Question

The ratio between the root mean square speed of $H$ at $50K$ and that of $O_2$ at $800K$ is:

• A. $4$
• B. $2$
• C. $1$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $1$

The expression for the root mean square speed is $u_{rms}=\sqrt{\frac{3RT}{M}}$.
Thus the ratio of the root mean speeds of hydrogen and oxygen at two different temperatures is $\Rightarrow \frac{u_{rms}\left(H_{2}at50K\right)}{u_{rms}\left(O_{2}at800K\right)}=\frac{\sqrt{\frac{3R\times 50}{2}}}{\sqrt{\frac{3R\times 800}{32}}}=\sqrt{\frac{50}{2}\times \frac{32}{800}}=1$.