First slide

Rms speed

Question

Two vessels having equal volumes contain molecular hydrogen at 1 atm and helium at 2 atm , respectively . What is the ratio of the rms speeds of hydrogen molecule to that of helium molecule if both are at the same temperature?

Moderate

A

$\sqrt{\frac{4}{1}}$
B

$\sqrt{\frac{1}{4}}$
C

$\sqrt{\frac{1}{2}}$
D

$\sqrt{\frac{2}{1}}$

Solution

We know that
$\frac{V_{rms} H_{2}}{V_{r m s} He} = \sqrt{\frac{3 {RT}_{H_{2}}}{M_{H_{2}}} .} \sqrt{\frac{M_{H e}}{3 R T_{H e}}}$
Given: T_He= $T_{H_{2}}$ _.
Therefore,
$\frac{V_{{rms}_{H 2}}}{V_{{rms}_{He}}} = \sqrt{\frac{M_{He}}{M_{H 2}}} = \sqrt{\frac{4}{2}} = \sqrt{2}$

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