Energy Distribution of Hot Atoms in a Reactive System

Abstract

A binary system of hot and thermal atoms is considered in which interactions are governed by an inverse-power potential, and reactions between interacting atoms occur with a probability equal to a constant between two energies and zero elsewhere. Solutions of the time- and space-independent Boltzmann equation are obtained, and are used to develop criteria for the validity of the expression for the hot-atom collision density assumed by Wolfgang and Estrup in their kinetic theory of hot-atom reactions. It is found that this expression has its greatest validity for relatively isotropic scattering, a low reactivity and a large difference between the masses of the interacting species. Errors in the probability that a hot atom reacts before becoming thermalized which result from the assumed form of the collision density are generally of the order of 1%—10%, but for an interaction potential as soft as the inverse sixth power and equal masses the error may be as high as 25%.