The mean free path for a gas, with molecular diameter $d$ and number density $n$, can be expressed as:

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1.  **Definition:** The mean free path ($\lambda$) is the average distance a gas molecule travels between successive collisions.
2.  **Derivation Concept:** Consider a molecule of diameter $d$ moving with average speed $v$. It sweeps out a cylinder of volume $\pi d^2 v \Delta t$ in time $\Delta t$. The number of collisions is determined by the number density $n$. To account for the motion of all other molecules, a relative velocity factor of $\sqrt{2}$ is introduced.
3.  **Formula:** The standard expression derived in the Kinetic Theory of Gases is $\lambda = \frac{1}{\sqrt{2}n\pi d^2}$.
4.  **Analysis of Options:** Option A matches the standard formula. The other options have incorrect powers of $n$ or $d$.

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