Step 1:
The density of states is given by the formula:
\[ g(E) = \frac{V}{2\pi^2} \left(\frac{2m_e}{\hbar^2}\right)^{3/2} E^{1/2} \]
where \(V\) is the volume, \(m_e\) is the mass of the electron, \(\hbar\) is the reduced Planck's constant, and \(E\) is the
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