Question

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. $< C_{H} > = \sqrt{2} < C_{He} >$
• B. $< C_{H} > = < C_{He} >$
• C. $< C_{H} > = 2 < C_{He} >$
• D. $< C_{H} > = \frac{< C_{He} >}{2}$

Answer 1

Answer: (C)

$< C_{H} > = 2 < C_{He} >$

Answer 2

Average velocity of gas molecule is

$v_{av} = \sqrt{\frac{8RT}{\pi M}}$Ž$v_{av} \propto \frac{1}{\sqrt{M}}$

Ž$\frac{< C_{H} >}{< C_{He} >} = \sqrt{\frac{M_{He}}{M_{H}}} = \sqrt{\frac{4}{1}} = 2$ Ž $< C_{H} > = 2 < C_{He} >$