Mean free path

In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a result of one or more successive collisions with other particles.

Imagine a beam of particles being shot through a target, and consider an infinitesimally thin slab of the target (see the figure). The atoms (or particles) that might stop a beam particle are shown in red. The magnitude of the mean free path depends on the characteristics of the system. Assuming that all the target particles are at rest but only the beam particle is moving, that gives an expression for the mean free path:

$${\displaystyle \ell =(\sigma n)^{-1},}$$

where ℓ is the mean free path, n is the number of target particles per unit volume, and σ is the effective cross-sectional area for collision.

The area of the slab is L², and its volume is L² dx. The typical number of stopping atoms in the slab is the concentration n times the volume, i.e., n L² dx. The probability that a beam particle will be stopped in that slab is the net area of the stopping atoms divided by the total area of the slab:

$${\displaystyle {\mathcal {P}}({\text{stopping within }}dx)={\frac {{\text{Area}}_{\text{atoms}}}{{\text{Area}}_{\text{slab}}}}={\frac {\sigma nL^{2}\,dx}{L^{2}}}=n\sigma \,dx,}$$

where σ is the area (or, more formally, the "scattering cross-section") of one atom.

The drop in beam intensity equals the incoming beam intensity multiplied by the probability of the particle being stopped within the slab: