Equipartition Theorem and Microscopic Motion

[kkaplanoz]

Homework Statement

What is the typical rotational frequency f_rot for a molecule like N2 at room temperature T = 298 K? Assume that d for this molecule is 10^-10 m. Take the atomic mass of N2 to be m = 4.65 *10^-26 kg.

Homework Equations

w = omega
w_x^2 = (2kbT)/(md^2) (where kb is boltzmann's constant)
f=w/(2*pi)

The Attempt at a Solution

When plugging in the numbers, w_x is equal to 4.20568*10^12. Dividing this by 2*pi gives the frequency as 6.69*10^11. This is not right. I did a practice problem that was the same setup and got that one right. Where did I go wrong?

Thanks!

 

[anathema]

I can confirm that your attempt at a solution is correct. However, it is possible that you may have made a calculation error or used the wrong value for boltzmann's constant. I would suggest double checking your calculations and making sure that all units are consistent. Also, you may want to try using a different source for boltzmann's constant to ensure accuracy. If you are still having trouble, feel free to post your calculations and we can help you troubleshoot further. Good luck!

 

[Moetasim]

I would first check my calculations to make sure I did not make any errors. It is possible that a small mistake was made in the calculation, leading to an incorrect answer. I would also double check that the formula used is the correct one for calculating the rotational frequency of a molecule at room temperature.

If the calculations and formula are correct, then there may be other factors at play that could affect the rotational frequency of a molecule like N2 at room temperature. For example, the actual size and shape of the molecule may impact its rotational behavior. Additionally, there could be interactions with other molecules in the surrounding environment that could affect the molecule's motion.

In order to get a more accurate answer, it may be necessary to consider these additional factors and potentially use more advanced methods to calculate the rotational frequency. This could include using computer simulations or conducting experiments to observe the behavior of N2 molecules at room temperature. Overall, it is important to consider all possible factors and to continue to refine and improve our understanding of the Equipartition Theorem and microscopic motion.