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The discussion focuses on calculating the typical rotational frequency of nitrogen molecules (N2) at room temperature using the root mean square angular speed formula. Participants explore the relationship between translational and rotational motion, emphasizing the moment of inertia and the conversion of angular velocity to frequency. Despite using the correct formulas, there is confusion regarding the calculated values, particularly the resulting velocity and frequency not aligning with expected outcomes. The conversation highlights the importance of understanding the distribution of energy between rotational and translational motions in gas molecules. Overall, the participants seek clarity on the calculations and the underlying principles of molecular motion.
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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.
 
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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?
 
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
 
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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?!
 
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