Print ViewEquipartition Theorem and Microscopic Motion

[jaded18]

What is the typical rotational frequency f_rot for a molecule like N_2 (nitrogen) at room temperature (25 C)? Assume that d for this molecule is 1 angstrom = 10^{-10} m. Take the atomic mass of N_2 to be 4.65 * 10^{-26} kg.
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I know that the rms angular speed which is the root mean square (rms) of the x component of velocity of the gas particles is = sqrt(2k_B(T)/(m(d^2))) where k_B is the Boltzman constant 1.38*10^-23 J/K.

 

[Astronuc]

typical rotational frequency

Think about moment of inertia. How much of the energy is distributed in rotational motion versus translational motion?

Or assuming the rotational motion comes from collisions based on a translational speed, how does one transform the typical translational speed into a rotational velocity?

 

[jaded18]

what do i do with the rotational speed that i calculated to get rotational frequency??'

molecule has moment of inertia I about the axis and is rotating with angular velocity omega about that axis with associated rotational kinetic energy (1/2) I omega_x^2

 

[jaded18]

all righty. i found this equation relating frequency and veolcity --> angular velocity=2(pi)f
but i DONT UNDERSTAND why I'm not getting the right answer. i get velocity to be 4.2057*10^12 m/s and i SHOULD be able to get frequency by dividing it by 2pi, but f=6.69*10^11 is not right!

whats wrOong?!