Question

# The electron configuration for chromium is $\left[ Ar \right]4{{s}^{1}}\text{ }3{{d}^{5}}$. Select the best explanation for this irregular electron configuration. A. A half-filled d orbital is slightly lower in energy than the 4s, thus filling first. B. The 4s orbital is at a lower energy than the 3d orbital, thus filling first. C. Chromium is a transition metal and its electrons are loosely held. D. d orbitals are dominant and shield electrons from orbitals close in energy.

Hint: According to Hund’s principle which states that, when electron starts filling up subshells, they do it such that the electrons of the same spin must solely occupy the orbitals within the subshell first and then the electrons of opposite spin will start filling up the remaining space in the orbitals.

Fully-filled orbital $>$ half-filled orbital $>$ partially-filled orbital
So, in $4{{s}^{1}}\text{ }3{{d}^{5}}$we see that both the s and p orbitals are half-filled. In case of chromium, the expected electronic configuration is $4{{s}^{2}}\text{ }3{{d}^{4}}$, yet actually we see that one electron from 4s gets transferred to 3d orbital making it $4{{s}^{1}}\text{ }3{{d}^{5}}$. This happens because $4{{s}^{1}}\text{ }3{{d}^{5}}$ being a more stable configuration.
Electron orbitals are most stable when fully-filled or half-filled, hence the most stable configuration of electrons for 3d subshells is either $3{{d}^{10}}$or $3{{d}^{5}}$. In the case of chromium, after $4{{s}^{2}}\text{ }3{{d}^{4}}$ configuration is attained, and electron from s-orbital gets transferred to 3d subshell because $3{{d}^{5}}$ is much more stable configuration than $3{{d}^{4}}$. This is why the configuration for chromium is $4{{s}^{1}}\text{ }3{{d}^{5}}$.
$1s\text{ }<\text{ }2s\text{ }<\text{ }2p\text{ }<\text{ }3s\text{ }<\text{ }3p\text{ }<\text{ }4s\text{ }<\text{ }3d\text{ }<\text{ }4p$ and so on. Same results are seen in $Cu$ where the expected configuration is $[Ar]4{{s}^{2}}3{{d}^{9}}$ but the observed configuration is $[Ar]4{{s}^{1}}3{{d}^{10}}$