If $\mathrm{n}$ is the number density and $\mathrm{d}$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

<p>The mean free path $\lambda$ is the average distance covered by a molecule between two successive collisions. It is given by the formula:</p> <p>$\lambda = \frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}$</p> <p>Where:</p> <ul> <li>$n$ is the number density of the molecules, i.e., the number of molecules per unit volume,</li> <li>$d$ is the diameter of the molecules, and</li> <li>$\sqrt{2}$ 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.</li> </ul> <p>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.</p> <p>Therefore, the correct answer is:</p> <p>Option A: $\frac{1}{\sqrt{2} \mathrm{n} \pi \mathrm{d}^2}$</p>