The mean free path increases as the number density of gas molecules decreases.

Solution

Physics sir · 4 steps

Fewer molecules in the box means fewer to bump into, so each one travels farther between hits.

1. What it measures. The mean free path λ is the average distance a molecule travels between two successive collisions.

   λ = 1/(√2 π d² n)

2. Read the formula. Here d is the molecular diameter and n is the number of molecules per unit volume. For a given gas d is fixed, so λ ∝ 1/n.
3. Why physically. A molecule collides with any other molecule whose centre comes within a distance d of its path. When n drops, fewer such molecules lie along that path, so collisions happen less often and the distance between them grows.
4. So. Halving n doubles λ. The statement is true.

The idea to keep. Mean free path goes as 1/(n d²). At fixed temperature n ∝ p, so a lower pressure, a thinner gas or smaller molecules all give a longer free path.

Answer from the NTA final answer key. Solution by PrepWiser.