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At a certain temperature, the r.m.s velocity for $O_{2}$ is 400 m/sec . At the same temperature, the r.m.s velocity for $H_{2}$ molecules will be

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100 m/sec

25 m/sec

1600 m/sec

6400 m/sec

answer is C.

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Detailed Solution

$V_{rms} = \sqrt{\frac{3 RT}{M}}$

$For O_{2}; (V_{rms}) = V_{1} = \sqrt{\frac{3 {RT}_{1}}{M_{1}}}$

$For H_{2} : {(V_{rms})}_{2} = V_{2} = \sqrt{\frac{3 {RT}_{2}}{M_{2}}}$

$\frac{V_{1}}{V_{2}} = \sqrt{\frac{M_{2}}{M_{1}}} \Rightarrow \frac{400}{V_{2}} = \sqrt{\frac{2}{32}}$

$∴ V_{2} = 1600 m / s$

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