The mean free path of gas molecules depends on the diameter $d$ of the molecules as

Solution

1. The mean free path $\lambda$ of gas molecules is defined by the kinetic theory formula $\lambda =\frac{1}{\sqrt{2}\pi n{d}^2}$.
2. In this expression, $n$ represents the number density of the gas molecules and $d$ represents the molecular diameter.
3. Since $\sqrt{2}$, $\pi$, and $n$ are constants for a given gas state, the relationship simplifies to $\lambda \propto \frac{1}{d^2}$.
4. Hence the answer is (D).