If one has a diatomic molecule with energy levels(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\epsilon_l = \frac{h^2 l(l+1)}{2I}

[/tex]

l = 0,1,2,3,4,5...

if the degneracy is given by [tex]g_l = (2l+1)[/tex]

How does one show that the Helmholtz free energy at low temperature ([tex]h^2/Ikt[/tex] large)

is given by

[tex]

F = -3kT e^{-h^2 / IkT} + ...

[/tex]

I got as far as getting the partition function to be

[tex]

Z = \sum_{l=0}^{\inf} (2l+1)e^{-h^2 l(l+1)/2IkT}

[/tex]

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# Free energy of a rotational system.

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