Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2A / Section A / 16 / a / Solution

Let $s=[S_1]$ and treat the quencher concentration as a constant reservoir. Weak steady excitation, one emitting population, and the three specified processes giveDividing the fluorescence photon-production rate by the absorbed photon rate therefore givesThis assumes no saturation, photochemical loss, reabsorption, static association or additional excited-state decay, and that each counted absorbed photon reaches the stated $S_1$ population. In this restricted scheme ${\varphi }_0=1$ and the unquenched lifetime is ${\tau }_0=1/k_F$.