[CHM 331] Problem 18.34

[Andrew J. Pounds]

So I said I would send some help for problem 34.  Part "a" is pretty 
straight forward -- you just use the same eigenvalue equations you used 
before to calculate enegies. Part "b" is much more interesting -- how 
many times does the molecule rotate in one vibrational period.

Start off by calculating the period for the rotation.  A few equations 
are helpful here...

$E_\mathrm{rot}=\frac{1}{2}I\omega^2$

$\omega=2 \pi \nu = \frac{2 \pi}{T_{\mathrm{rot}}}$

where $T_{\marthrm{rot}}$ is the period of the rotation.

After some work I got that to be on the order of $10^{-13}$ s.


For vibration...

$T_{\mathrm{vib}}=\frac{1}{\nu} = 2 \pi \sqrt{\frac{\mu}{k}}$

Plugging in the correct constants and atomic parameters here results in 
a value around $10^{-14}$ s.


What does that mean?  It means that for every time the molecule rotates 
it is vibrating at least 10 times.  Try to picture that in your head!

Keep the questions coming and see you in the morning.

-- 
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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