The ratio of vapour densities of two gases at the same temperature is , then the ratio of r.m.s. velocities will be: [2025]

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Solution

Q.
The ratio of vapour densities of two gases at the same temperature is $\frac{4}{25}$ , then the ratio of r.m.s. velocities will be: [2025]

1 $\frac{25}{4}$

2 $\frac{2}{5}$

3 $\frac{5}{2}$

4 $\frac{4}{25}$

Ans.
(3)

$v_{rms} = \sqrt{\frac{3 R T}{M}}$

$\frac{v_{1}}{v_{2}} = \sqrt{\frac{M_{2}}{M_{1}}} = \sqrt{\frac{25}{4}} = \frac{5}{2}$

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