The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If T is the temperature of the gas, then

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$T (H_{2}) > T (N_{2})$

$T (H_{2}) = T (N_{2})$

$T (H_{2}) = \sqrt{7} T (N_{2})$

$T (H_{2}) < T (N_{2})$

answer is C.

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Detailed Solution

$\sqrt{\frac{3 RT}{M}} for H_{2} = \sqrt{7} \times \sqrt{\frac{3 RT}{28}} for N_{2} ∴ T_{H_{2}} < T_{N_{2}} [∵ \frac{1}{\sqrt{2}} T_{H_{2}} = \sqrt{7} \times \frac{1}{2 \sqrt{7}} T_{N_{2}} or T_{H_{2}} = \frac{1}{2} \cdot T_{N_{2}}]$

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