Mean Free Path

Understanding this requires the mean free path expression given in NCERT Class 11, Chapter 13 (Kinetic Theory), namely $\lambda =\frac{1}{\sqrt{2}n\pi d^2}$, where $n$ is the number density of molecules and $d$ is the molecular diameter. The mean free path is the average distance a molecule travels between successive collisions, and it is inversely proportional to the number density. When the number density $n$ is doubled while temperature and molecular size stay fixed, $\lambda$ becomes half of its original value, since molecules now encounter obstacles twice as often. The option that the path doubles inverts the inverse relationship. The option that it stays unchanged ignores the dependence on density entirely. The option of a fourfold increase wrongly assumes an inverse square dependence on density. The molecular diameter enters through the effective collision cross-section, which represents the target area a molecule presents to others as it moves through the gas. A plausibility check supports the answer: packing twice as many molecules into the same volume clearly means each molecule collides sooner, so shorter travel between collisions and a halved mean free path is exactly what we expect physically.