The mean free path ($\\lambda$) of a gas molecule is defined as the average distance travelled by the molecule between two successive collisions. According to the Kinetic Theory of Gases, it is given by the expression: $\\lambda = \\frac{1}{\\sqrt{2}\\pi n d^2}$ where $n$ is the number density (number of molecules per unit volume) and $d$ is the diameter of the molecule. Since the diameter $d = 2r$ (where $r$ is the radius), substituting this into the equation gives: $\\lambda = \\frac{1}{\\sqrt{2}\\pi n (2r)^2} = \\frac{1}{4\\sqrt{2}\\pi n r^2}$ Therefore, the mean free path is inversely proportional to the square of the radius ($\\lambda \\propto \\frac{1}{r^2}$).