Q14(a). Non-degenerate and six-fold levels in a cubic box
For a particle confined at constant potential within a cubic box, determine the quantum numbers of (i) the lowest excited state that is not degenerate (2 marks); (ii) the lowest energy level with a degeneracy of 6 (3 marks).
Answer in brief
(i) (nx, ny, nz) = (2, 2, 2), E = 12h²/8mL²; (ii) (1, 2, 3) and its permutations, E = 14h²/8mL², g = 6.
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Coversparticle in a 3-D boxcubic boxdegeneracyquantum numbersenergy levels
All parts of Question 14
- 14(a) Non-degenerate and six-fold levels in a cubic box5 marks
- 14(b) Energies of the two levels for a 0.5 nm box5 marks
- 14(c) Wavelength of the (2,2,2)–(1,2,3) transition5 marks
- 14(d) Quantum efficiency in the uranyl oxalate actinometer5 marks