Rate Constants for Unimolecular Processes

The spontaneous emission of electromagnetic radiation from an excited molecule is a imimolecular process that follows first-order kinetics. Suppose a photoexcited molecule exhibits fluorescence as its only decay pathway. If there are No photoexcited molecules at time to, then at a subsequent time t the number of molecules still in the excited state (N) is given by 

In many measurements. If is taken to be the magnitude of the detector (e.g., photomultiplier) response to fluorescence at a tmax- 

For most molecules fluorescence is only one of the processes that deactivate an electronically excited state. If a molecule can decay by both fluorescence (with rate constant kf) or radiationless decay (with rate constant ka), the time dependence of a population of excited states is given by 

In general, if there are i first-order, unimolecular decay processes that deactivate an excited singlet state, each with rate constant kf, then the observed singlet lifetime (ts) is 

The quantiun yield of fluorescence equals the rate constant for fluorescence divided by the sum of the rate constants for all decay processes  

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