mean free path, \(\lambda\)
The average distance a molecule travels between collisions. For a molecule, \(\lambda = (\sqrt{2}\ \pi \ n\ d_{\text{m}}^{2})^{-1}\), where \(n\) is the number of molecules per unit volume and \(d_{\text{m}}\) is their mean diameter. For O2 at one atmosphere and \(25\ ^{\,\unicode{x26ac}}\text{C}\), this distance is only \(9.7\times 10^{-6}\ \text{cm}\); at \(10^{-6}\) atmospheres and \(25\ ^{\,\unicode{x26ac}}\text{C}\) it is \(9.7\ \text{cm}\). For an aerosol particle, the mean free path, \(\lambda _{\text{B}}\) in the stokes region (see Stokes law) is given by: \(\lambda _{\text{B}} = \sqrt{\frac{3\ k\ T}{m}}\ m\ B\) where \(m\) is the mass of the particle, \(k\) is the Boltzmann constant (\(1.381\times 10^{-23}\ \text{J K}^{-1}\)), \(T\) is the temperature (\(\text{K}\)) and \(B\) is the mobility.
Green Book,2nd ed., p. 56 (
PAC, 1990, 62, 2167. 'Glossary of atmospheric chemistry terms (Recommendations 1990)' on page 2201 (