The integral yield of a reaction involving hot hydrogen atoms has been evaluated as a function of the initial energy of the hot atom. On the assumption that the cross section for the reaction is given by the excitation function ▪ or another function of similar general form, expressions for the integral product yield were derived from the kinetic theory of hot reactions. Stochastic calculations, in which the thermal motion of the substrate was included, were also carried out. For the excitation functions considered, and for elastic collisions between the hydrogen atom and the substrate, the integral product yield is an approximately linear function of the initial energy of the hot atom over the range from 1.4 to 2.5 times the threshold energy. Simple extrapolation to zero of yields measured in this energy range would give an apparent threshold higher than the true value, and in general the true threshold is expected to be 90% ± 10% of the apparent value obtained by extrapolation.