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<p><font face="serif">Okay -- so now some of the genius of using the
units of reciprocal meters for the energy axis will show up.
Convert your vibrational energies that are in reciprocal cm to
reciprocal meters by multiplying them by 100. So for hydrogen
you will convert 4401 cm-1 to 440100 m-1.</font></p>
<p><font face="serif">Divide this by 2 to get 220050 m-1. That is
your lowest vibrational energy level. Add 440100 to it to get
660150, that's your next energy level. Do that three more times
to complete the diagram for the lowest five energy levels within
the harmonic approximation.<br>
</font></p>
<p>Because the Morse potential has a minimum at zero, you can then
just draw in those energy levels at the appropriate locations in
your wells using the energy scale on the y-axis as your guide.<br>
</p>
If your're wondering why I can do this think about it this way. <br>
<br>
We use wavenumbers to represent energy because they are proportional
to energy -- with the constants of proportionality being Planck's
constant and the speed of light.<br>
<br>
<img style="vertical-align: middle"
src="cid:part1.0222AFDA.7CCEFE1D@mercer.edu" alt="$E = h\nu =
hc\tilde{\nu}$"><br>
<br>
<img style="vertical-align: middle"
src="cid:part2.EEB7634F.BDC8821C@mercer.edu"
alt="$\tilde{\nu}=\frac{E}{hc}$"><br>
<br>
I could have done this entire exercise with Joules or Ergs on the
Y-Axis, but then you would have had to slog through a whole
different set of problems related to scaling items on your graph
with scientific notation involved in the axis labels. I've never
seen that work out well for students...<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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