Question

At a certain temperature, the $rms$ velocity for $O_2$ is $400m/sec$. At the same temperature, the $rms$ velocity for $H_2$ molecules will be

• A. $100m/s$
• B. $25m/s$
• C. $1600m/s$
• D. $6400m/s$

Answer 1

The correct option is C $1600m/s$

Given $V_{O_2}=400m/s$ Mass of $O_2$ , $M_{O_2}=32$ and Mass of $H_2$, $M_{H_2}=2$

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

$\Rightarrow \frac{V_{H_2}}{V_{O_2}}=\sqrt{\frac{M_{O_2}}{M_{H_2}}}$

$\Rightarrow V_{H_2}=400\times \sqrt{\frac{32}{2}}=1600m/s$