Time-resolved fluorescences from varied K excited states are monitored as a function of H-2 pressure. According to a three-level model, the rate coefficients of collisional deactivation for the K 6 S-2, 7 S-2, and 8 S-2 states at 473 K have been determined to be 4.94 +/- 0.15, 5.30 +/- 0.15, and 5.44 +/-0.15x10(-9) cm(3) molecule(-1) s(-1). In addition, the collision transfer of S-2-D-2 transition may be derived to be 5.03 +/- 0.21, 4.68 +/- 0.30, and 4.89 +/- 0.36x10(-9) cm(3) molecule(-1) s(-1), showing dominance of the S-2-state deactivation processes owing to the effect of near-resonance energy transfer. As the temperature is varied, the activation energies for the collisions of K(6 S-2), K(7 S-2), and K(8 S-2) atoms with H-2, respectively, may be estimated to be 5.38 +/-0.33, 4.39 +/- 0.16, and 3.23 +/- 0.19 kJ/mol. The first two values are roughly consistent with the theoretical calculations of 3.1 and 0.9 kJ/mol in C-infinity v symmetry predicted by Rossi and Pascale. The obtained energy barriers are small enough to allow for occurrence of the harpoon mechanism, a model applicable to the reactions between H-2 and alkali atoms such as K, Rb, and Cs. Among them, K-H-2 collisions appear to be the first case to possess a slight energy barrier. This finding of energy barrier may account for the discrepancy for the state reactivity towards H-2 observed between K (or Rb) and Cs atoms.