{"id":70,"date":"2017-08-18T08:55:02","date_gmt":"2017-08-18T08:55:02","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/chemistry\/?page_id=70"},"modified":"2017-09-18T17:35:10","modified_gmt":"2017-09-18T17:35:10","slug":"quantum-mechanics-part-i","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/chemistry\/quantum-mechanics-part-i\/","title":{"rendered":"Quantum Mechanics Part I"},"content":{"rendered":"<div class=\"twelve columns\" style=\"margin-top: 10%;\">\n<div class=\"advance\">\n<p><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/the-periodic-table\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/atomic-structure-periodicity-and-matter\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/quantum-mechanics-part-ii\">Next Lesson\u27a1<\/a><\/p>\n<\/div>\n<p><!-- UPDATE NEXT\/PREVIOUS ABOVE --><\/p>\n<p><!-- CONTENT STARTS HERE --><\/p>\n<h1 id=\"title\">Atomic Structure, Periodicity, and Matter:Quantum Mechanics Part I<\/h1>\n<h4>Objective<\/h4>\n<p>In this lesson we will review the experimental evidence that led to the quantum mechanical model of the atom.<\/p>\n<h4>Previously we covered&#8230;<\/h4>\n<ul>\n<li>Early attempts to classify elements including the laws of triads and octaves<\/li>\n<li>Developing the modern periodic table, beginning with Mendeleev<\/li>\n<li>Interpreting of the information found in the periodic table<\/li>\n<li>The families of elements in the periodic table including metals, nonmetals, and metalloids<\/li>\n<li>The <em>s<\/em>, <em>p<\/em>, <em>d<\/em>, and <em>f<\/em>-blocks of elements<\/li>\n<li>Periodic and group trends of the elements including atomic radius, ionic radius, ionization energy,<br \/>\nelectronegativity, and electron affinity<\/li>\n<\/ul>\n<section>\n<h3>The Failure of the Physics of Newton and Maxwell<\/h3>\n<p>By the end of the 19<sup>th<\/sup> century, Newtonian, or classical mechanics and classical electromagnetic theory<br \/>\n(summarized in what are known as Maxwell\u2019s equations) had been used successfully to interpret matter as particulate,\u00a0consisting of individual atoms, and light as an electromagnetic wave. While certain experimental observations, such\u00a0as the diffraction and interference of light could be explained in terms of classical physics, the processes\u00a0involved in the absorption and emission of light by matter and the interaction of positive and negative charges in\u00a0the atom could not. Four unexplained phenomena were of particular importance: black body radiation, the\u00a0<abbr title=\"When light of appropriate frequency is absorbed by a metal object, electrons are ejected, and the metal object becomes positively charged.\">photoelectric\u00a0effect<\/abbr>, the absorption and emission of light by atoms, and the structure and stability of the\u00a0atom.<\/p>\n<h3>Black Body Radiation<\/h3>\n<p>The English physicists Rayleigh and Jeans used classical electrodynamics and statistical ideas in deriving their\u00a0radiation law to predict the frequency distribution expected for radiation from hot objects, called <abbr title=\"A black body absorbs 100% of the electromagnetic radiation that falls on it and radiates electromagnetic radiation with a spectrum characteristic of its temperature\">black\u00a0body radiation.<\/abbr> The Rayleigh-Jeans radiation law agreed with experiments for long wavelength, low\u00a0frequency components of the distribution, but its prediction, dubbed the \u201cultraviolet catastrophe,\u201d that one would\u00a0observe infinite amounts of short wavelength, high frequency radiation was completely incorrect.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/quantummechancis2.blackbody.png\" \/><\/center><\/p>\n<p class=\"figcaption\">Frequency distributions for black body radiation.<br \/>\nThe graph shows that as temperature decreases the peaks of the black body radiation curves move to lower intensities\u00a0and longer wavelengths which goes against the prediction of Rayleigh and Jeans.<\/p>\n<h3>Planck\u2019s Quantum Hypothesis<\/h3>\n<p>Quantum physics began in 1900 with Max Planck\u2019s derivation of his radiation law, which correctly predicted the\u00a0spectral distribution of a black body radiation. Planck modeled a black body as a collection of a very large number\u00a0of electric charges, each of which vibrates at the same frequency <em>\u03bd<\/em>. In contemporary terms, these charges\u00a0would be electrons bound to surface atoms of the black body, and would absorb and emit electromagnetic radiation.<\/p>\n<p>Planck discovered that to make his solution fit experimental results he was forced to make two assumptions. In the\u00a0first of these, his <abbr title=\"Planck proposed that in a black body, allowed oscillator energies were multiples of a discrete amount, or quantum, of energy, and an oscillator could absorb or emit energy only in integral multiples of energy.