Electron Configuration of Multielectron Atoms

The Pauli exclusion principle, Hund’s rule of maximum multiplicity, and the aufbau principle can be extended to envisage the electron configuration of any element.

Consider writing the electron configuration for sodium. The core electron distribution in sodium is exactly that of the preceding element, neon. The single valence electron occupies the 3s orbital.

Neon belongs to the eighteenth column of the periodic table — the noble gases. The electron configurations of these elements facilitate the condensed depiction of the electron configuration for other elements. For any element, the core electron configuration is the same as that of the noble gas that precedes it in the periodic table.

The electron configuration of sodium, for example, can be written as neon core, 3s¹.

The core electron configuration of potassium is 1s² 2s² 2p⁶ 3s² 3p⁶, leaving one valence electron. Now, does the nineteenth electron enter the 3d subshell? 

Recall that the 4s subshell has substantial penetrating ability, which often leads to it having a lower energy than the 3d subshell does. The aufbau principle, therefore, would hold that the 4s subshell fills prior to the 3d subshell. The core of the preceding noble gas, argon, is used to write the condensed configuration.

Although these principles provide a starting point, the actual electron configurations must be confirmed experimentally. In several elements among the transition elements, lanthanides, and actinides, the orbital energies are in a different relative order, and the aufbau principle may not be completely followed.

In the transition elements, the 3d and 4s subshells have similar energies. The 4s subshell is often filled completely. For example, in scandium, the electron configuration is argon core, 4s² 3d¹. In zinc, the 4s and 3d subshells are filled to their maximum capacities.

However, the ground states of some metals, such as chromium and copper, have singly occupied 4s orbitals. Chromium is particularly notable because two subshells are partially filled, which deviates from the aufbau principle.
Across the lanthanide series, extending through cerium to lutetium, the 6s and 4f subshells have similar energies. The electron configuration for neodymium is xenon core, 6s² 4f⁴. 

Meanwhile, cerium has an unusual electron configuration of xenon core, 6s² 4f¹ 5d¹ because its 6s, 4f, and 5d subshells are unusually close in energy.