A particle moves in a straight line between collisions. The average distance traveled by a particle between two collisions is known as the mean free path. The mean free path depends on the cross section, and is given by One consequence of the requirement that the gas be dilute is that . In other words the diluteness implies that the mean free path is much larger than the particle size so that a typical particle trajectory consists of long straight segments interrupted by almost discontinuous changes of direction when collisions occur. If the gas is dilute, the probability of three body collisions is much lower than for two body collisions and they can be neglected.
Collisions can change f in two ways.
Some velocities originally having velocities will have some different velocity after the collision. This causes a decrease in f . Some particles have other velocities may have the velocity after a collision, increasing f . The impact parameter is s , and the angle of deflection is . Suppose two particle with initial velocities and have velocities and after a collision.