\">quantum hypothesis<\/abbr>, he postulated that allowed oscillator energies were multiples of a discrete amount or quantum of energy, <img decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_001.gif\" \/>. Therefore an oscillator might have energy <img decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_001.gif\" \/>, <img decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_003.gif\" \/>, <img decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_004.gif\" \/>, and so on, and could absorb or emit energy only in multiples of <img decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_001.gif\" \/>.<\/p>\n<p>His second assumption was that <img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_001.gif\" width=\"18\" height=\"24\" align=\"absmiddle\" \/> is proportional\u00a0to the oscillator frequency <em>\u03bd<\/em>, <img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_001.gif\" width=\"18\" height=\"24\" align=\"absmiddle\" \/> =\u00a0<em>h\u03bd<\/em>. Planck chose the value of the proportionality constant <em>h<\/em> so that predictions of his model\u00a0matched experimental observations. The currently accepted value of <em>h<\/em> is 6.62608 \u00d7 10<sup>\u221234<\/sup> J\u00b7s.\u00a0Given the magnitude of Planck\u2019s constant, the difference in energy between a quantum with energy\u00a0(<em>n<\/em>)<em>h\u03bd<\/em> and one with energy (<em>n<\/em> + 1)<em>h<\/em><em>\u03bd<\/em> is so small that the spectrum of radiation\u00a0from a black body would appear to be continuous.<\/p>\n<p>Planck\u2019s quantum hypothesis was at complete odds with classical physics, and was not immediately accepted by Planck\u2019s\u00a0contemporaries or by Planck himself. It was only after it had successfully explained a great many phenomena that it\u00a0became a part of the structure of modern physics.<\/p>\n<hr \/>\n<h3>The Photoelectric Effect<\/h3>\n<p>When light of sufficiently short wavelength lluminates a clean surface of a metal object, the metal object becomes\u00a0positively charged. This is called the <em>photoelectric effect<\/em>\u2014electrons are ejected from the metal when short\u00a0wavelength light is absorbed\u2014and was first observed in 1887 by Wilhelm Hallwachs, a doctoral student of Heinrich\u00a0Hertz, while they were studying the generation of electromagnetic waves\u2014research which proved Maxwell\u2019s earlier\u00a0prediction that light was an electromagnetic wave.<\/p>\n<p>Subsequently, Hallwachs, Philipp Lenard, who had also worked with Hertz, and the English physicist J.J. Thomson\u00a0demonstrated that the effect of light on a metal was to eject electrons from the metal, but other details of the\u00a0process were puzzling. The effect of ordinary waves, such as water or sound waves, depends on the amount of energy\u00a0the waves deliver. This, in turn, depends on wave intensity\u2014the amount of energy delivered per unit time per unit\u00a0area\u2014and on the time during which the wave acts, but it does <em>not<\/em> depend on the wave frequency. Increasing\u00a0or decreasing either wave intensity or the interaction time increases or decreases the effect, but changing the wave\u00a0frequency does not.<\/p>\n<p>On the basis of classical wave theory, increasing the intensity of light should increase the kinetic energy of the\u00a0ejected electrons, no matter what the frequency of the light used. However, with the photoelectric effect, light\u00a0whose frequency (<em>v<\/em>) was below <em>v<\/em><sub>0<\/sub>, a minimum value characteristic of the particular\u00a0metal used, had no effect\u2014no electrons were ejected, no matter what the intensity of the light. With light with a frequency (<em>v<\/em>) greater than <em>v<\/em><sub>0<\/sub>, the minimum frequency necessary for electron ejection,\u00a0and the kinetic energy of the ejected electrons was proportional to the difference between the frequency of the\u00a0light used and the minimum frequency needed for light to eject electrons. These results could not be explained in<br \/>\nterms of classical mechanics.<\/p>\n<h3>Einstein\u2019s Photon Hypothesis<\/h3>\n<p>In 1905, Einstein realized that he could explain the photoelectric effect if he extended Planck\u2019s quantum hypothesis\u00a0to light. Einstein proposed that electromagnetic energy itself is quantized, and that a beam of light consists of\u00a0<abbr title=\"Einstein proposed that light consists of particle-like photons, each with a discrete amount of energy, equal to Planck\u2019s constant (h) times the frequency (v) of the light, Ephoton= hv.\">photons<\/abbr>,\u00a0each with energy proportional to its frequency, \u00a0<em>E<\/em><sub>photon<\/sub> = <em>h\u03bd<\/em>.<\/p>\n<p>If the photon energy is less than the minimum energy needed to eject an electron, <em>E<\/em><sub>0<\/sub> =\u00a0<em>hv<\/em><sub>0<\/sub>, there will be no photoelectric effect.