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Mathematics for Physics

116 Electron Configurations

A representation of how electrons are distributed among the allowed shells, subshells, and quantum states of an atom that is used to write the ground-state occupation of an atom.

The configuration notation. A configuration lists the occupied subshells with their electron counts, as in \(1s^{2}2s^{2}2p^{6}\). A subshell is the set of orbitals sharing \(n\) and \(\ell\). This principle is used to summarize the Pauli filling of an atom.

Subshell capacity. Each subshell holds at most \(2(2\ell+1)\) electrons. This principle is used to close the \(s\), \(p\), \(d\), and \(f\) blocks.

The subshell capacity is

\[ N_{\ell} = 2(2\ell+1) \]

where

  • \(N_{\ell}\) is the maximum number of electrons in the subshell.
  • \(\ell\) is the orbital quantum number.

Construction by Aufbau and Hund’s rule. The configuration is built by the Aufbau order and by Hund’s rule. This principle is used to write the ground configuration before spectroscopic terms.

116.1 References

  1. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — electron configurations.
  2. Atkins, P., de Paula, J., & Keeler, J. Atkins’ Physical Chemistry. — atomic configurations.