Energy Distribution of Hot Atoms in a Reactive System

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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%.