<\/p>\n<p>When photons with energy equal to or greater than the minimum necessary for electron ejection (<em>E<\/em> =\u00a0<em>h\u03bd<\/em> \u2265 <em>hv<\/em><sub>0<\/sub> = <em>E<\/em><sub>0<\/sub>) are absorbed by a metal, electrons will be ejected,\u00a0and their <abbr title=\"The energy of a moving object. K = \u00bdmv2, where m is the mass of the moving object, and v is its speed.\">kinetic energy<\/abbr> (<em>K<\/em>)\u00a0will be the difference between the photon energy and the minimum amount of energy required for electron ejection, <em>K = h\u03bd<\/em> &#8211; <em>hv<\/em><sub>0<\/sub>.<\/p>\n<section class=\"question\">\n<h4>Question<\/h4>\n<p>If light of frequency 8.00 \u00d7 10<sup>14<\/sup> Hz is shined on lithium, how fast will the photoelectrons that are ejected be moving?<\/p>\n<p><em>Hints: The kinetic energy of a photoelectron is equal to the difference between the energy of the photons\u00a0used,\u00a0h\u03bd, and the minimum photon energy needed to eject electrons, hv<sub>0<\/sub>. The mass of an electron is\u00a0m<sub>e<\/sub>= 9.11 \u00d7 10<sup>\u221231<\/sup> kg.<br \/>\n<\/em><\/p>\n<p><a class=\"button button-primary q-answer\"> Reveal Answer <\/a><\/p>\n<p class=\"q-reveal\"><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_016.gif\" width=\"530\" height=\"66\" \/><br \/>\nSolving for the speed of the electron <em>v<\/em>,<br \/>\n<em>v<\/em> = <img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_017.gif\" width=\"40\" height=\"52\" \/> = <img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_018.gif\" width=\"124\" height=\"52\" \/> = 3.66 \u00d7 10<sup>5<\/sup> m\/s<\/p>\n<\/section>\n<h3>The Photon as Particle\u2014Momentum Without Mass<\/h3>\n<p>Einstein\u2019s explanation of the photoelectric effect meant that energy exchange between light and atoms involved quanta of\u00a0energy, but there is more to the story. In 1922 A.H. Compton discovered that while photons, unlike particles, have zero\u00a0mass, they are like particles in that they have momentum. In classical physics the momentum (<em>p<\/em>) of a particle\u00a0is the product of its mass (<em>m)<\/em> and its velocity (<em>v)<\/em>, <em>p<\/em> = <em>mv<\/em>, but a photon\u2019s momentum\u00a0is equal to Planck\u2019s constant (<em>h<\/em>) divided by the photon wavelength <em>(\u03bb)<\/em>, <em>p<\/em> = <img loading=\"lazy\" decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_019.gif\" width=\"17\" height=\"41\" \/>.<\/p>\n<h3>Matter as Wave<\/h3>\n<p>In 1924, Louis de Broglie, a graduate student at the University of Paris, proposed that the wave-particle duality of\u00a0light was true of matter as well\u2014that if a photon has both wave and particle-like properties, a material particle\u00a0should also. The de Broglie relationship between the momentum of a particle and the particle wavelength, <em>p =\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_019.gif\" width=\"17\" height=\"41\" \/><\/em>, was verified in 1927 by G. P.\u00a0Thomson in England and C. J. Davisson and L. Germer in the United States, who showed that beams of electrons were\u00a0diffracted by thin metal films or by metal crystals in the same way as were X-rays of the same wavelength.<\/p>\n<p>You may find the biography of the electron amusing. J.J. Thompson demonstrated that the electron was a particle in\u00a01897, and received the Nobel Prize for that discovery in 1906. In 1937 G. P. Thomson was awarded the Nobel Prize for\u00a0his discovery in 1927 that the electron was a wave. J. J. and G.P. were father and son\u2014so the father proved the\u00a0electron was a particle and the son proved it wasn\u2019t.<\/p>\n<h3>Absorption and Emission of Light by Hydrogen and Other Atoms<\/h3>\n<p>Atomic absorption and emission spectra consist of narrow lines, and so are called line or discrete spectra, as\u00a0distinct from the continuous emission spectrum of light from the sun or from an incandescent lamp. Figure 2 below\u00a0shows the four lines of the hydrogen emission spectrum that are in the visible region, the Balmer series of spectral\u00a0lines.<\/p>\n<p><center><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/quantummechanics7.Hspectrum.png\" width=\"650\" height=\"86\" \/><\/center><\/p>\n<p class=\"figcaption\">Figure 2<\/p>\n<p>In 1885 Johann Balmer found that the reciprocal wavelengths (<img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_021.gif\" width=\"17\" height=\"41\" \/>) of the four hydrogen lines in the visible spectrum, all that were known then, were given by the formula:<\/p>\n<p class=\"center\"><img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_021.gif\" width=\"17\" height=\"41\" \/>= <em>R<img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_023.gif\" width=\"72\" height=\"45\" \/><\/em><\/p>\n<p>where the constant <em>R<\/em> = 1.096776\u00d710<sup>7<\/sup> m<sup>\u20131<\/sup> and each integral value of <em>m<\/em> &gt;2\u00a0corresponded to a