The dynamics of a direct reaction between a gas phase H atom and an H atom adsorbed on a Cu surface are explored. This exothermic Eley-Rideal reaction is studied by implementing both 3D quantum and quasiclassical scattering calculations. The metal surface is assumed to be hat. The effects of substituting either or both of the H atoms with D are examined in detail for five different model potential energy surfaces. The reaction cross sections, and the translational, rotational, and vibrational state distributions of the product molecules are computed. A process is considered in which the incident atom transfers enough of its kinetic energy normal to the surface into its motion parallel to the surface and into the adsorbed particle to become trapped. These trapped "hot" atoms can go on to react with other adsorbed atoms, giving "hot" products, as in the Eley-Rideal reaction. We examine the dependence of this mechanism on isotopic substitution and incident energy, in an effort to determine how one might distinguish between the two processes.