To solve this problem, we need to understand the concept of mean free path in the context of gas molecules.$\\$The mean free path $(\lambda)$ is the average distance a molecule travels between collisions.$\\$For a gas, the mean free path is given by the formula:$\\ \lambda = \frac{1}{\sqrt{2} \pi n d^2} \\$where:$\\$• $n$ is the number density of the gas molecules (number of molecules per unit volume),$\\$• $d$ is the diameter of the molecule.$\\$Since the diameter $d$ is twice the radius $r$ of the molecule, we have $d = 2r. \\$Substituting $d = 2r$ into the formula for $\lambda,$ we get:$\\ \lambda = \frac{1}{\sqrt{2} \pi n (2r)^2} \\$Simplifying the expression:$\\ \lambda = \frac{1}{4 \sqrt{2} \pi n r^2} \\$From this expression, it is clear that the mean free path $\lambda$ is inversely proportional to $r^2. \\$Therefore, the correct answer is Option 2.