At a certain temperature, the r.m.s velocity for $O_{2}$ is 200m/sec:At the same temperature the r.m.s Velocity for $H_{2}$ molecule will be

100 m / s e c

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25 m / s e c

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800 m / s e c

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6400 m / s e c

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Solution

The correct option is D $800 m / s e c$
We know $r m s$ , velocity $(V_{r m s}) = \sqrt{\frac{3 R T}{M}}$

since here (temperature) is same in both cases so,

$V_{r m s} = \frac{K}{\sqrt{M}}$ where $K =$ constant $= \sqrt{3 R T}$

given $V_{r m s}$ of $O_{2} = 200 m / s = \frac{K}{\sqrt{32}} \Rightarrow K = 200 \sqrt{32}$

and hence for $H_{1}; M_{H_{2}} = 2 a m u$

$V_{r m s} H_{2} = \frac{K}{\sqrt{2}}$

$= \frac{200 \sqrt{32}}{\sqrt{2}} = 200 \sqrt{16} = 200 \times 4$

so $V_{r m s} o f H_{2} = 800 m / s$ so $(C)$ option is correct.

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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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