Q. The ratio of the vapour densities of two gases at a given temperature is $9:8$. The ratio of the rms velocities of their molecules is
A) $3:2\sqrt{2}$
B) $2\sqrt{2}:3$
C) $9:8$
D) $8:9$
Explanation
(b) Root mean square speed
$v_{rms} \propto \frac{1}{\sqrt{\rho}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \frac{{v_{rms}}_{1}}{{v_{rms}}_{2}} = \sqrt{\frac{\rho_{2}}{\rho_{1}}}$
Given, $\frac{\rho_{1}}{\rho_{2}} = \ \frac{9}{8}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \frac{{v_{rms}}_{1}}{{v_{rms}}_{2}} = \sqrt{\frac{8}{9}} = \frac{2\sqrt{2}}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.