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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...<br>
<br>
For rotational levels the fraction <img style="vertical-align:
middle" src="cid:part1.02090907.03010500@mercer.edu"
alt="$N_J/N_0$">, which is the relative population of rotational
levels above the ground state can be represented as...<br>
<br>
<img style="vertical-align: middle"
src="cid:part2.01030201.08000501@mercer.edu" alt="$\frac{N_J}{N_0}
= (2J+1) e^{-hcJ(J+1)\tilde{B}/kT}$"><br>
<br>
When I use this equation by hand I generally compute the quantity <img
style="vertical-align: middle"
src="cid:part3.00090606.06000300@mercer.edu"
alt="$hc\tilde{B}/kT$"> 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.<br>
<br>
<br>
Similarly, for vibrational levels you can use<br>
<br>
<img style="vertical-align: middle"
src="cid:part4.00040400.08050405@mercer.edu" alt="$f_i =
(1-e^{-hc\tilde{\nu}/kT})e^{-ihc\tilde{\nu}/kT}$"><br>
<br>
and here I precompute the term <img style="vertical-align: middle"
src="cid:part5.02060906.04040201@mercer.edu"
alt="$hc\tilde{\nu}/kT$"> for rapid recall.<br>
<br>
<br>
<br>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
<a class="moz-txt-link-freetext" href="http://faculty.mercer.edu/pounds_aj">http://faculty.mercer.edu/pounds_aj</a>
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