spectral line. Balmer suggested that his formula might be a special case of a more general\u00a0equation, and in 1888 J. R. Rydberg and W. Ritz, working independently, found that reciprocal wavelengths for the\u00a0complete hydrogen spectrum, from the infrared to the ultraviolet, are given by\u00a0<img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_021.gif\" width=\"17\" height=\"41\" \/>= <em>R<img loading=\"lazy\" decoding=\"async\" class=\"non_block_image no_margin\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/s4_025.gif\" width=\"80\" height=\"45\" \/><\/em><\/p>\n<p>where <em>n<\/em> and <em>m<\/em> are integers, with <em>n<\/em> \u2265 1, and <em>m<\/em> &gt; <em>n<\/em>. Rydberg\u2019s formula\u00a0also applies to <abbr title=\"Ions such as He+, Li2+, and Be3+, which have a single electron\">hydrogenic ions<\/abbr>, ions with a single electron, such as He<sup>+<\/sup>, Li<sup>2+<\/sup>, and Be<sup>3+<\/sup><\/p>\n<p>Absorption and emission spectra of gaseous atoms of other elements are much more complex than the hydrogen spectrum,\u00a0not surprising in light of the fact that only hydrogen has a single electron. There are no simple Rydberg-like\u00a0expressions for spectral lines of elements with two or more electrons.<\/p>\n<h3>An Empirical Model of the Atom\u2014Electrons in Shells<\/h3>\n<p>The amount of energy needed to remove an electron from a gaseous atom, its binding or <abbr title=\"The amount of energy needed to remove an electron from an atom\">ionization energy<\/abbr> <em>(IE)<\/em>,\u00a0can be measured in a variety of ways. The first ionization energy, the energy required to remove the least tightly\u00a0held electron from a gaseous atom, provides important clues about the structure of an atom.<\/p>\n<p>Remember that, as we move across a row of the periodic table, the ionization energy is lowest for the first element\u00a0and greatest for the last. Moving across the second and third rows of the periodic table, the ionization energy\u00a0falls slightly at two points, between the second and third elements and between the fifth and sixth elements in the\u00a0period. There is a gradual decrease in ionization energy as we move down a column or family of the periodic\u00a0table.<\/p>\n<p>The pattern of ionization energies is consistent with a simple but useful empirical model of the atom, the <abbr title=\" An empirical model of the atom in which electrons occupy shells, with the nucleus at the center\">electron shell model<\/abbr>, in which electrons in an atom occupy spherical shells with the nucleus at the\u00a0center. Electrons in shells closer to the nucleus are held more tightly than electrons in shells farther from the\u00a0nucleus.<\/p>\n<p>In the electron shell model electrons in atoms of hydrogen and helium occupy the first shell, electrons in atoms of\u00a0the elements lithium through neon occupy the first and second shells, electrons in atoms of sodium through argon\u00a0occupy the first, second, and third shells, and with potassium and calcium we begin filling a fourth electron shell.\u00a0Each electron shell is assigned a number <em>n<\/em>; <em>n<\/em> = 1 for the first shell, which is closest to the\u00a0nucleus; <em>n<\/em> = 2 for the next shell, and so on.<\/p>\n<p>The drops in ionization energy that occur as we move from the second to the third element and from the fifth to the\u00a0sixth element in both the second and third rows of the periodic table suggest the possibility that within a given\u00a0electron shell electrons can occupy subshells with somewhat different energy levels. In order to decide this\u00a0question and further refine our electron shell model, we need to know how all of the electrons in an atom are\u00a0distributed.<\/p>\n<h3>Electron Configurations Determined by Photoelectron Spectroscopy<\/h3>\n<p>More detailed information about the arrangement and energy of individual electrons in the shells of an atom is\u00a0provided by <abbr title=\"High-energy ultraviolet or X-ray photons with energies sufficient to remove any electron from an atom are used to ionize atoms. This technique gives ionization energies for all of the electrons in an atom.\">photoelectron\u00a0spectroscopy<\/abbr> (PES). This technique involves illuminating a sample of gaseous atoms with\u00a0high-energy ultraviolet or X-ray photons of known energy <em>h\u03bd<\/em>. The energy of the photons used is greater than\u00a0that needed to remove even the most tightly held electron from an atom, and so any electron in an atom can be\u00a0ejected. Energy in excess of that needed to remove a particular electron from an atom is carried away as kinetic\u00a0energy (<em>K<\/em>) by the ejected electron.<\/p>\n<p>In a PES experiment two quantities are measured simultaneously; the kinetic energy <em>K<\/em> and number of ejected\u00a0electrons that have that kinetic energy. The ionization energy <em>IE<\/em> is the difference between the photon\u00a0energy <em>h\u03bd<\/em> and the kinetic energy <em>K<\/em>.