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Question
The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about
Options
125 m s−1
2000 m s−1
8000 m s−1
31 m s−1.
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Solution
2000 ms−1
Given,
Molecular mass of hydrogen, MH = 2
Molecular mass of oxygen, Mo = 32
RMS speed is given by,
\[v_{rms =} \sqrt{\frac{3RT}{M}}\]
\[ \Rightarrow \sqrt{\frac{3RT}{M_O}} = 500\]
Now ,
\[ \Rightarrow \frac{v_{Orms}}{v_{Hrms}} = \frac{\sqrt{\frac{3RT}{M_O}}}{\sqrt{\frac{3RT}{M_H}}}\]
\[ \Rightarrow \frac{v_O rms}{v_{Hrms}} = \frac{\sqrt{\frac{3RT}{32}}}{\sqrt{\frac{3RT}{2}}}\]
\[ \Rightarrow \frac{v_{Orms}}{{v_H}_{rms}} = \frac{1}{4}\]
\[ \Rightarrow \frac{500}{v_{Hrms}} = \frac{1}{4}\]
\[ \Rightarrow v_{Hrms} = 4 \times 500 = 2000 {\text { ms }}^{- 1} \]
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