Step 1:
The energy levels of an electron in a three-dimensional cubical box are given by the equation:
\[E_{n_X n_Y n_Z} = \frac{n_X^2 + n_Y^2 + n_Z^2}{2} \frac{h^2}{8mL^2}\]
where \(n_X\), \(n_Y\), and \(n_Z\) are the quantum numbers, \(h\) is Planck's constant,
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