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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Solution

Q.
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is [2024]

1 $\frac{1}{32}$

2 $\frac{1}{2 \sqrt{2}}$

3 $\frac{1}{4}$

4 $\frac{2 \sqrt{2}}{1}$

Ans.
(4)

$V_{r m s} = \sqrt{\frac{3 R T}{M}}$

$\frac{V_{H e}}{V_{O_{2}}} = \sqrt{\frac{M_{O_{2}}}{M_{H e}}} = \sqrt{\frac{32}{4}} = \sqrt{8} = 2 \sqrt{2}$

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