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The Chemical Educator

ISSN: 1430-4171 (electronic version)

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Abstract Volume 14 Issue 6 (2009) pp 255-257

Term Symbols and Hydrogen Atom Degeneracy

David Keeports

Department of Chemistry and Physics, Mills College, 5000 MacArthur Boulevard, Oakland, CA 94613, dave@mills.edu
Received April 21, 2009. Accepted September 2, 2009.

Published online: 31 December 2009

Abstract. At the level of a general chemistry course, electrons in atoms possess four quantum numbers n, l, ml, and ms. For the hydrogen atom, energy depends only upon the principle quantum number n. Restrictions upon quantum numbers lead to a 2n2-fold degeneracy formula for a particular n. However, in a physical chemistry class, a more realistic and complete picture of atomic quantum numbers, energies, and degeneracy emerges. Spectroscopic terms characterizing atomic angular momentum are introduced. It is recognized that due to spin-orbit interaction in the hydrogen atom, ml and ms are no longer valid quantum numbers, and the existence of three new quantum numbers, s, j and mj, is acknowledged. Precise spectroscopic data shows that a hydrogen atomís energy is no longer a function of n alone when n > 1. Presented here is an argument based upon term symbols showing that while 2n2 is not the correct degeneracy formula for the hydrogen atom, it is in fact the number of distinct hydrogenic states consistent with a given n. The purpose of this article is to reconcile the general chemistry approach to the problem of hydrogen atom degeneracy with the physical chemistry approach. I write this article from the perspective of an instructor of physical chemistry whose students are sometimes puzzled by the seeming inconsistency of their general chemistry and physical chemistry courses with regard to the question of hydrogen atom degeneracy.

Key Words: In the Classroom; physical chemistry; general chemistry

(*) Corresponding author. (E-mail: dave@mills.edu)

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Issue date: Dec 31, 2009

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