The lifetimes are important because they determine the time course of the emission [/(t)] from the excited state:
[where /(0) is the intensity at time t = 0 and the lifetime - is for either fluorescence or phosphorescence]. We can define the natural lifetime (-o) of fluorescence and phosphorescence as the inverse of the radiative rate constant for that state:
With these definitions we can redefine the quantum yields in terms of the lifetimes:
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