Equilibrium Statistical Distribution of Diatomic Molecules over Vibrational-Rotational States

Equilibrium Statistical Distribution of Diatomic Molecules over Vibrational-Rotational States 

Assuming the vibrational energy of diatomic molecules with respect to ground state (w = 0) is = hcov the number density of molecules with v vibrational quanta according to (3-9) is 

The total number density of molecules, N, is a sum of densities in different vibrational states (w)  

Distribution (3-10) can then be renormalized with respect to the total number density N  

To find the Boltzmann vibrational-rotational distribution N j(J2j N j = A ), we can use again general relation (3-9), taking rotational energy as Ar = BJ J - -1) and 

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