<\/p>\n<p class=\"center\"><em>IE = h\u03bd \u2013 K <\/em><\/p>\n<p>So the more tightly an electron is held in an atom by the attractive force of the nucleus, the larger its ionization\u00a0energy and the smaller the kinetic energy of the ejected photoelectron.<\/p>\n<p>The results of a PES experiment can be displayed as a spectrum of signal intensity\u2014the magnitude of the photoelectron\u00a0current\u2014versus the ionization energy. (Note: The ionization energy <em>decreases<\/em> from left to right in a PES\u00a0spectrum.) Peak heights are proportional to the number of electrons occupying a particular energy level.<\/p>\n<p><center><img decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/quantummechanics9.PESspectrumneon.png\" alt=\"PES spectrum of neon \" \/><\/center><\/p>\n<p class=\"figcaption\">PES spectrum of neon<\/p>\n<p>The figure above represents a PES spectrum of neon. There are three peaks in the spectrum of neon, at 82.8, 4.68, and\u00a02.08 MJ\/mol, with ratios of relative intensity (as compared to the intensity of the single peak in the spectrum of\u00a0hydrogen) 2:2:6, respectively. The peak at 82.8 MJ\/mol corresponds to two electrons occupying the <em>n<\/em> = 1\u00a0shell that is closest to the nucleus. The pattern of first ionization energies suggests that there are eight\u00a0electrons in the <em>n<\/em> = 2 shell, but the PES spectrum for neon shows that these electrons occupy two\u00a0subshells. The peak at 4.68 MJ\/mol corresponds to two electrons in one subshell and that at 2.08 MJ\/mol corresponds\u00a0to six electrons in a second subshell somewhat farther from the nucleus than the first.<\/p>\n<p>Table 1 summarizes experimental PES results for the first ten elements in the periodic table.<\/p>\n<table class=\"gas_law_table\" border=\"1\" cellspacing=\"0\" cellpadding=\"0\">\n<thead>\n<tr>\n<th width=\"117\"><strong>Element\/<em>IE <\/em><\/strong>(MJ\/mol)<\/th>\n<th width=\"56\"><strong> 1<sup>st<br \/>\n<\/sup>peak <\/strong><\/th>\n<th valign=\"top\" width=\"91\">\n<p class=\"white_lesson_header\" align=\"center\"><strong> Relative Intensity <\/strong><\/p>\n<\/th>\n<th valign=\"top\" width=\"56\">\n<p class=\"white_lesson_header\" align=\"center\"><strong> 2<sup>nd<br \/>\n<\/sup>peak <\/strong><\/p>\n<\/th>\n<th valign=\"top\" width=\"84\">\n<p class=\"white_lesson_header\" align=\"center\"><strong> Relative Intensity <\/strong><\/p>\n<\/th>\n<th valign=\"top\" width=\"56\">\n<p class=\"white_lesson_header\" align=\"center\"><strong> 3<sup>rd<br \/>\n<\/sup>peak <\/strong><\/p>\n<\/th>\n<th valign=\"top\" width=\"92\">\n<p class=\"white_lesson_header\" align=\"center\"><strong> Relative Intensity <\/strong><\/p>\n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">H<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">1.31<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">1<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\"><\/td>\n<td valign=\"top\" width=\"84\"><\/td>\n<td valign=\"top\" width=\"56\"><\/td>\n<td valign=\"top\" width=\"92\"><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">He<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">2.37<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\"><\/td>\n<td valign=\"top\" width=\"84\"><\/td>\n<td valign=\"top\" width=\"56\"><\/td>\n<td valign=\"top\" width=\"92\"><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">Li<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">5.28<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">0.52<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">1<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\"><\/td>\n<td valign=\"top\" width=\"92\"><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">Be<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">10.7<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">0.90<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\"><\/td>\n<td valign=\"top\" width=\"92\"><\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">B<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">18.0<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">1.36<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">0.8<\/p>\n<\/td>\n<td valign=\"top\" width=\"92\">\n<p class=\"center\">1<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">C<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">27.3<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">1.72<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">1.09<\/p>\n<\/td>\n<td valign=\"top\" width=\"92\">\n<p class=\"center\">2<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">N<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">38.4<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">2.45<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">1.40<\/p>\n<\/td>\n<td