Q. At room temperature (27$℃)\ $the rms speed of the molecules of a certain diatomic gas is found to be 1920 m$s^{- 1}$. The gas is
A) $Cl_{2}$
B) $O_{2}$
C) $N_{2}$
D) $H_{2}$
Explanation
(d) $C_{rms} = \ \sqrt{\frac{3RT}{M}}$
Or $M = \frac{3RT}{C_{rms}^{2}} = \ \frac{3 \times 8.31\ \times 300}{(1920)^{2}}$
= 2 $\times 10^{- 3}$ kg = 2g
Since, $M$ = 2 for the hydrogen molecule. Hence, the gas is hydrogen.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.