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!

Homework Help: Equipartition Theorem and Microscopic Motion

  1. Sep 5, 2012 #1
    1. The problem statement, all variables and given/known data
    What is the typical rotational frequency frot for a molecule like N2 at room temperature (25°C)? Assume that d for this molecule is 10-10m. Take the atomic mass of N2 to be mN2=4.65x10-26kg. You will need to account for rotations around two axes (not just one) to find the correct frequency.

    2. Relevant equations
    rms angular speed: ω=sqrt{(2kT)/(md2)}
    k=1.381x10-23 J/(molecule*K)

    3. The attempt at a solution
    For my first attempt, I plugged the given numbers into sqrt{(3kT)/(md2)}. I used 3 instead of 2 because I was accounting for the two different axes. I'm not sure if the was the correct way to go about it. Secondly, I divided the given mass by 2. Then, I divided my answer by 2pi.
  2. jcsd
  3. Sep 6, 2012 #2
    The formula you have is derived from equating [itex]\frac 1 2 kT[/itex] to rotational energy, which is [itex]\frac {J \omega^2} {2}[/itex], where [itex]J = \frac {md^2} {2}[/itex] is the moment of inertia of two masses m on a weightless rod d. But you have two degrees of freedom, so you must equate [itex]kT[/itex]. That means instead [itex]2kT[/itex] you have in the formula you must take [itex]4kT[/itex], not [itex]3kT[/itex].

    As follows from the above, you should not divide m by two, because you are already given the atomic mass.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook