How To Get More from Ionization Energies in the Teaching of Atomic Structure Paolo Mirone University of Modena, 41 100 Modena, Italy
An element of atomic number Z displays Z progressive ionization energies. T h e whole set of such energies is known for each of t h e first 20 elements, and many of them are known for t h e next 20, resulting in more than 450 values. This wealth of experimental data could be exploited more extensively and profitably than is done a t present in t h e teaching of atomic structure, provided t h a t a suitable graphical presentation is adopted. Plotting the square roots of ionization energies a s functions of Z yields a graph showing several interesting features: 1. Ionization energies group into "bands" separated one from an-
other by a gap large with respect to the mean energy of the lower band (Fig. 1).The regular increase of the ionization energy of a given element within a hand is readily explained, at least to afirst approximation, as the consequence of decreasingscreening of the nuclear charge bv the remainina electrons (or, in other words, as the result of&&easine interele&nic re~ulsions).On the other hand, the large gap between two successive PCjds can only be explained if the electrons located in the uppei band are substantially nearer to the nucleus. Thus the shell model for the electronic structure of atoms emerges quite plainly from the diagram of Figure 1. ~~~~
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Within a band, the interval separating the two highest values from the lower ones is somewhat larger than the nearby intervals (see also Fig. 2). This shows that there is agmup of twoelectrons (s electrons) that are bound somewhat mare strongly than the others (p electrons). The hand beeinnine with ~otassium(Z= 19)contains 12 values in correrpondenee with zinc (Z = 30). However, heginning uith zinc, the gap separatmg the LO highe~tvalue$ from the lower onen begins t u rise with increasing atomic number. In spite uf the incompleteness of data, it appears that there is a group of 10 electrons (d electrons) with ionization energies placing themselves between those of 3p and 4s electrons. 4. A slightly larger interval hetween the ionization energies of the third and fourth p electrons (and of the fifth and sixth d electrons) marks the disappearance of the el&etrostatic repulsion between two electrons occupying the same orhital, in agreement with Hund's rule of maximum multiplicity (see also Fig. 2). 5. For a aiven isoeleetronie series (for example Na, Ma+. AIZ+,. . .) the plot of the square root of the ionization energy isremarkably linear with Z, in fair agreement with the equation: ~
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Ei),= ("R
z-S
~
2
Screening Constants and Effective Prlnclpal QuantumNumbers tor Some lsoelectronic Series
First termof the series
He
LI
Ne
Na
Ar
Sc2+
(He)2s22pe 10 7.28 1.938
(Ne)3s 11 8.85 2.854
(Ne)3s23p6
(Ar) 3d
Electron configuration Number of electrons
15'
(He) 2s
2
S n'
0.65 0.997
3 1.70 1.983
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Journal of Chemical Education
IS
14.60 2.709
19 17.26 2.643
Cut
(Ar) 3dX0
28 25.57 2.527
Cu (Ar) 3d1°4s
29 26.22 3.234
Figure 1. Known ioniratlon energlasol tna first39 elements (ianlzaton ensrg ea of lsslecbonsars r;noun uplo Z = 201. Dam taken fromhendbook of ChemWand P h y b i ~65th ~ . ed :Weast. R. C.: Astls. M. J . : Bew, W. H.. Eds: CRC: Boca Raton, FL. 1984; 0 E-65. hased on the one-electron approximation,' where RH = 1312.0 kJ mol-I is the ionization energy of the hydrogen atom, S is a screening constant, and n* is an effective quantum number. The table reports the values of S and n* obtained for a few "borderline" isoeleetranic series by fitting E!I2 to the square root of the above equation. The results are in good agreement with those obtained by Agmon2through a fit of E,lZ2 to the same equation divided by ZZ. Besides demonstrating the shell structure of atoms, the graph of Figure 1 illustrates a number of subtler features that could otherwise be derived only through sophisticated quantum-mechanical calculations or the analysis of complex spectra. Therefore, i t could afford a useful support, entirelv hased on exnerimental data, to the teaching of the --------. electronic structure bf atoms. At the undergraduate or advanced secondary level, the graph would complement, on the experimental side, the usual presentation of orbital theory. At a more elementaw level, where this sort of presentation is hound to he reduced to a set of dogmatic statements, the intelligent use of the graph would convey much of the information usually supplied through the so-called orbital model. Last hut not least, the graph of Figure 1shows the importance of interelectronic repulsions, a feature generally over. looked by naive treatments of atomic structure. ~~
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Acknowledgment
Financial support from Minister0 della Pubblica Istruzione, Rome, is acknowledged. 2
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Plmentel. G. C.; Spratley, R. D. Understanding Chemistry; Holden-Day: San Francisco. 1971; Chapter 13. Agmon, N. J. Chem. Educ. 1988,175.42-44.
10 12 14 Order of ionization
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Figure 2. Ionization energies of argon. Volume 66
Number 2
February 1991
133
