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Frequency of Oscillation of a Molecule

  1. May 26, 2009 #1
    1. The problem statement, all variables and given/known data

    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 =ro by the expression,

    v = (1/2pi).sqrt([d2V/dr2r=ro/(m)])

    where m is the reduced mass

    2. Relevant equations

    None given

    3. 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
     
  2. jcsd
  3. May 26, 2009 #2

    diazona

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    Homework Helper

    hmmm...
    [tex]\nu = \frac{1}{2\pi}\sqrt{\frac{1}{m}\left.\frac{\mathrm{d}^2V}{\mathrm{d}r^2}\right|_{r=r_0}}[/tex]
    yep,
    [tex]2\pi\nu = \omega[/tex]
    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.
     
  4. May 28, 2009 #3
    Thanks
     
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