Question

The ratio between the root mean square speed 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

As we know,
$v_{rms}=\sqrt{\frac{3RT}{M}}$

For $H_2$ at 50 $K$,

$v_1=\sqrt{\frac{3R\times 50}{2}}$

For $O_2$ at 800 $K$,

$v_2=\sqrt{\frac{3R\times 800}{32}}$

$\therefore \frac{v_1}{v_2}=\frac{\sqrt{\frac{3R\times 50}{2}}}{\sqrt{\frac{3R\times 800}{32}}}=1$

Hence, the correct answer is option $\text{C}$.