1. Recall the formula for mean free path

For a gas, the mean free path $\lambda$ of a molecule is given by

where:

• $n$ = number density of molecules
• $\sigma$ = collision cross-section

2. Write the collision cross-section

If $d$ is the diameter of a molecule, then the collision cross-section is

3. Substitute into the formula

Thus,

4. Match with the options

Comparing with the given choices:

• A: $\dfrac{1}{\sqrt{2} n \pi d^2}$ ✅
• B: $\dfrac{1}{\sqrt{2} n^2 \pi^2 d^2}$ ❌
• C: $\dfrac{1}{\sqrt{2 n \pi d^2}}$ ❌
• D: $\sqrt{2} n \pi d^2$ ❌

Therefore, the correct option is A.