Chapter 3, Problem 3J.15E

Interpretation Introduction

Interpretation:

The energies for three lowest levels in cubic box have to be calculated. Whether energy levels are degenerate or not and if they are degenerate then the quantum numbers related to it has to be calculated.

Concept Introduction:

The formula to calculate energy of the $3\text{-D}$ box is as follows:

  $E=\frac{h^2}{8m_e{L}^2}\left(n_x^2+n_y^2+n_z^2\right)$        (1)

Here,

$m_e$ is mass of electron.

$L$ is length of cube.

$h$ is Plank’s constant.

$n_x$, $n_y$ and $n_z$ are the quantum numbers.

Degeneracy is defined as two or more quantum states present in a quantized energy level. For example, d orbital has five degeneracies as it contains five orbitals of similar energies.