Q73 · CSIR-NET Chemistry, June 2016

Paper: CSIR-NET June 2016 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Marks: 2 · Difficulty: Medium

For a particle of mass $m$ confined in a rectangular box with sides 2 a and a , the energy and degeneracy of the first excited state, respectively, are

(a)$\frac{\mathrm{h}^{2}}{8 \mathrm{m}}\left(\frac{2}{\mathrm{a}^{2}}\right), 1$

(b)$\frac{\mathrm{h}^{2}}{8 \mathrm{m}}\left(\frac{17}{4 \mathrm{a}^{2}}\right), 2$

(c)$\frac{\mathrm{h}^{2}}{8 \mathrm{m}}\left(\frac{5}{4 \mathrm{a}^{2}}\right), 1$

(d)$\frac{\mathrm{h}^{2}}{8 \mathrm{m}}\left(\frac{5}{\mathrm{a}^{2}}\right), 2$

Answer

Answer: A ✓ checked by 4AB · confidence medium

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

Explanation

E = (h²/8m)(n_x²/4a² + n_y²/a²). Ground (1,1): 5h²/32ma². First excited (2,1): (1/a² + 1/a²) → 2h²/8ma² = h²/4ma², non-degenerate (the (1,2) level, 17h²/32ma², lies higher).

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