The mean free path of molecules of a gas, (radius r) is inversely proportional to 
 

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

where n is the number density and d is the diameter of the molecule.

As d = 2r

$\therefore \lambda =\frac{1}{4\sqrt{2}n\pi r^2} \text{ or } \lambda \propto \frac{1}{r^2}$