The mean free path of molecules of a gas, (radius 'r') is inversely proportional to :

Question

Find net kinetic energy (maximum possible) associated with 20 diatomic molecules (Here k_B is Boltzmann constant and T is absolute temperature of diatomic gas).

Answer 1

To determine the relationship between the mean free path of gas molecules and the radius of the molecules, we need to understand the concept of mean free path.

The mean free path (\lambda) is the average distance a gas molecule travels before colliding with another molecule. It is given by the formula:

\(\lambda = \frac{kT}{\sqrt{2}\pi d^2 P}\)

where:

k is the Boltzmann constant,
T is the absolute temperature,
d is the diameter of the molecule,
P is the pressure.

The diameter (d) of a molecule is related to its radius (r) by d = 2r. Substituting this, the expression for the mean free path becomes:

\(\lambda = \frac{kT}{\sqrt{2}\pi (2r)^2 P}\)

Simplifying further:

\(\lambda = \frac{kT}{8\pi r^2 P}\)

This equation shows that the mean free path (\lambda) is inversely proportional to the square of the radius of the gas molecules (r^2).

Therefore, among the given options, the correct answer is:

Option: r^2

Answer 2