Question

If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

• A. $\frac{1}{\sqrt{2 n \pi d^2}}$
• B. $\sqrt{2 n \pi d^2}$
• C. $\frac{1}{\sqrt{2 \pi d^2}}$
• D. $\frac{1}{\sqrt{2 n^2 \pi^2 d^2}}$

Answer 1

Answer: (C)

$\frac{1}{\sqrt{2 \pi d^2}}$

Answer 2

The mean free path $\lambda$ of a molecule is defined as the average distance that a molecule travels between two successive collisions. It is given by the formula:

$\lambda = \frac{1}{\sqrt{2} \pi d^2 n},$

where:
- $n$ is the number density of molecules (i.e., the number of molecules per unit volume),
- $d$ is the diameter of the molecule,
- $\pi$ is the mathematical constant.

Explanation: The formula for the mean free path is derived from kinetic theory, considering the probability of collisions between molecules in a given volume. The factor $\sqrt{2}$ accounts for the random distribution of molecular velocities and the likelihood of collisions occurring.

Thus, the average distance covered by a molecule between two successive collisions is represented by:

$\lambda = \frac{1}{\sqrt{2} \pi d^2 n}.$

Therefore, the correct option is (3).