The K atoms were prepared in either the 6S or the 4D state by two-photon absorption using an OPO laser. The cross sections for deactivation of K(6S) and K(4D) by collisions with H2 were measured. The temperature of the cell body was controlled at 413 K, and H2 pressure was varied between 4 and 40 Pa. The effects of K(6S, 4D)-K collisions could be neglected in our experimental condition. On excitation of K(6S) state, the decay signal of the time-resolved fluorescence from the 6S→4P transition was monitored. The logarithmic plot for the time-resolved fluorescence of K(6S) atom was shown and the slope yielded an effective lifetime. When the pressure of H2 was successively increased, the time-resolved spectrum obviously had contributions from two components. At the beginning of the decay, the population of K(6S) was simply determined by the two-photon excitation and the decay curve provided the information on the effective lifetime of the K(6S) state under H2 collisions. After a prolonged period, the additional contribution of the K(6S) population from K(4D) state became important. The population of the K(4D) state increased with increasing the pressure of H2, which leading to more intense emission of the 4D→4P transition by comparison with the case in the absence of H2. The effective lifetime for depopulation of the 4D state by collisions with H2 can be treated analogously to the 6S state. Based on the Stern-Volmer equation, radiation lifetimes are (97±15) ns for the 6S state and (300±45) ns for the 4D state. The radiation lifetimes in the absence of H2 collisions agree with those previously reported. The total cross sections for deactivation of excited K atoms by means of collisions with H2 are (1.6±0.3)×10-14 cm2 for the 6S state and (40±6)×10-14 cm2 for the 4D state. Upon excitation to the K(6S) state, the dependence on H2 pressure of integrated fluorescence in the transition 4D→4P was measured. The cross section (1.4±0.3)×10-14 cm2 for the transition 6S→4D was obtained. The authors conclude that the channel for energy depletion from the 6S state is predominantly through the physical quenching to the 4D state, although the KH product has been observed in the chemical reaction.