As before, the presence of a fast, radiationless decay transition results in the population of the pump band being quickly depleted ("N"4 ≈ 0). In a four-level system, any atom in the lower laser level "E"2 is also quickly de-excited, leading to a negligible population in that state ("N"2 ≈ 0). This is important, since any appreciable population accumulating in level 3, the upper laser level, will form a population inversion with respect to level 2. That is, as long as "N"3 > 0, then "N"3 > "N"2, and a population inversion is achieved. Thus optical amplification, and laser operation, can take place at a frequency of ν32 ("E"3-"E"2 = "h"ν32).