The RMS velocity of hydrogen gas is $\sqrt{7}$ times to that of nitrogen. If T is temperature then the correct relationship is

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$T_{H_{2}} < T_{N_{2}}$

$T_{H_{2}} > T_{N_{2}}$

$T_{H_{2}} = T_{N_{2}}$

$T_{H_{2}} = \sqrt{7} T_{N_{2}}$

answer is C.

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Detailed Solution

$\frac{r_{H_{2}}}{r_{N_{2}}} = \sqrt{\frac{M_{N_{2} .} T_{H_{2}}}{M_{H_{2}} . T_{N_{2}}}} \frac{\sqrt{7}}{1} = \sqrt{\frac{28}{2} . \frac{T_{H_{2}}}{T_{N_{2}}}} \frac{7}{1} = \frac{28}{2} . \frac{T_{H_{2}}}{T_{N_{2}}} ∴ T_{N_{2}} > T_{H_{2}}$

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