Q. In the two vessels of same volume, atomic hydrogen and helium at pressure $1\ atm$ and $2\ atm$ are filled. If temperature of both the samples is same, then average speed of hydrogen atoms $< C_{H} >$ will be related to that of helium $< C_{He} >$ as
A) $< CH > = \sqrt{2} < C_{He} >$
B) $< C_{H} > = < C_{He} >$
C) $< C_{H} > = 2 < C_{He} >$
D) $< C_{H} > = \frac{< C_{He} >}{2}$
Explanation
(c) Average velocity of gas molecule is
$v_{av} = \sqrt{\frac{8RT}{\pi M}} \Rightarrow v_{av} \times \frac{1}{\sqrt{M}}$
$\Rightarrow \frac{< C_{H} >}{< C_{He} >} = \sqrt{\frac{M_{He}}{M_{H}}} = \sqrt{\frac{4}{1}} = 2 \Rightarrow < C_{H} > = 2 < C_{He} >$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.