A particle in three dimensional cubic box of length L has energy of (14 h²)/(8 mL²). The degeneracy of the state is

Q84 · CSIR-NET Chemistry, June 2012

Paper: CSIR-NET June 2012 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Particle In A Box · Marks: 2 · Difficulty: Medium

A particle in three dimensional cubic box of length L has energy of $\frac{14 \mathrm{h}^{2}}{8 \mathrm{mL}^{2}}$. The degeneracy of the state is

(a)2

(b)3

(c)6

(d)9

Answer

Answer: C ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation

nx² + ny² + nz² = 14 = 1 + 4 + 9. The permutations of (1, 2, 3) give 6 states (c).

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