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A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is:
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The correct answer is:
$\frac{2 \sqrt{2}}{1}$
$\begin{aligned} & \mathrm{V}_{\mathrm{ms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}_{\mathrm{w}}}} \\ & \Rightarrow \frac{\mathrm{V}_{\mathrm{O}_2}}{\mathrm{~V}_{\mathrm{He}}}=\sqrt{\frac{\mathrm{M}_{\mathrm{w}, \mathrm{He}}}{\mathrm{M}_{\mathrm{w}, \mathrm{O}_2}}} \\ & =\sqrt{\frac{4}{32}}=\frac{1}{2 \sqrt{2}} \\ & \frac{\mathrm{V}_{\mathrm{He}}}{\mathrm{V}_{\mathrm{O}_2}}=\frac{2 \sqrt{2}}{1} \\ & \end{aligned}$
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