JEE Main · 2025 · 22 Jan 2025 · Shift 2 · Atomic Structure

Niobium (Z = 41) is an Aufbau exception: instead of the naively expected $[\mathrm{Kr}]4d^{3}5s^2$, it adopts $[\mathrm{Kr}]4d^{4}5s^1$, because shifting one 5s electron into the 4d subshell gives a more stable, closer-to-half-filled d configuration. Niobium therefore has $x=4$ electrons in 4d.

Ruthenium (Z = 44) is likewise anomalous: instead of $[\mathrm{Kr}]4d^{6}5s^2$, it settles as $[\mathrm{Kr}]4d^{7}5s^1$, again trading a 5s electron for extra d-subshell stability. Ruthenium therefore has $y=7$ electrons in 4d.

$x+y=4+7=11$.