The mean free path of the molecules of two gases having molecular diameters  $1\stackrel{o}{A}$  and $2\stackrel{o}{A}$ is N: 1. Gases are under identical conditions of temperature, pressure  and volume. Find N.

Mean free path is given by  $\lambda =\frac{1}{\sqrt{2}{d}^{2}n}\alpha \frac{1}{d^2}$
Where, n = number density of molecules and d = molecular diameter.
Since, pressure, volume, temperature are same, using PV= nRT, number of moles  (and hence number of molecules) is also same.
Hence, required ratio is  $\frac{{\lambda }_1}{{\lambda }_2}=\frac{d_2^2}{d_1^2}=4$.