The mean free path of the molecules of two gases having molecular diameters  1Ao  and 2Ao is N: 1. Gases are under identical conditions of temperature, pressure  and volume. Find N.

Mean free path is given by  λ=12d2nα1d2Where, 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  λ1λ2=d22d12=4.