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

The Correct Option is C

The mean free path \( \lambda \) of a molecule is the average distance it traverses between consecutive collisions. This is mathematically expressed as:

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

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

Kinetic theory forms the basis for this formula, which accounts for collision probabilities among molecules within a defined volume. The \( \sqrt{2} \) factor incorporates the random nature of molecular velocities and collision probabilities.

Consequently, the average distance a molecule travels between two successive collisions is given by:

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

Option (3) is therefore correct.