A Mnemonic Method for Assigning the Electronic Configurations of Atoms Nerea lza' and Manuel Gil Departamento de Quimica Fisica I, Facultad de Ciencias Quimicas, Universidad Complutense, Madrid 28040, Spain In a first-year general chemistry course, the study of electron configurations of isolated atoms is a basic topic (14).Besides the fundamental theories, students must learn how to build these confirnrrations. Thev must realize that the electron d i s t r i h ~ t i o ~ different in atomic orhitals occurs i n the Dresence of a decreasine order of nuelear-attraction energy. T h e consequence>f penetration a n d shielding is that the energies of the orbitals in a manyelectron atom in general lie in the order s < p < d < f for the same energy level (n). Furthermore, the order of occupation of the orbitals that leads to the ground-state configuration minimizes the total energy. Values of atomic-energy levels have been calculated (5, 6 ) as a function of the atomic number, and for the majority of the elements, several diagrams (7, 8) have shown the following order for electron occupation.
As an aid to memorizing this sequence, several devices and schemes have appeared in this Journal (9-18). Most of them are based on establishing one particular orbital arrangement, and subsequently filling the gaps by following the arrows according to a given rule. These methods fail to predict the exceptions to the filling order. A careful examination of the order illustrated above allows orbitals of sublevels to be grouped i n sets each of which is repeated once, except the 1s set. Thus, by simply memorizing these repeating orbital sets, the electronic configuration of any element can be determined. Steps of the Method This method can be applied to building configurations by following three rules. Allocate Atomic Orbitals to Repeating Sets. Every set, except the first, begins with a n s orbital and ends with a p orhital.
2s
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25
--
15-
-1s I 1
I
I
I
I
I
I
2
3
4
5
6
7
Principal Quantum Number, n Generalized energy-level diagram for atomic orbitals that shows the approximate sequence of energies and filling.
Comparison with energy diagrams (see t h e figure) clearly shows that this new arrangement of orbitals gives energy differences that are higher between orhital sets (4 and lower between the p orbital of each set and the rest of the orbitals in that set (4. Fill Each Subleuel.
Number Orbitals in Increasing Order of the Principal Quantum Numbel: If the set holds d orhitals, its energy level will he (n - I), where n has the value of the principle quantum number for the s and p orhitals in the same set. If the set holds f orbitals, its energy level will he (n - 21, where n has the initially established value. This rule was first formulated by Chiang and Tseng (19) and can be simplified by the form
which gives rise to 'Author lo whom corres~ondenceshould be addressed.
Beginning a t 1s with the maximum number of electrons allowed, continue filling until the Z value of the atomic number of the element is reached. For example, for hafnium or unnilpentium (Z = 1051,
I t should be noted that these orbital sets correspond to the periods of the periodic table. The observation of electronic configurations of all elements from the periodic table shows that all exceptions to the filling order correspond to electron switches among s, d, or f orbitals within the same set. These electron switches never occur among s, d, f, and p orhitals because the first three types of orbitals have similar energies, but the enerVolume 72 Number 11 November 1995
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gies of p orbitals are quite different (see the figure). So, there are no electron switches among orbitals from different sets because their energy differences are increased. The elements chromium (Z= 241, copper (Z= 291, rhodium (Z = 451, and silver (Z = 47) with the ground electronic configurations,
orbitals always appear in each set with higher energy and a greater gap than m the rest of the orbitals. The exceptional configurations are limited to elements whosevalenee shell e l e c t r o n s arein s. d. or f o r b i t a l s from the same orbital set. No alteration in filling order occurs while p orbitals are added to each orbital set.
Although it presents the same general limitation as similar methods, the ease and rapidity of the present method in the building of electronic configurations should he of considerable help to students.
Literature Cited are four exceptional configurations in the fourth and fifth periods of the periodic table. The other exceptions in these periods are 41Nb,4 2 M ~4,4 R ~and , "Pd.
Conclusion The improvement of our mnemonic device over other
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similar methods for ~redictineelectronic confieurations of elements is summarized below. It is n e c e s s a r y only to draw a linear diagram. When filled to c a p a c i t y , only the repeating orbital sets must be memorized in order to know directly the electronic configuration. Interest in the use of mnemonic devices in c h e m i c a l education has recently been reported (20). Orhital arrangement within these sets affords information an their relative energies ( e n e r g y d i f f e r e n c e s ) . Established orbital sets are separated by wide gaps of energy, and the p
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Journal of Chemical Education
~ o n s : ~ e w ~ a1989; r k , p 182. 4. Petrueci. R. H.Generoi Chemistry PrLnciples a n d Modern Applicotiona. 5th ed.; Maemillan: New York,1989; p 183. 5. Moore, C. E. Atomic Energy h u e i s ; Circular of the Natmnsl Bureau o f Standards 467, Washington. DC. 1949,Val. 1: 1952,Vol. 2: 1958,Vol. 3. 6. Herman, P.; Skillman, S. Atomic Structum Colcuioiions: PrenticeHall: Englewood Cliffs,NJ, 1963. 7. Latter, R. Phys Re". 1955.99.510. 8. Keller. R. N. J. Chem. Edue 1962.39.289. 9. Haka1a.R. W. J. Cham. Edue. 1948.25.229. 10. Simmons,L.M. J. Chem. Edue 1948.23.698. 11. Carpentel A K J. Chsm. Educ. 1993.60.562. 12. SfrongIl1,F. C. J. Chsm. Edue 1985.62.466: J Chpm Educ. 1959,36,3M. 13. Hovland. A. K J. Chsm. Educ 1986.63.607. 14. Grenda, S. C. J. Chem. Educ 1998.65.697. 15. Dsrsex J.A. J Clwm Educ. 1988,65,1036. 16. Mamens Osorio, H. yon: Goldschmidt, A. J. Chrm. Edue 1989.66.758. 17. Rieck. D. F. J. Chem. Educ. 1990,67,398. 18. Singh. R.;Dikshit,S. K J. Chum. E d u . 1991.68.396. 19. Chiane H..Ch.:Tseng, C h . 8 J. Chem. Educ. 1984.61.216. 20. Quig1ey.M. N. J Chem. Educ 1992,69,138.