valign=\"top\" width=\"92\">\n<p class=\"center\">3<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">O<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">51.1<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">2.72<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">1.31<\/p>\n<\/td>\n<td valign=\"top\" width=\"92\">\n<p class=\"center\">4<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">F<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">67.2<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">3.88<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">1.68<\/p>\n<\/td>\n<td valign=\"top\" width=\"92\">\n<p class=\"center\">5<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td valign=\"top\" width=\"117\">\n<p class=\"center\">Ne<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">82.8<\/p>\n<\/td>\n<td valign=\"top\" width=\"91\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">4.68<\/p>\n<\/td>\n<td valign=\"top\" width=\"84\">\n<p class=\"center\">2<\/p>\n<\/td>\n<td valign=\"top\" width=\"56\">\n<p class=\"center\">2.08<\/p>\n<\/td>\n<td valign=\"top\" width=\"92\">\n<p class=\"center\">6<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td class=\"figcaption\" colspan=\"7\" valign=\"top\">Sources: National Institute of Standards and Technology (NIST).<br \/>\n<u>X-ray Photoelectron Spectroscopy Database.<\/u> U.S. Secretary of Commerce on behalf of the United States<br \/>\nof America, 2003. Available online at: <a class=\"fineprint_a\" href=\"http:\/\/srdata.nist.gov\/xps\/index.htm\">http:\/\/srdata.nist.gov\/xps\/index.htm<\/a>.<br \/>\nSpencer, Bodner and Rickard, <u>Chemistry: Structure and Dynamics, Second Edition<\/u>, John Wiley, 2003.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"figcaption\">Table 1: Photoelectron Ionization Energies and Peak Intensities for Gaseous Atoms of Elements 1 through 10<\/p>\n<h3>Electron Configurations and the Electron Shell Model<\/h3>\n<p>We have described the electron shell model for the first ten elements. Spectroscopic studies of the remaining<br \/>\nelements have led to an understanding of the arrangement of the electrons in atoms of every element and their<br \/>\nelectron configurations. The structure of the electron shell model for an atom can be described using the following<br \/>\nrules:<\/p>\n<ul>\n<li>Each electron shell is assigned a number <em>n<\/em>; <em>n<\/em> = 1 for the first shell, which is closest to\u00a0the nucleus; <em>n<\/em> = 2 for the next shell, and so on.<\/li>\n<li>Subshells are labeled as <em>s<\/em>, <em>p<\/em>, <em>d<\/em>, <em>f<\/em>, etc.<\/li>\n<li>There are <em>n<\/em> subshells in the <em>n<\/em><sup>th<\/sup> shell, so in the <em>n<\/em> = 1 shell there is an\u00a0<em>s<\/em> subshell; in the <em>n<\/em> = 2 shell there is an <em>s<\/em> subshell and a <em>p<\/em> subshell; in\u00a0the <em>n<\/em> = 3 shell there is an <em>s<\/em> subshell, a <em>p<\/em> subshell, and a <em>d<\/em> subshell; and\u00a0so on.<\/li>\n<li>Within a given shell, removing an electron from the <em>s<\/em> subshell requires the most energy, with\u00a0successively less energy needed to remove electrons from <em>p<\/em>, <em>d<\/em>, and <em>f<\/em> subshells.<\/li>\n<li>An <em>s<\/em> subshell can hold two electrons, a <em>p<\/em> subshell can hold six electrons, a <em>d\u00a0<\/em>subshell can hold ten electrons, and an <em>f<\/em> subshell can hold fourteen electrons.<\/li>\n<\/ul>\n<p>Lowest energy or ground state electron configurations for the first twenty elements are as follows:<\/p>\n<table class=\"gas_law_table\" cellspacing=\"0\" cellpadding=\"0\">\n<tbody>\n<tr>\n<td width=\"107\">H (<em>Z<\/em> = 1)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>1<\/sup><\/td>\n<td width=\"107\">Na (<em>Z<\/em> = 11)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>1<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">He (<em>Z<\/em> = 2)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup><\/td>\n<td width=\"107\">Mg (<em>Z<\/em> = 12)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">Li (<em>Z<\/em> = 3)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>1<\/sup><\/td>\n<td width=\"107\">Al (<em>Z<\/em> = 13)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>1<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">Be (<em>Z<\/em> = 4)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup><\/td>\n<td width=\"107\">Si (<em>Z<\/em> = 14)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">B (<em>Z<\/em> = 5)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>1<\/sup><\/td>\n<td width=\"107\">P (<em>Z<\/em> = 15)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">C (<em>Z<\/em> = 6)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>2<\/sup><\/td>\n<td width=\"107\">S (<em>Z<\/em> = 16)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>4<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">N (<em>Z<\/em> = 7)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>3<\/sup><\/td>\n<td width=\"107\">Cl (<em>Z<\/em> = 17)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>5<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">O (<em>Z<\/em> = 8)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>4<\/sup><\/td>\n<td width=\"107\">Ar (<em>Z<\/em> = 18)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">F (<em>Z<\/em> = 9)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>5<\/sup><\/td>\n<td width=\"107\">K (<em>Z<\/em> = 19)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup>4<em>s<\/em><sup>1<\/sup><\/td>\n<\/tr>\n<tr>\n<td width=\"107\">Ne (<em>Z<\/em> = 10)<\/td>\n<td width=\"152\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup><\/td>\n<td width=\"107\">Ca (<em>Z<\/em> = 20)<\/td>\n<td width=\"150\">1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup>4<em>s<\/em><sup>2<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p class=\"figcaption\">Z = atomic number of the element<\/p>\n<p>You can predict subshell electron populations for most of the elements with <em>Z<\/em> = 1 through 56 using the<br \/>\nfollowing order of filling subshells.<\/p>\n<p><center><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/americanboard.org\/Subjects\/chemistry\/wp-content\/uploads\/sites\/3\/2017\/08\/quantummechanics10.orderoffillingsubshells.gif\" width=\"650\" height=\"20\" \/><\/center>Note that in the first row of transition elements (scandium through zinc) the 3<em>d<\/em> subshell fills after the 4<em>s<\/em><br \/>\nsubshell, and in the second row of transition elements (yttrium through cadmium) the 4<em>d<\/em> subshell fills<br \/>\nafter the 5<em>s<\/em> subshell. For example, the electron configuration of cobalt (<em>Z<\/em> = 27) is<br \/>\n1<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup>4<em>s<\/em><sup>2<\/sup>3<em>d<\/em><sup>7<\/sup>.<\/p>\n<p>There are exceptions to this order of filling among the first and second transition series elements, because the\u00a04<em>s<\/em> and 3<em>d<\/em> subshells in the first transition series and the 5<em>s<\/em> and 4<em>d<\/em> subshells\u00a0in the second transition series are very close in energy. We find that half full and completely full <em>d\u00a0<\/em>subshells are more stable than other configurations. As a result, while we would predict, for example that the\u00a0electron configuration for copper (<em>Z<\/em> = 29) would be\u00a01<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup>4<em>s<\/em><sup>2<\/sup>3<em>d<\/em><sup>9<\/sup>,\u00a0it is actually\u00a01<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup>4<em>s<\/em><sup>1<\/sup>3<em>d<\/em><sup>10<\/sup>.<\/p>\n<p>Interestingly, when a transition element atom ionizes, it is the electrons in the outermost <em>s<\/em> subshell that<br \/>\nare most easily removed. Thus, for example, the electron configuration for the Co<sup>+2<\/sup> ion is\u00a01<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup>3<em>d<\/em><sup>7<\/sup>,\u00a0not\u00a01<em>s<\/em><sup>2<\/sup>2<em>s<\/em><sup>2<\/sup>2<em>p<\/em><sup>6<\/sup>3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>6<\/sup>4<em>s<\/em><sup>2<\/sup>3<em>d<\/em><sup>5<\/sup>.<\/p>\n<hr \/>\n<h3>Core and Valence Electrons<\/h3>\n<p>There are two categories of electrons, <abbr title=\"The inner shell electrons in an atom. They are not involved in bonding.\">core<\/abbr>, or inner\u00a0electrons, and <abbr title=\"Electrons in the outermost shell of an atom that are involved in bonding\">valence<\/abbr>,\u00a0or outer shell electrons. Valence electrons in the first two elements, hydrogen and helium, occupy the first shell.\u00a0The two electrons in the first shell are core electrons for the next eight elements, lithium through neon; the\u00a0valence electrons of these elements occupy the second shell. In the next eight elements the ten electrons in the\u00a0first and second shells are core electrons; as for the preceding eight elements, valence electrons occupy the\u00a0outermost third shell. In writing electron configurations, core electrons are often represented by the symbol for\u00a0the noble gas with the same electron configuration enclosed in brackets. For example, the electron configuration for\u00a0silicon can be written as [Ne]3<em>s<\/em><sup>2<\/sup>3<em>p<\/em><sup>2<\/sup>; that for potassium as [Ar]4<em>s<\/em><sup>1<\/sup>.<\/p>\n<p>There is a close correspondence between electron shells and the structure of the periodic table for the first 20\u00a0elements; each shell corresponds to a row of the periodic table. This correspondence between electron shells and\u00a0rows of the periodic table is more complicated for transition elements, but still serves as a useful model of atomic\u00a0structure.