Q 11-12-105JEE MainJEE Main 2021 (18 Mar, Shift 2)Easy
Consider a sample of oxygen behaving like an ideal gas. At 300 K, the ratio of root-mean-square (RMS) velocity to the average velocity of the gas molecule would be:
(Molecular weight of oxygen is 32 g mol$^{-1}$; $R = 8.3$ J K$^{-1}$ mol$^{-1}$)
Answer: (C) $\sqrt{\frac{3\pi}{8}}$
$$\frac{v_{rms}}{v_{avg}} = \frac{\sqrt{3RT/M}}{\sqrt{8RT/\pi M}} = \sqrt{\frac{3\pi}{8}}$$ The ratio does not depend on the gas or the temperature.
Solution by Sreeraj P, M.Sc Physics