Step 1: Define mean free path.
The mean free path is the average distance a gas molecule travels between two collisions. A larger molecule or a crowded gas means more collisions and a shorter path.
Step 2: Write the formula.
The mean free path is \[ \lambda = \frac{1}{\sqrt{2}\,\pi d^2 n} \] where $d$ is the molecular diameter and $n$ is the number of molecules per unit volume.
Step 3: Spot the diameter term.
The diameter $d$ appears as $d^2$ in the bottom of the fraction. So \[ \lambda \propto \frac{1}{d^2} \] The path is inversely proportional to the square of the diameter.
Step 4: Understand why.
A bigger molecule has a bigger target area, which grows with $d^2$. A bigger target means collisions happen sooner, so the free path shrinks.
Step 5: Check temperature.
At fixed pressure and volume, raising temperature does not directly change the path in the simple form asked. The question is about the diameter, not temperature.
Step 6: State the answer.
The mean free path is inversely proportional to the square of the molecular diameter. \[ \boxed{\lambda \propto \frac{1}{d^2}} \]