<\/p>\n<p>While only valence electrons are involved in chemical bonding, there are interactions between both core electrons\u00a0and the nucleus with valence electrons, and these interactions have a significant influence on the chemical\u00a0properties of a given atom. As the number of core electrons increases, there is a corresponding increase in nuclear\u00a0charge and in the volume core electrons occupy.<\/p>\n<p>These simultaneous changes have two opposing effects on valence electrons. Because core electrons occupy shells that\u00a0lie between the nucleus and the valence shell, they shield or screen valence electrons from the full charge on the\u00a0nucleus. This means that the effective or <abbr title=\"The effective or net nuclear charge acting on valence electrons\">core charge<\/abbr> acting\u00a0on valence electrons is smaller than the full nuclear charge. While the actual magnitude of the effective nuclear<br \/>\ncharge that acts on valence electrons in a given atom cannot be measured, it is defined qualitatively as the sum of\u00a0the positive charge on the nucleus and the negative charge of the core electrons.<\/p>\n<p>Core Charge = (+Nuclear Charge) + (\u2013Charge on Core Electrons)<\/p>\n<p>Thus, for example, the core charge in an oxygen atom is +6, equal to the sum of the +8 charge on the oxygen nucleus<br \/>\nand the -2 charge of the two core electrons.<\/p>\n<ul>\n<li>The positive charge on the nucleus increases.<\/li>\n<li>The core charge\u2014the effective nuclear charge for valence electrons\u2014increases.<\/li>\n<li>The number of valence electrons increases.<\/li>\n<\/ul>\n<p>As the nuclear charge increases across a row, core electrons, whose numbers are fixed for elements in a given row,\u00a0are pulled closer to the nucleus, reducing the volume the core electrons occupy in the atom, and allowing valence\u00a0electrons to move somewhat closer to the nucleus. This and the increase in the core charge across a row means that\u00a0the attractive forces acting on the valence electrons grow stronger across a row.<\/p>\n<p>While attractive forces between valence electrons and the nucleus grow stronger as the charge on the nucleus\u00a0increases across a row, repulsive forces between valence electrons also grow stronger as electrons are pulled closer\u00a0to the nucleus and each other. However, because electrons within the valence shell do not screen each other from the\u00a0charge on the nucleus as effectively as electrons in inner shells screen those in outer shells, there is a net\u00a0increase in the attractive forces between the valence electrons and the nucleus in elements in a row from left to\u00a0right across a row in the periodic table. As a result, on average, ionization energies increase and atomic radii\u00a0decrease from left to right across a row.<\/p>\n<p>As we move down a column in the periodic table, the number of filled core electron shells increases, and so the\u00a0volume occupied by core electrons increase. As a result, the distance between valence electrons in the outermost\u00a0shell and the nucleus increases, weakening the attraction between the nucleus and electrons in the valence shell, so\u00a0ionization energies decrease and atomic radii increase from top to bottom down a column.<\/p>\n<p>These trends are consistent with the decrease in metallic character of elements from left to right across a period\u00a0and the increase in metallic character of elements from the top to the bottom of a group.<\/p>\n<p><!-- CONTENT ENDS HERE --><\/p>\n<p><!-- UPDATE NEXT\/PREVIOUS BELOW --><\/p>\n<div class=\"advance\">\n<p><a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/the-periodic-table\">\u2b05 Previous Lesson<\/a>\u00a0<a class=\"button\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/atomic-structure-periodicity-and-matter\">Workshop Index<\/a>\u00a0<a class=\"button button-primary\" href=\"http:\/\/americanboard.org\/Subjects\/chemistry\/quantum-mechanics-part-ii\">Next Lesson\u27a1<\/a><\/p>\n<\/div>\n<p><a class=\"backtotop\" href=\"#title\">Back to Top<\/a><\/p>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson\u27a1 Atomic Structure, Periodicity, and Matter:Quantum Mechanics Part I Objective In this lesson we will review the experimental evidence that led to the quantum mechanical model of the atom. Previously we covered&#8230; Early attempts to classify elements including the laws of triads and octaves Developing the modern periodic table, beginning with [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-70","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/70","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/comments?post=70"}],"version-history":[{"count":32,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/70\/revisions"}],"predecessor-version":[{"id":810,"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/pages\/70\/revisions\/810"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/chemistry\/wp-json\/wp\/v2\/media?parent=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}