Q 11-12-056JEE MainJEE Main 2024 (30 Jan, Shift 1)Easy
At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^\circ\text{C}$?
Answer: (D) $20\ \text{K}$
$v_{rms} = \sqrt{3RT/M}$, so equal speeds need equal $T/M$:
$$\frac{T_{H_2}}{2} = \frac{320}{32} \Rightarrow T_{H_2} = 20\ \text{K}$$
Solution by Sreeraj P, M.Sc Physics