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Chapter 6: Q1E (page 1401)

For a particle in a three-dimensional cubical box, what is the degeneracy (number of different quantum states with the same energy) of the energy levels (a)3π2h2/2mL2and (b)9π2h2/2mL2?

Short Answer

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Step by step solution

01

Degeneracy

The term "degeneracy" refers to the existence of two or more distinct quantum states with the same energy.

In a cubical box with side L, the allowed energies for a particle of mass m are given by;


As a result, the degenerate states have the samevalue.

02

Degeneracy of the energy levels at 3π2h2/2mL2

(a) As, the given energy level;

On comparing the equations;


This is unique to the combination

Hence, this energy level has degeneracy=1.

03

Degeneracy of the energy levels at 9π2h2/2mL2

(b) As, the given energy level;


On comparing the equations;


This is unique to the combination


Hence, this energy level has degeneracy=3.

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