Suppose the molecules of a gas are spheres of diameter d. Focus on a single molecule with the average speed v. It will suffer collision with any molecule that comes within a distance d between the centres. In time Δt, it sweeps a volume `πd^2 v Δt` wherein any other molecule will collide with it.

If n is the number of molecules per unit volume, the molecule suffers `nπd^2 v Δt` collisions in time Δt.

Thus the rate of collisions is `nπd^2 v` or the time between two successive collisions is on the average,

`tau=1/(npivd^2)`

The average distance between two successive collisions, called the `text(mean free path)` `l`, is :

`l=vtau=1/(npid^2)`

All molecules are moving and the collision rate is determined by the average relative velocity of the molecules. Thus we need to replace `v` br `v_r`.

A more exact treatment gives

`l=1/(sqrt2 nd^2)`