# Small Oscillations

1. Sep 18, 2006

### GreenLRan

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. Sep 19, 2006

### silverdiesel

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, $$w= \sqrt{ \frac{k_{eff}}{m}}$$, thus $$v= {2}{pi}^{-1} \sqrt{ \frac{k_{eff}}{m}}$$ where m=1/2m

Last edited: Sep 20, 2006