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Question: Two vessels having equal volume contains molecular hydrogen at one atmosphere and helium at two atmo...

Two vessels having equal volume contains molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If both samples are at the same temperature, the mean velocity of hydrogen molecules is

A

Equal to that of helium

B

Twice that of helium

C

Half that of helium

D

2\sqrt{2} times that of helium

Answer

2\sqrt{2} times that of helium

Explanation

Solution

vav∝1Mv_{av} \propto \frac{1}{\sqrt{M}} Ž vH2vHe=MHeMH2=42=2\frac{v_{H_{2}}}{v_{He}} = \sqrt{\frac{M_{He}}{M_{H_{2}}}} = \sqrt{\frac{4}{2}} = \sqrt{2}

Ž vH2=2vHev_{H_{2}} = \sqrt{2}v_{He}