CBSE-XI-Physics
24: Kinetic Theory of Gases
- #9The rms speed of oxygen at room temperature is about 500 m/s. The rms speed of hydrogen at the same temperature is about
(a) 125 m s-1
(b) 2000 m s-1
(c) 8000 m s-1
(d) 31 m s-1.digAnsr: bAns : (b) 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}}``
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`` \Rightarrow \sqrt{\frac{\mathit{3}RT}{{M}_{O}}}=500``
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Now,
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`` \Rightarrow \frac{{v}_{Orms}}{{v}_{Hrms}}=\frac{\sqrt{{\displaystyle \frac{3RT}{{M}_{O}}}}}{\sqrt{{\displaystyle \frac{3RT}{{M}_{H}}}}}``
`` \Rightarrow \frac{{v}_{O}rms}{{v}_{Hrms}}=\frac{\sqrt{{\displaystyle \frac{3RT}{32}}}}{\sqrt{{\displaystyle \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{\,\mathrm{\,ms\,}}^{-1}``
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Hence, the correct answer is
(b).