A) 400 m/s
B) 1600 m/s
C) 3200 m/s
D) 6400 m/s
Correct Answer: B
Solution :
We know that, \[{{v}_{rms}}=\sqrt{\frac{3RT}{M}}\] \[\therefore \] \[{{v}_{rms}}\propto \frac{1}{\sqrt{M}}\](As T is constant) \[\Rightarrow \] \[\frac{{{({{v}_{rms}})}_{{{O}_{2}}}}}{{{({{v}_{rms}})}_{{{H}_{2}}}}}=\sqrt{\frac{{{M}_{{{H}_{2}}}}}{{{M}_{{{O}_{2}}}}}}\] \[\Rightarrow \] \[\frac{400}{{{({{v}_{rms}})}_{{{H}_{2}}}}}=\sqrt{\frac{2}{32}}=\frac{1}{4}\] \[\Rightarrow \] \[{{({{v}_{rms}})}_{{{H}_{2}}}}=4\times 400=1600\,m\text{/}s\]
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