In hydrogen: energy depends only on n (all subshells degenerate). In multi-electron atoms: energy depends on both n and l. For same n: s < p < d < f (s electrons are closer to nucleus, experience less shielding). Shielding (screening): inner electrons partially block the nuclear charge from outer electrons. = Z - sigma. Penetration: s orbital has the highest probability near the nucleus, followed by p, d, f. Greater penetration means less shielding and lower energy. This explains why 4s fills before 3d despite having higher n: 4s has greater penetration (lower energy in neutral atoms). However, in transition metal cations, 3d is lower in energy than 4s (shielding changes), so 4s electrons ionise first.
Part of JPC-07 — Atomic Structure: Quantum Numbers & Electronic Config
Orbital Energies in Multi-Electron Atoms
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