A theoretical model of laser excited potassium vapour induced by nanosecond laser pulses tuned to the first resonance, 4s-4p and 4p -nl transitions has been studied. All the important collisional ionization, photoionization, electron collisions and radiative interactions are included in this mode. The numeric al model studies the temporal variation of the Electron Energy Distribution Function (EEDF); the dependence of the (EEDF) on potassium vapor density and laser energy; the variation of atomic ion density; molecular ion and electron density. The applied comp uter simulation model is based on the numerical solution of a set of rate equations that describe the rate of change of the ground and excited states populatio n, beside the atomic ion K⁺ density; molecular ion K₂⁺ and electron density formed during the int eraction. The calculations showed that, the non-equilibrium shape of the electrons occurs due to the relaxation of fast electrons produced by super elastic collision with residual excited potassium atoms. Also the results showed a competition between the p rocesses reponsible for producing K⁺. Finally, the model may be useful for interesting applications such as laser isotopes separation and alkali laser systems.