Frequency of Oscillation of a Molecule

[dm9292]

Homework Statement

Show that the frequency of oscillation, v, of a molecule is related to the form of the inter - atomic potential V(r) about the equilibrium separation, r =r_o by the expression,

v = (1/2pi).sqrt([d²V/dr²_r=ro/(m)])

where m is the reduced mass

Homework Equations

None given

The Attempt at a Solution

I really don't know where to start it was set as a 'challenge question' in a book i have borrowed.

I was thinking the second derivative had something to do with the spring constant. Or it maybe involved the Morse or Leonard Jones Potential. The thing is I don't know how to relate any of these things.

Is the term in square roots the frequency? I.e based on the formula w= 2piv

 

[diazona]

hmmm...
$$\nu = \frac{1}{2\pi}\sqrt{\frac{1}{m}\left.\frac{\mathrm{d}^2V}{\mathrm{d}r^2}\right|_{r=r_0}}$$
yep,
$$2\pi\nu = \omega$$
You're on the right track to think about the spring constant. As a first step, try writing a Taylor series for the potential around the point r_0.

 

[dm9292]

Thanks