The rms velocity of the molecules in a sample of helium is ${(\frac{5}{7})}^{t h}$ of that of the molecules in a sample of hydrogen. If the temperature of the hydrogen gas is $0 ° C$ .The temperature of the helium sample is nearly equal to

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$100^{\circ} C$

$273^{\circ} C$

$0^{\circ} C$

$546^{\circ} C$

answer is A.

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Detailed Solution

$\begin{aligned} v_{ms} = \sqrt{\frac{3 RT}{M}} \\ ∴ vHe = \frac{5}{7} vH \Rightarrow \sqrt{\frac{3 {RT}_{He}}{M_{He}}} = \frac{5}{7} \sqrt{\frac{3 {RT}_{H}}{M_{H}}} \\ \Rightarrow T_{He} = 273 K = 0^{\circ} C \end{aligned}$

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