Question

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

• A. equal to that of helium
• B. twice that of helium
• C. half that of helium
• D. $\sqrt{2}$ times that of helium

Answer 1

Answer: (D)

$\sqrt{2}$ times that of helium

Answer 2

Given $V _{ RMS }=\sqrt{\frac{3 RT }{ M }}$ i.e. Ratio of RMS velocities $=\sqrt{\frac{T M_{\text {helim }}}{T M_{\text {hydrogen }}}}$ Both the temperatures are equal. Ratio of RMS velocities $=\sqrt{\frac{4}{1}}=2$ Hence RMS velocity of hydrogen would be twice as much as the RMS for helium.