Question

Mean free path is inversely proportional to (n = number density, d = diameter of particle)

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

Hint:

The mean free path depends on both the number density of particles and the size of the particles. The smaller the particles or the higher the density, the shorter the mean free path.

Answer 1

The Correct Option is C

The mean free path \( \lambda \) is the average distance a particle can travel before colliding with another particle. The mean free path is inversely proportional to the number density \( n \) (the number of particles per unit volume) and the cross-sectional area of the particles. The formula for the mean free path is given by: \[ \lambda \propto \frac{1}{n \cdot \sigma} \] where \( \sigma \) is the effective collision cross-section of the particles, which is proportional to the square of the particle diameter \( d \).
Thus, the mean free path is inversely proportional to \( d \), the diameter of the particles, as given in option (C).