The Mean Free Path and the Collision Cross Section

Abstract

An uncharged particle can only have its direction of motion changed by a collision. Between collisions the particle moves in a straight line with constant velocity v over a distance given by

$$D = lv$$

where τ is the time between collisions. The diffusion coefficient can then be written n particles per unit volume experiences nvQ collisions per unit time. The time between succcssivc collisions is Just the reciprocal of this quantity

$$l = v\tau $$

and the path length is

$$\tau = \frac{1}{{nvQ}}$$

The denser the medium, the shorter the path length.