Part of JPC-07 — Atomic Structure: Quantum Numbers & Electronic Config

Hund's Rule and Pauli Principle

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Pauli exclusion principle: no two electrons have the same set of all four quantum numbers. Consequence: maximum 2 electrons per orbital (with opposite spins). Hund's rule of maximum multiplicity: in degenerate orbitals (same subshell), electrons occupy each orbital singly (all parallel spins) before pairing begins. This minimises electron-electron repulsion and maximises exchange energy. Exchange energy: a stabilisation that occurs when electrons with parallel spins are in different degenerate orbitals. Number of exchange pairs = nC2 = nn12\frac{n-1}{2}, where n = number of parallel spin electrons. Half-filled (d5d^5, f7f^7) and fully-filled (d10d^{10}, f14f^{14}) subshells have maximum exchange energy, contributing to extra stability.

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