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  • Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1 A and 2 A. The gases may be considered under identical conditions of temperature, pressure and volume.

Calculate the ratio of the mean free paths of the molecules of two gases having molecular diameters 1 A and 2 A. The gases may be considered under identical conditions of temperature, pressure and volume.

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Mean free path formula, \lambda =\frac{1}{\sqrt{2}}\pi d^{2}n

Here, n = number of molecules per unit volume. In our case, n will be constant.

Here, d = diameter of molecules.

Now, \lambda \propto \frac{1}{d^{2}}

So,\frac{\lambda _{1}}{\lambda _{2}}=\frac{d_2^{2}}{d_1^{2}}=\frac{4}{1}

Hence, \lambda _{1}:\lambda _{2}=4:1

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