Time dependent theory of hot-atom reactions

A simple time dependent theory of hot-atom reactions in a dilute host gas is developed based on Porter's stochastic theory of hot-atom reactions. Kinetic equations governing the time behavior of the hot-atom probability distribution as well as the concentration of hot atoms are derived. If the frequency of collisions is significantly larger than the reaction rate, it is shown that the probability distribution will relax to a steady state form. The steady state distribution can be used to define hot-atom reaction rate constants and these constants are directly related to product yields. By comparing the time dependent theory to usual kinetic type theories, it is shown that whenever the steady state theory is valid, it gives results identical to those based on the Miller-Dodson formula