Mean Free Path

Mean Free Path

The molecule of a gas move with high speeds at a given temperature but even then a molecule of the gas takes a very long time to go from one point to another point in the container of the gas. This is due to the fact that a gas molecule suffers a number of collisions with other gas molecules surrounding it. As a result of these collisions, the path followed by a gas molecule in the container of the zig – zag as shown in figure. During two successive collision, a molecule of a gas moves in a straight line with constant velocity and the distance travelled by a gas molecule between two successive collisions is known as Free Path.


Mean Free Path: It is the average distance travelled by a moving particle between two successive impacts in a system of agitated particles, which results in the change in their energy, physical properties or the direction of motion.

Mean Free Path

Molecules of a gas are considered to be spheres of diameter d. We will focus on a single molecule that is moving with an average speed v.

From the image shown above, we can say that it will suffer collision with many molecules coming in its path. Let us say in time Δt, it sweeps a volume πd²vΔt, wherein any other molecule will collide with it. Here, if n is the number of molecules per unit volume, the molecules will suffer nπd²vΔt collisions in the given time Δt.

The time between two successive collisions is given by, τ = 1/ (nvπd²).

The average distance between two successive collisions, called the mean free path l is given by l = τ x v = 1/ (nπd²).

Factors affecting Mean Free Path:

  • Density: As the density increases, the molecules come closer to each other, thus increasing the number of collisions, and decreasing the mean free path.
  • Number of molecules: As the number of molecules increases the probability of collision increases and the thus the mean free path decreases.
  • Radius of the molecule: As the radius of the molecule increases the space between the molecules decreases causing number of collisions to increase, thus decreasing the mean free path.
  • Pressure, temperature and other physical factors also affect the density of the gas and thus affect the mean free path.