Brownian Motion in a Gas of Noninteracting Molecules

Abstract

The Brownian motion of a hard spherical particle in a gas whose molecules interact only with the particle but not with each other is considered from three points of view. (a) The generalized Fokker‐Planck equation for the process is derived by the classical method of Lord Rayleigh. (b) The hypothesis of the phenomenonlogical theory of Brownian motion that the distribution of changes of momentum of the particle is normal is investigated with some mathematical rigor. (c) The formula for the friction constant recently given by Kirkwood is applied to this case. It is found that the plateau value in this formula exists in this case and that the value obtained agrees with Rayleigh's method. The hypothesis of the phenomenonological theory is found to be justified for times long enough for many collisions to have taken place. The theoretical formula for the friction constant is compared with Millikan's data for the friction constant for oil droplets in air at low pressures. It is found to agree with Millikan's data with respect to the form of the dependence on density and temperature. The theoretical values for hard spheres are somewhat lower than the data for oil droplets.