A numerical study, stimulated by existing experimental results concerning the temporal dynamics of internally generated radiations, is presented for a four-level system of the potassium atom. An intense nanosecond duration laser pulse excites the two-photon transition 4S 1=2 $ 6S 1=2 and initiates the generation of internal radiations from quantum noise. It is shown that the temporal profiles of the generated radiations along the atomic path-1,, evolve differently as a function of certain system parameters. It is also shown that the excitation laser intensity affects the parametric emissions along path-1 and the population of the states. The path-2 emissions, which also depend on the excitation laser intensity, are most probably due to amplified spontaneous emission (ASE), without population inversion, in the case of strong excitation. We finally examine the radiation dynamics under the effect of the elastic dephasing collisions between the potassium atoms with the buffer gas atoms.