The mean free path of a gas molecule depends on:

Solution

Physics sir · 3 steps

Picture one molecule sweeping out a cylinder: how fat it is and how crowded the gas is both matter.

1. Collision cylinder. A molecule of diameter d hits any other molecule whose centre comes within d of its own. So as it moves a distance L, it sweeps out a cylinder of cross-section π d² and volume π d² L.
2. Count the hits. With n molecules per unit volume, the number of collisions in that length is n π d² L. Allowing for the motion of the other molecules adds a factor √2.

   λ = 1/(√2 n π d²)

3. So. λ falls as n rises and falls as d² rises, so it depends on both the molecular diameter and the number density. The answer is (c).

The idea to keep. Mean free path is distance per collision. Bigger molecules (larger d) or a more crowded gas (larger n) both mean more collisions, so λ ∝ 1/(n d²).

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