1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Small Oscillations

  1. Sep 18, 2006 #1
    Estimate the spring constant in units of eV/A^2 for the hydrogen (H2) molecule from the potential energy curve shown below, where r is the distance between protons. From the spring constant and the reduced mass m=1/2m(proton), compute the vibrational frequency. This frequency corresponds to infrared light.


    I tried approximating using V(x)~=V(xe)+1/2k(x-xe)^2 , but i end up with an imaginary term for k. I also tried various other things.. to many to list. but any help would be great!

    (correct answer: "approximate V(r) near r=0.74A by V(r)= 1/2k(r-.74)^2 - 4.52eV with k~=47eV/A^2. Freq.(vib)=1/(2pi)*sqrt(2k/m(proton))=1.5e4Hz)
  2. jcsd
  3. Sep 19, 2006 #2
    hmm, well I am not a homework helper so take my advice with a grain of salt (I am just a sophmore physics major). I had a question very similiar to this recently. The effective spring constant is equivolent to the second deriviative of the potential curve evaluated at the minimum point in the potential curve, presumably where the proton will be oscilating. For this curve, at the .74 angstoms. So, were not talking about the Taylor expansion of the entire curve, just the second derivative term.

    Further, [tex]w= \sqrt{ \frac{k_{eff}}{m}}[/tex], thus [tex]v= {2}{pi}^{-1} \sqrt{ \frac{k_{eff}}{m}}[/tex] where m=1/2m
    Last edited: Sep 20, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Small Oscillations
  1. Small oscillations (Replies: 2)

  2. Small Oscillations (Replies: 3)

  3. Small Oscillations (Replies: 16)