Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Boltzmann distribution!

  1. May 20, 2006 #1
    Hi all,

    can anyone see what is going wrong in the following problem please (this is really important, so if you have any hints that would be fantastic!)

    The restoring force corresponding to a change in length of the bnd between Hydrogen atoms in H2 is k = 2400 N/m, find the fraction of molecules at room temperature in the first vibrational state.

    Now, the energy levels for rotational motion are

    [tex] E(J) = J(J+1)*h^2/8*pi^2*I [/tex]

    , where I = 0.5md^2

    for the ground state J= 0 and

    E(0) = 1.22*10^(-21)J

    similarly E(1) = 2.44*10^(-21)J

    which is 9 times degenerate

    For the first vibrational energy level we have:

    [tex] E= (n+1/2)*h*f [/tex]

    where [tex] 2*pi*f = root (k/u) [/tex]

    , where u is the reduced mass

    now taking n to be 1, I get an energy of 2.69 * 10(-19)J

    putting that in the formula for the Boltzmann distribution I do not get the desired result of e^^(-44). I am pretty certain that the error lies in the first vibrational energy state - can anyone see what is wrong here? That would be really helpful!
    Last edited: May 20, 2006
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted