A quantum-mechanical particle of mass m is contained within a three-dimensional box with all sides of the same length L. What is the degeneracy of the level with energy 9h² / 8mL²? A) 9 B) 2 C) 1 D) 6

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Quizplus · Accepted Answer

The energy levels of a particle in a 3D box are given by E = (h^2/8mL^2)(n_x^2 + n_y^2 + n_z^2). For the energy level 9h^2/8mL^2, the possible combinations of (n_x, n_y, n_z) that satisfy n_x^2 + n_y^2 + n_z^2 = 9 are (1, 1, 3), (1, 3, 1), (3, 1, 1), (1, 2, 2), (2, 1, 2), and (2, 2, 1), giving a degeneracy of 6.

A Quantum-Mechanical Particle of Mass M Is Contained Within a Three-Dimensional