Madelung Rule Exceptions — 3d Transition Metals
Exchange energy drives Cr and Cu away from naive aufbau predictions. Adjust K to see the threshold.
K (exchange integral):
0.18 eV
K = 0 → no exceptions | K = 0.18 eV → Cr + Cu exceptions
Energy Analysis (promote one 4s → 3d)
Exchange gain
ΔN
pairs
× K
—
3d–4s gap
(promotion cost)
—
—
Electron Configuration
—
—
Z = —
Physics checks