Calculate the maximum number of possible exchange pairs for the electrons present in the half-filled — Atomic Structure Chemistry Question

💡 Solution & Explanation

Chromium ($Z=24$) has an anomalous ground-state configuration to maximize exchange energy: $[Ar] 4s^1 3d^5$. The $3d$ subshell contains exactly $5$ unpaired electrons with parallel spins. The number of possible exchange pairs for $n$ electrons with parallel spins residing in degenerate orbitals is given by the combination formula $\frac{n(n-1)}{2}$. For the $5$ electrons in the $3d$ subshell, $n=5$. Therefore, the number of exchange pairs is $\frac{5 \times (5-1)}{2} = \frac{5 \times 4}{2} = \frac{20}{2} = 10$.