Explain the reason for exceptional electronic configuration of copper and chromium.

The exceptional electronic configurations of copper (Cu) and chromium (Cr) can be explained by considering their electron configurations in the ground state and the stability gained by achieving a half-filled or fully-filled d subshell.

Copper (Cu):
In the ground state, the electron configuration of copper is [Ar] 3d^10 4s^1. The expected electron configuration based on the Aufbau principle would be [Ar] 3d^9 4s^2. However, copper exhibits an exceptional configuration by promoting one electron from the 4s orbital to the 3d orbital, resulting in a half-filled 3d subshell (3d^10) and a completely filled 4s subshell (4s^0). This arrangement is energetically favorable due to the increased stability resulting from the half-filled or fully-filled subshells.
The exceptional electronic configuration of copper is attributed to the relatively low energy difference between the 3d and 4s orbitals. The 3d orbitals have a higher effective nuclear charge and are closer to the nucleus, making them more stable compared to the 4s orbital. By promoting one electron from the 4s orbital to the 3d orbital, the overall energy of the system is minimized.

Chromium (Cr):
The ground state electron configuration of chromium is [Ar] 3d^5 4s^1. Similar to copper, chromium exhibits an exceptional electronic configuration to achieve a more stable arrangement. Instead of forming an expected configuration of [Ar] 3d^4 4s^2, one electron is promoted from the 4s orbital to the 3d orbital. This results in a half-filled 3d subshell (3d^5) and a partially filled 4s subshell (4s^1).
The exceptional electronic configuration of chromium can be explained by Hund's rule and the exchange energy concept. According to Hund's rule, electrons prefer to occupy different orbitals within the same subshell before pairing up in a single orbital. By having five unpaired electrons in the 3d subshell, chromium maximizes the number of unpaired electrons, which leads to a lower overall energy due to favorable electron-electron repulsions. Additionally, the exchange energy, arising from the alignment of electron spins, contributes to the stability of the half-filled configuration.

In summary, the exceptional electronic configurations of copper and chromium can be explained by the stability gained through achieving a half-filled or fully-filled d subshell. The relatively low energy difference between the 3d and 4s orbitals allows for electron promotion, leading to the observed configurations.