[CHM 331] Vibrational and Rotational Population Equations

[Andrew J. Pounds]

You might find these helpful... its sometimes hard to find these 
relating populations back to spectroscopic constants you can easily look 
up in a table...

For rotational levels the fraction $N_J/N_0$, which is the relative 
population of rotational levels above the ground state can be 
represented as...

$\frac{N_J}{N_0} = (2J+1) e^{-hcJ(J+1)\tilde{B}/kT}$

When I use this equation by hand I generally compute the quantity 
$hc\tilde{B}/kT$ and store it in the memory of my calculator for rapid 
recall.  I also, as you might have guessed, tend to use CGS units in my 
calculations so I can just pull everything in directly from the tables 
without converting.  You do what works best for you.


Similarly, for vibrational levels you can use

$f_i = (1-e^{-hc\tilde{\nu}/kT})e^{-ihc\tilde{\nu}/kT}$

and here I precompute the term $hc\tilde{\nu}/kT$ for rapid recall.



-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Mercer University,  Macon, GA 31207   (478) 301-5627
http://faculty.mercer.edu/pounds_aj

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