JEE Main 2025 Apr 7 Shift 2, Chemistry Q18: Quantum Numbers

Origin of half-filled subshell stability:

(A) Symmetrical distribution — Correct.
Electrons occupy every orbital of the subshell singly (e.g. $3d^5$: one electron in each of the five d orbitals), giving a symmetric charge cloud.

(B) Smaller coulombic repulsion — Correct.
Single occupancy keeps electrons in separate orbitals, minimising electron-electron repulsion compared to paired configurations.

(C) Electrons with same spin in non-degenerate orbitals — Incorrect.
The orbitals of a subshell (three p, five d, seven f) are degenerate, not non-degenerate. Hund's rule requires parallel spins in degenerate orbitals, so this statement misidentifies the underlying condition.

(D) Larger exchange energy — Correct.
Electrons with parallel spins in different degenerate orbitals can exchange positions. Each such exchange releases stabilisation energy $K$; a half-filled subshell maximises the number of parallel-spin pairs, giving the maximum exchange energy.

(E) Smaller mutual shielding — Correct.
Electrons in different orbitals of the same subshell shield each other less effectively than paired electrons, so each experiences a larger effective nuclear charge $Z_{\text{eff}}$, adding to stability.

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$\therefore$ Correct statements: (A), (B), (D) and (E).