Mean free path
The mean free path is the average path length traveled by the particles (for example, atom, molecule, ion, or electron) in a given material without interaction with other particles. An interaction is doing any kind of energy or momentum change of the particle, thus understood each collision process.
If a particle in the respective medium through a route of this length, nor 1 / e, or about one-third of the particles, no shock have executed.
Estimation in gases
For a basic gas, which does not necessarily have to be a perfect gas, is obtained as the estimation:
With
- The particle density ( number of particles per unit volume)
- The cross -section.
Here, the plane spanned by the cross section in the direction of movement is based on the cylinder volume, which includes a further particles within the mean free path length on average.
For molecules equilibrium considerations allow the assumption of a Maxwellian equilibrium function a more precise estimate:
With a minimum distance.
Examples
Mean free path of a gas molecule
The mean free path of a gas molecule in air is about 68 nanometers under standard conditions.
The following table lists free path of gas molecules at different pressures to:
Mean free path of electrons
The mean free path of electrons is an important parameter in applications of electron beams in a vacuum ( eg certain surface-sensitive analytical methods or in Braun tubes ). For electron mean free path is a function of the kinetic energy.
In the solid state, it can be estimated for most metals with the " universal curve". At energies around 100 eV it is for most metals at least, since processes in the solid state (eg plasmons, ...) can be excited. At higher and lower energies, the mean free paths in solids are larger.
In gaseous insulating materials (eg, sulfur hexafluoride ) the mean free path affects the electrical breakdown strength.
If electrons in momentum space considered (see Fermi sphere ), so it 's hard to argue with a length, and therefore we consider the mean free flight time.