Q. A cubical box with porous walls containing an equal number of $O_{2}$ and $H_{2}$ molecules is placed in a large evacuated chamber. The entire system is maintained at constant temperature $T.$ The ratio of $v_{rms}$ of $O_{2}$ molecules to that of the $v_{rms}$ of $H_{2}$ molecules, found in the chamber outside the box after a short interval is
A) $\frac{1}{2\sqrt{2}}$
B) $\frac{1}{4}$
C) $\frac{1}{\sqrt{2}}$
D) $\sqrt{2}$
Explanation
(b) Temperature remain constant so
$v_{rms} \propto \frac{1}{\sqrt{M}} \Rightarrow \frac{v_{O_{2}}}{v_{H_{2}}} = \sqrt{\frac{M_{H_{2}}}{M_{O_{2}}}} = \sqrt{\frac{1}{16}} = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.