The shock tube technique with D- and H-atom atomic resonance absorption spectrometric (ARAS) detection has been used to measure rate constants for two isotopic modifications of the most fundamental chemical reaction, H + H-2 --> H-2 + H: D + H-2 --> HD + H (1) and H + D-2 --> HD + D (2). Hydrogen atoms were produced from the thermal decomposition of either C2D5I or C2H5I. Ethyl iodide decomposition above similar to1150 K is fast, and the product ethyl radicals decompose even faster, giving ethylene and hydrogen atoms. This clean source of atoms then allows for first-order analysis of both reactant and product hydrogen atoms for determining rate constants. The rate constant results can be described by the Arrhenius expressions k(1) = 3.17 x 10(-10) exp(-5207K/T) cm(3) molecule(-1) s(-1), over the temperature range 1166-2112 K, and k(2) = 2.67 x 10(-10) exp(-5945K/T) cm(3) molecule(-1) s(-1), over the temperature range 1132-2082 K. These new results are compared to earlier results and supply additional values for evaluating the rate behavior for both reactions over the very large temperature range similar to200-2200 K. These evaluations are then compared to recent quantum mechanical scattering calculations of the thermal rate behavior that are based on a new and quite accurate potential energy surface (i.e., globally accurate to similar to0.01 kcal mol(-1)). Within experimental error, there is now complete convergence between the experimental evaluation and the new theory, bringing to completion a 75-year effort in chemical kinetics and dynamics. This is the first completely solved problem in chemical kinetics.