28.9 The Exclusion Principle and the Periodic Table 917this curve. First, the curve peaks at a value of r 0.052 9 nm, the Bohr radius forthe first (n 1) electron orbit in hydrogen. This means that there is a maximumprobability of finding the electron in a small interval centered at that distancefrom the nucleus. However, as the curve indicates, there is also a probability offinding the electron in a small interval centered at any other distance from the nucleus.In other words, the electron is not confined to a particular orbital distancefrom the nucleus, as assumed in the Bohr model. The electron may be found atvarious distances from the nucleus, but the probability of finding it at a distancecorresponding to the Bohr radius is a maximum. <strong>Quantum</strong> mechanics alsopredicts that the wave function for the hydrogen atom in the ground state is sphericallysymmetric; hence the electron can be found in a spherical region surroundingthe nucleus. This is in contrast to the Bohr theory, which confines the positionof the electron to points in a plane. The quantum mechanical result is often interpretedby viewing the electron as a cloud surrounding the nucleus. An attempt atpicturing this cloud-like behavior is shown in Figure 28.13. The densest regions ofthe cloud represent those locations where the electron is most likely to be found.If a similar analysis is carried out for the n 2, 0, state of hydrogen, a peakof the probability curve is found at 4a 0 . Likewise, for the n 3, 0 state, thecurve peaks at 9a 0 . Thus, quantum mechanics predicts a most probable electrondistance to the nucleus that is in agreement with the location predicted by theBohr theory.P1s(r)a 0 = 0.0529 nmFigure 28.12 The probability perunit length of finding the electronversus distance from the nucleusfor the hydrogen atom in the 1s(ground) state. Note that the graphhas its maximum value when r equalsthe first Bohr radius, a 0 .yr28.9 THE EXCLUSION PRINCIPLEAND THE PERIODIC TABLEEarlier, we found that the state of an electron in an atom is specified by four quantumnumbers: n, , m , and m s . For example, an electron in the ground state of hydrogencould have quantum numbers of n 1, 0, m 0, and m s 1 2. As itturns out, the state of an electron in any other atom may also be specified by thissame set of quantum numbers. In fact, these four quantum numbers can be usedto describe all the electronic states of an atom, regardless of the number of electronsin its structure.How many electrons in an atom can have a particular set of quantum numbers?This important question was answered by Pauli in 1925 in a powerful statementknown as the Pauli exclusion principle:No two electrons in an atom can ever have the same set of values for the set of quantumnumbers n, , m , and m s .zFigure 28.13 The sphericalelectron cloud for the hydrogenatom in its 1s state. The Pauli exclusion principlexThe Pauli exclusion principle explains the electronic structure of complex atomsas a succession of filled levels with different quantum numbers increasing in energy,where the outermost electrons are primarily responsible for the chemicalproperties of the element. If this principle weren’t valid, every electron would endup in the lowest energy state of the atom and the chemical behavior of the elementswould be grossly different. Nature as we know it would not exist—and wewould not exist to wonder about it!As a general rule, the order that electrons fill an atom’s subshell is as follows:once one subshell is filled, the next electron goes into the vacant subshell that islowest in energy. If the atom were not in the lowest energy state available to it, itwould radiate energy until it reached that state. A subshell is filled when it contains2(2 1) electrons. This rule is based on the analysis of quantum numbersto be described later. Following the rule, shells and subshells can contain numbersof electrons according to the pattern given in Table 28.3.The exclusion principle can be illustrated by an examination of the electronicarrangement in a few of the lighter atoms.Hydrogen has only one electron, which, in its ground state, can be described by1either of two sets of quantum numbers: 1, 0, 0, 2 or 1, 0, 0, 1 . The electronicconfiguration of this atom is often designated as 1s 1 2. The notation 1s refers to aTIP 28.3 The ExclusionPrinciple is More GeneralThe exclusion principle stated here isa limited form of the more generalexclusion principle, which states thatno two fermions (particles with spin1/2, 3/2, . . .) can be in the samequantum state.
