Why does the 4s subshell fill before the 3d subshell?

• Raising n raises orbital energy. Electrons are attracted to the nucleus. To pull an electron farther away from the nucleus, you have to work against that attraction. That means an electron farther from the nucleus has more energy than electron closer in; energy is required to move the electron out, and energy can be released when the electron moves in. So we expect outer shells to have higher energies than inner shells, because increasing n increases the average distance between the nucleus and the electron.

  For atoms heavier than copper this effect dominates, and 4s electrons have higher energy than 3d electrons.

• Raising l raises orbital energy. Higher l values result in orbitals with more nuclear nodes (a node being a place where the probability of finding the electron is zero). We say high-l orbitals are "less penetrating" because their electrons have a lower probability of being found at or near the nucleus. That gives high-l orbitals (like d orbitals) more energy than low-l orbitals (like s orbitals) within the same shell.

  This effect causes 4s orbitals to have lower energy than 3d orbitals for elements lighter than copper. (Although for hydrogen, the unoccupied 4s and 3d orbitals have nearly identical energies).

• Within a subshell, more unpaired spins means a lower overall energy. Quantum mechanics predicts that the motions of electrons with paired spins are "correlated". Paired electrons move together, while electrons with unpaired spins can stay farther away from each other on average. Since electrons repel each other, paired electrons have more energy than unpaired electrons, all other things being equal. This spin correlation effect explains why Cr has a [Ar] 4s¹3d⁵ configuration rather than a [Ar]4s²3d⁴ configuration- the former has more unpaired electron interactions than the latter.

Author: Fred Senese senese@antoine.frostburg.edu