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The radiative lifetimes and total cross sections for deactivation of K(7 2S ) and K(5 2D ) by collisions with H2 have been studied. In the sample vapor, the K atoms were prepared in either the 7 2S or the 5 2D state by two-photon absorption using a dye laser. The decay signal of the time-resolved fluorescence from the 7 2S–4 2P1/2 or 5 2D–4 2P3/2 transition was then monitored. Based on the Stern–Volmer equation, the radiative lifetimes are (157±5) ns for the 7 2S state and (569±12) ns for the 5 2D state. The total cross sections for deactivation of excited K atoms by means of collisions with H2 are (150±2) A2 for the 7 2S state and (39±4) A2 for the 5 2D state. The radiative lifetimes in the absence of H2 collisions agree with those previously reported. The cross sections for quenching by H2 have been measured for the first time and are interpreted in terms of the harpoon mechanism. The cross section for the transition 7 2S–5 2D has been measured; this transition has been proved to be the predominant channel for the depopulation of the 7 2S state. [ABSTRACT FROM AUTHOR]