Question

At a certain temperature, if the r.m.s. velocity of $O_2$ is 400 m/s then at the same temperature the r.m.s. velocity of $H_2$ molecules will be

• A. 400 m/s
• B. 1600 m/s
• C. 3200 m/s
• D. 6400 m/s

Answer 1

Answer: (B)

We know that, $v_{rms}=\sqrt{\frac{3RT}{M}}$ $\therefore$ $v_{rms}\propto \frac{1}{\sqrt{M}}$ (As T is constant) $\Rightarrow$ $\frac{{(v_{rms})}_{O_2}}{{(v_{rms})}_{H_2}}=\sqrt{\frac{M_{H_2}}{M_{O_2}}}$ $\Rightarrow$ $\frac{400}{{(v_{rms})}_{H_2}}=\sqrt{\frac{2}{32}}=\frac{1}{4}$ $\Rightarrow$ ${(v_{rms})}_{H_2}=4\times 400=1600m\text{/}s$