# Boltzmann distribution!

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

$$E(J) = J(J+1)*h^2/8*pi^2*I$$

, 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:

$$E= (n+1/2)*h*f$$

where $$2*pi*f = root (k/u)$$

, 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!

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