 Fluorescence lifetime

For the constant-rate model in fluorescence quantum yield, fluorescence lifetime is the mean residence time in the emitting excited state and the $1/e$ timescale of its exponential decay. The detected fluorescent photon rate after an ideal instantaneous pulse is $I(t)=\eta k_{\mathrm{r}}{N}_0{e}^{-t/\tau }$ for $t\ge 0$. Its amplitude and its decay timescale are separate quantities.

For a stipulated example, rates $(k_{\mathrm{r}},k_{\mathrm{nr}})=(0.05,0.20){\mathrm{ns}}^{-1}$ give $\tau =4\mathrm{ns}$ and $\Phi =0.20$. Rates $(0.20,0.05){\mathrm{ns}}^{-1}$ give the same $\tau$ but $\Phi =0.80$. Conversely, doubling $N_0$ doubles the ideal amplitude without changing $\tau$. Equal fluorescence lifetimes need not imply equal brightness or equal fluorescence quantum yields.

Different environments can supply several populations, giving $I(t)={\sum }_j{A}_j{e}^{-t/{\tau }_j}$ rather than one exponential decay. A fitted single timescale then depends on the selected model and detection band. FRET donor lifetime uses the change in a donor's decay when transfer introduces an additional loss route; the FRET branch develops that interpretation.