= Solution
Rearrangement gives the <Stern-Volmer equation>
$$
\boxed{\frac{\phi_0}{\phi_Q}=1+k_Q\tau_0[Q].}
$$
Thus a straight-line plot against $[Q]$ has unit intercept and slope $K_{\rm SV}=k_Q\tau_0$. \b[Determine $k_Q=K_{\rm SV}/\tau_0$ using an independently measured unquenched lifetime], or use known $k_F$ in the restricted model. Yield measurements alone do not separate two unknown <rate constants>. Equivalently the slope of $1/\phi_Q$ is $k_Q/k_F$.
Use the absorbed intensity rather than incident intensity to normalize samples, and correct solvent/background signals, quencher <absorption> and <fluorescence> reabsorption. Under <dynamic fluorescence quenching> the lifetime ratio should follow the same straight line as the yield ratio. A reduced intensity without the corresponding lifetime change suggests <static fluorescence quenching> or an optical artefact; curvature can also indicate multiple populations or more complicated kinetics.
Back to article page
