To solve this problem, we need to understand the concept of mean free path in a gas.$\\$The mean free path $(\lambda)$ is the average distance a molecule travels between collisions.$\\$It is given by the formula:$\\ \lambda = \frac{1}{\sqrt{2} n \pi d^2} \\$where:$\\$• $n$ is the number density of the gas (number of molecules per unit volume),$\\$• $d$ is the diameter of a molecule,$\\$• $\pi$ is the mathematical constant Pi, approximately equal to 3.14159,$\\$• $\sqrt{2}$ is a factor that arises from the geometry of molecular collisions.$\\$Now, let's analyze the options given:$\\$Option 1: $\frac{1}{\sqrt{2} n \pi d^2} \\$Option 2: $\frac{1}{\sqrt{2} n^2 \pi d^2} \\$Option 3: $\frac{1}{\sqrt{2} n^2 \pi^2 d^2} \\$Option 4: $\frac{1}{\sqrt{2} n \pi d} \\$The correct formula for the mean free path is:$\\ \lambda = \frac{1}{\sqrt{2} n \pi d^2} \\$Therefore, the correct option is Option 1.$\\$This corresponds to the standard expression for the mean free path in kinetic theory of gases.