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=1600\,m\text{/}s $