[CHM 331] Energy Levels on Morse Plots

[Andrew J. Pounds]

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.

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.

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.

If your're wondering why I can do this think about it this way.

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.

$E = h\nu = hc\tilde{\nu}$

$\tilde{\nu}=\frac{E}{hc}$

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...


-- 
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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