Q. The $r.m.s.$ velocity of a gas at a certain temperature is $\sqrt{2}$ times than that of the oxygen molecules at that temperature. The gas can be
A) $H_{2}$
B) $He$
C) $CH_{4}$
D) $SO_{2}$
Explanation
(c) $v_{rms} \propto \frac{1}{\sqrt{M}} \Rightarrow \frac{v_{1}}{v_{2}} = \sqrt{\frac{M_{2}}{M_{1}}}$
$\therefore\frac{1}{\sqrt{2}} = \sqrt{\frac{M_{2}}{32}} \Rightarrow M_{2} = 16.$ Hence the gas is $CH_{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.