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Mathematics for Physics

95 Aufbau Principle

A systematic rule that is used to build the ground-state electron configuration of an atom by filling subshells in order of increasing energy, where a subshell is the set of orbitals sharing \(n\) and \(\ell\).

Lowest-energy filling. Electrons occupy the lowest available subshells first. This principle is used to write the ground configuration from hydrogen through the heavier atoms.

The \(n+\ell\) order. The usual filling order follows increasing \(n+\ell\), and for equal \(n+\ell\) the smaller \(n\) fills first. This principle is used to remember the sequence \(1s\), \(2s\), \(2p\), \(3s\), \(3p\), \(4s\), \(3d\).

The two-electron orbital capacity. Each orbital holds at most two electrons of opposite spin. This principle is used together with the Pauli principle to stop filling a subshell when it is full.

Note: Aufbau is German for building up.

95.1 References

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