Q. Calculate the ratio of rms speeds of oxygen gas molecules to that of hydrogen gas molecules kept at the same temperature.
A) 1:4
B) 1:8
C) 1:2
D) 1:6
Explanation
(a) Root mean square velocity
$v_{rms} \propto \frac{1}{\sqrt{M}}$
So $\frac{{\left( v_{rms} \right)_{O}}_{2}}{{\left( v_{rms} \right)_{H}}_{2}} = \sqrt{\frac{{M_{H}}_{2}}{{M_{O}}_{2}}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sqrt{\frac{2}{32}} = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.