Pure potassium vapor or K-H2 mixture was irradiated in a glass fluorescence cell with pulses of 710 nm radiation from an OPO laser, populating K2(1Λｇ) state by two-photon absorption. Cross sections for 1Λｇ-3Λｇ transfer in K2 were determined using methods of molecular fluorescence. During the experiments with pure K vapor, the cell temperature was varied between 553 and 603 K. The K number density was determined spectroscopically by the white-light absorption measurement in the blue wing of the self-broadened resonance D2 line. The resulting fluorescence included a direct component emitted in the decay of the optically excitation and a sensitized component arising from the collisionally populated state. The decay signal of time-resolved fluorescence from 1Λｇ→1 １Σ＋ｕ transition was monitored. It was seen that just after the laser pulse the fluorescence of the photoexcited level decreased exponentially. The effective lifetimes of the 1Λｇ state can be resolved. The plot of reciprocal of effective lifetimes of the 1Λｇ state against K densities yielded the slope that indicated the total cross section for deactivation and the intercept that provided the radiative lifetime of the state. The radiative lifetime (20±2) ns was obtained. The cross section for deactivation of the K2(1Λｇ) molecules by collisions with K is (2.5±0.3)×10-14 cm2. The time-resolved intensities of the K2 3Λｇ→1 ３Σ＋ｕ(484 nm) line were measured. The radiative lifetime (16.0±3.2) ns and the total cross section (2.5±0.6)×10-14 cm2 for deactivation of the K2(3Λｇ) state can also be determined through the analogous procedure. The time-integrated intensities of 1Λｇ→1 １Σ＋ｕ and 3Λｇ→1 ３Σ＋ｕ transitions were measured. The cross section (1.1±0.3)×10-14 cm2 was obtained for K2(1Λｇ)＋K→K2(3Λｇ)+K collisions. During the experiments with K-H2 mixture, the cell temperature was kept constant at 553 K. The H2 pressure was varied between 40 and 400 Pa. The effects of K2-K collisions could not be neglected. These effects were subtracted out using the results of the pure K experiments. The cross section (2.7±1.1)×10-15 cm2 was obtained for K2(1Λｇ)+H2→K2(3Λｇ)+H2 collisions. The cross section is (6.8±2.7)×10-15 cm2 for K2(3Λｇ)＋Ｈ２→ states out of K2(3Λｇ)+H2 collisions.