The mean free path of gas molecules is proportional to n^th power of diameter of molecules. Here n is

CONCEPT:

Mean Free Path (λ): 

• The distance travelled by a gas molecule between two successive collisions is known as a free path.
  \(λ = \frac{{Total\;distance\;travelled\;by\;a\;gas\;molecule\;between\;successive\;collisions\;\;}}{{Total\;number\;of\;collisions}}\)
• During two successive collisions, a molecule of gas moves in a straight line with constant velocity, and the mean free path of a gas molecule is given by
  \(λ = \frac{1}{{\sqrt 2 \pi n{d^2}}}\)

Where n = number of molecules per unit volume and d = diameter of a molecule

EXPLANATION:

• The mean free path of a gas molecule is given by

\(⇒ λ = \frac{1}{{\sqrt 2 \pi n{d^2}}}\)

⇒ λ ∝ d^-2