Question

The ratio between the $rms$ velocity of $H_2$ at 50 $K$ and that of $O_2$ at 800 $K$ is :

• A. 4
• B. 2
• C. 1
• D. 1/4

Answer 1

The correct option is C 1

The molecular speed of $H_2$ is, $V_{rms\left(H_2\right)}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times R\times 50}{2}}=\sqrt{75R}$

The molecular speed of $O_2$ is,$V_{rms\left(O_2\right)}=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times R\times 800}{32}}=\sqrt{75R}$

By comparing these above 2 we get, $\frac{V_{rms\left(H_2\right)}}{V_{rms\left(O_2\right)}}=1$

Hence, the correct option is $C$.