The abstraction kinetics for atomic hydrogen (H-at) removal of chemisorbed D and atomic deuterium (D-at) removal of chemisorbed H are studied on single crystal Si surfaces. The surface H and D coverages are measured in real time by mass analyzing the recoiled H+ and D+ ion signals. On both Si(100) and Si(111) surfaces, the abstraction reactions are efficient, and have very low activation energies similar or equal to 0.5-1 kcal/mol. For abstraction from surfaces containing only monohydride species, the abstraction reaction probability is similar or equal to 0.36 times the adsorption rate of H-at or D-at. For the same H-at and D-at exposures, the reaction rates for H-at removal of adsorbed D and D-at removal of adsorbed H are nearly identical. All observations are consistent with a generalized Eley-Rideal abstraction mechanism, and a two-dimensional quantum-mechanical model is used to calculate reaction probabilities for these reactions. According to the model, the activation energies are due to enhanced abstraction rates from excited vibrational states of the adsorbed Si-H or Si-D bond. With SiH2 and SiH3 species present on the surface, the removal rate of H using D-at is decelerated, suggesting that the higher hydrides have a lower cross section for abstraction.