In a similar vein as Problem 16.4, derive in detail the rotational partition function given by Eq. (16.39)

\[\begin{equation*}
Q_{\mathrm{rot}}=\frac{8 \pi^{2} I k T}{h^{2}} \tag{16.39}
\end{equation*}\]

Data From Problem 16.4:

Starting with the quantum mechanical expression for the quantized translational energy levels as a function of the quantum numbers \(n_{1}, n_{2}\), and \(n_{3}\), derive in detail the translational partition function given by Eq. (16.38).

\[\begin{equation*}
Q_{\text {trans }}=\left(\frac{2 \pi m k T}{h^{2}}\right)^{3 / 2} V \tag{16.38}
\end{equation*}\]