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Appendix E - More on electronic configurations and electronic states: degenerate orbitals and the Pauli principle

Published online by Cambridge University Press:  05 June 2012

Andrew M. Ellis
Affiliation:
University of Leicester
Miklos Feher
Affiliation:
Neurocrine Biosciences, San Diego
Timothy G. Wright
Affiliation:
University of Nottingham
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Summary

The Pauli exclusion principle states that no two electrons in an atom or molecule can share entirely the same set of quantum numbers. This requirement follows from the nature of electronic wavefunctions, which must be antisymmetric with respect to the exchange of any identical electrons. This has an impact in the determination of the electronic states possible from a given electronic configuration.

Atoms

Consider, for example, the carbon atom, which has a ground electronic configuration 1s22s22p2. Suppose that one of the 2p electrons is excited to a 3p orbital. To determine the electronic states that are possible from this configuration, the process described in Section 4.1 can be followed. The 1s and 2s orbitals are full and so we can focus on the p electrons only. The possible values of the total orbital angular momentum quantum number L are 2, 1 or 0. Similarly, the total spin quantum number must be 1 or 0 and so the possible electronic states that result from the 1s22s22p13p1 configuration are 3D, 1D, 3P, 1P, 3S, and 1S. It is therefore initially tempting to propose that electronic states of the same spatial and spin symmetry arise from the ground electronic configuration. Such an assumption would be wrong because it ignores the Pauli principle.

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Electronic and Photoelectron Spectroscopy
Fundamentals and Case Studies
, pp. 266 - 268
Publisher: Cambridge University Press
Print publication year: 2005

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