with six electrons (<span class=\"MathJax_MathML\" id=\"MathJax-Element-926-Frame\"><span class=\"MathJax_MathContainer\"><span>\u2191\u2193\u2191\u2193\u2191\u2193)<\/span><\/span><\/span>. This \u201cfills\u201d the 1<em data-effect=\"italics\">s<\/em>, 2<em data-effect=\"italics\">s<\/em>, and 2<em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>subshells, so like helium, the neon atom tends not to share electrons with other atoms.<\/p>\n<p id=\"fs-id1170901571607\">The process of electron filling repeats in the third row. However, beginning in the fourth row, the pattern is broken. The actual order of order of electron filling is given by<\/p>\n<p id=\"fs-id1170901571612\">1<em data-effect=\"italics\">s<\/em>, 2<em data-effect=\"italics\">s<\/em>, 2<em data-effect=\"italics\">p<\/em>, 3<em data-effect=\"italics\">s<\/em>, 3<em data-effect=\"italics\">p<\/em>, 4<em data-effect=\"italics\">s<\/em>,<span>\u00a0<\/span><strong data-effect=\"bold\">3<em data-effect=\"italics\">d<\/em><\/strong>, 4<em data-effect=\"italics\">p<\/em>, 5<em data-effect=\"italics\">s<\/em>,<span>\u00a0<\/span><strong data-effect=\"bold\">4<em data-effect=\"italics\">d<\/em><\/strong>, 5<em data-effect=\"italics\">p<\/em>, 6<em data-effect=\"italics\">s<\/em>,<span>\u00a0<\/span><strong data-effect=\"bold\">4<em data-effect=\"italics\">f<\/em>, 5<em data-effect=\"italics\">d<\/em><\/strong>, 6<em data-effect=\"italics\">p<\/em>, 7<em data-effect=\"italics\">s<\/em>,&#8230;<\/p>\n<p id=\"fs-id1170902703517\">Notice that the 3<em data-effect=\"italics\">d<\/em>, 4<em data-effect=\"italics\">d<\/em>, 4<em data-effect=\"italics\">f<\/em>, and 5<em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>subshells (in bold) are filled out of order; this occurs because of interactions between electrons in the atom, which so far we have neglected. The<span>\u00a0<\/span><span data-type=\"term\" id=\"term357\">transition metal<\/span><strong data-effect=\"bold\">s<\/strong><span>\u00a0<\/span>are elements in the gap between the first two columns and the last six columns that contain electrons that fill the<span>\u00a0<\/span><em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-927-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) subshell. As expected, these atoms are arranged in<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-928-Frame\"><span class=\"MathJax_MathContainer\"><span>4l+2=4(2)+2=10\u00a0<\/span><\/span><\/span>columns. The structure of the periodic table can be understood in terms of the quantization of the total energy (<em data-effect=\"italics\">n<\/em>), orbital angular momentum (<em data-effect=\"italics\">l<\/em>), and spin (<em data-effect=\"italics\">s<\/em>). The first two columns correspond to the<span>\u00a0<\/span><em data-effect=\"italics\">s<\/em><span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-929-Frame\"><span class=\"MathJax_MathContainer\"><span>(l=0<\/span><\/span><\/span>) subshell, the next six columns correspond to the<span>\u00a0<\/span><em data-effect=\"italics\">p<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-930-Frame\"><span class=\"MathJax_MathContainer\"><span>l=1<\/span><\/span><\/span>) subshell, and the gap between these columns corresponds to the<span>\u00a0<\/span><em data-effect=\"italics\">d<\/em><span>\u00a0<\/span>(<span class=\"MathJax_MathML\" id=\"MathJax-Element-931-Frame\"><span class=\"MathJax_MathContainer\"><span>l=2<\/span><\/span><\/span>) subshell.<\/p>\n<p id=\"fs-id1170903064608\">The periodic table also gives information on molecular bonding. To see this, consider atoms in the left-most column (the so-called alkali metals including: Li, Na, and K). These atoms contain a single electron in the 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>subshell, which is easily donated to other atoms. In contrast, atoms in the second-to-right column (the halogens: for example, Cl, F, and Br) are relatively stingy in sharing electrons. These atoms would much rather accept an electron, because they are just one electron shy of a filled shell (\u201cof being noble\u201d).<\/p>\n<p id=\"fs-id1170902690725\">Therefore, if a Na atom is placed in close proximity to a Cl atom, the Na atom freely donates its 2<em data-effect=\"italics\">s<\/em><span>\u00a0<\/span>electron and the Cl atom eagerly accepts it. In the process, the Na atom (originally a neutral charge) becomes positively charged and the Cl (originally a neutral charge) becomes negatively charged. Charged atoms are called ions. In this case, the ions are<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-932-Frame\"><span class=\"MathJax_MathContainer\"><span>Na+<\/span><\/span><\/span><span>\u00a0<\/span>and<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-933-Frame\"><span class=\"MathJax_MathContainer\"><span>Cl\u2212<\/span><\/span><\/span>, where the superscript indicates charge of the ion. The electric (Coulomb) attraction between these atoms forms a NaCl (salt) molecule. A chemical bond between two ions is called an<span>\u00a0<\/span><span data-type=\"term\" id=\"term358\">ionic bond<\/span>. There are many kinds of chemical bonds. For example, in an oxygen molecule<span>\u00a0<\/span><span class=\"MathJax_MathML\" id=\"MathJax-Element-934-Frame\"><span class=\"MathJax_MathContainer\"><span>O2\u00a0<\/span><\/span><\/span>electrons are equally shared between the atoms. The bonding of oxygen atoms is an example of a<span>\u00a0<\/span><span data-type=\"term\" id=\"term359\">covalent bond<\/span>.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox\"><em>Download for free at http:\/\/cnx.org\/contents\/af275420-6050-4707-995c-57b9cc13c358@11.1<\/em><\/div>\n","protected":false},"author":615,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"4. 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