The mean free path $$\lambda$$ is the average distance covered by a molecule between two successive collisions. It is given by the formula:

$$\lambda = \frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}$$

Where:

• $$n$$ is the number density of the molecules, i.e., the number of molecules per unit volume,
• $$d$$ is the diameter of the molecules, and
• $$\sqrt{2}$$ arises from considering the relative motion of a pair of particles in a gas, taking into account that either particle can be moving towards the other, which effectively doubles the cross-sectional area through which they can collide.

This formula shows that the mean free path is inversely proportional to the number density $$n$$ of the molecules and the square of the diameter $$d$$ of the molecules. It also takes into account that collisions are more likely as the cross-sectional area of the molecules increases, or as the density of the molecules increases.

Therefore, the correct answer is:

Option A: $$\frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}$$