918 Chapter 28 Atomic <strong>Physics</strong>WOLFGANG PAULI (1900–1958)An extremely talented Austrian theoreticalphysicist who made important contributionsin many areas of modern physics,Pauli gained public recognition at the ageof 21 with a masterful review article onrelativity that is still considered one of thefinest and most comprehensive introductionsto the subject. Other major contributionswere the discovery of the exclusionprinciple, the explanation of the connectionbetween particle spin and statistics,and theories of relativistic quantum electrodynamics,the neutrino hypothesis, andthe hypothesis of nuclear spin.CERN/Courtesy of AIP Emilio Segre Visual ArchivesTABLE 28.3Number of Electrons in Filled Subshells and ShellsNumber of Number ofElectrons in Electrons inShell Subshell Filled Subshell Filled ShellK (n 1) s( 0) 2 2s( 0) 2L (n 2)p( 1) 68s( 0) 2M (n 3) p( 1) 6 18}d( 2) 10s( 0) 2}p( 1) 6N (n 4)d( 2) 1032f( 3) 14state for which n 1 and 0, and the superscript indicates that one electron ispresent in this level.Neutral helium has two electrons. In the ground state, the quantum numbers for1these two electrons are 1, 0, 0, and 1, 0, 0, 1 22. No other possible combinations ofquantum numbers exist for this level, and we say that the K shell is filled. The heliumelectronic configuration is designated as 1s 2 .Neutral lithium has three electrons. In the ground state, two of these are in the1s subshell and the third is in the 2s subshell, because the latter is lower in energythan the 2p subshell. Hence, the electronic configuration for lithium is 1s 2 2s 1 .A list of electronic ground-state configurations for a number of atoms is providedin Table 28.4. In 1871 Dmitri Mendeleev (1834–1907), a Russian chemist,arranged the elements known at that time into a table according to their atomicmasses and chemical similarities. The first table Mendeleev proposed containedmany blank spaces, and he boldly stated that the gaps were there only becausethose elements had not yet been discovered. By noting the column in which thesemissing elements should be located, he was able to make rough predictions abouttheir chemical properties. Within 20 years of this announcement, the elementswere indeed discovered.The elements in our current version of the periodic table are still arranged sothat all those in a vertical column have similar chemical properties. For example,consider the elements in the last column: He (helium), Ne (neon), Ar (argon), Kr(krypton), Xe (xenon), and Rn (radon). The outstanding characteristic of theseelements is that they don’t normally take part in chemical reactions, joining withother atoms to form molecules, and are therefore classified as inert. Because ofthis “aloofness,” they are referred to as the noble gases. We can partially understandtheir behavior by looking at the electronic configurations shown in Table 28.4,page 919. The element helium has the electronic configuration 1s 2 . In otherwords, one shell is filled. The electrons in this filled shell are considerably separatedin energy from the next available level, the 2s level.The electronic configuration for neon is 1s 2 2s 2 2p 6 . Again, the outer shell isfilled and there is a large difference in energy between the 2p level and the 3slevel. Argon has the configuration 1s 2 2s 2 2p 6 3s 2 3p 6 . Here, the 3p subshell is filledand there is a wide gap in energy between the 3p subshell and the 3d subshell.Through all the noble gases, the pattern remains the same: a noble gas is formedwhen either a shell or a subshell is filled, and there is a large gap in energy beforethe next possible level is encountered.The elements in the first column of the periodic table are called the alkalimetals and are highly active chemically. Referring to Table 28.4, we can understandwhy these elements interact so strongly with other elements. All of these alkali}
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An Abbreviated Table of Isotopes A.
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Some Useful Tables A.15TABLE C.3The
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Current, 568-573, 586direction of,
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PHYSICAL CONSTANTSQuantity Symbol V