= Solution
A quencher-independent intersystem-crossing rate adds to the unquenched decay rate:
$$
\phi_Q=\frac{k_F}{k_F+k_{\rm ISC}+k_Q[Q]},\qquad
\tau_0=\frac1{k_F+k_{\rm ISC}}.
$$
The normalized <Stern-Volmer equation> retains the same form, so \b[<intersystem crossing> does not bias $k_Q$ if the actual unquenched lifetime is used]. It reduces $\phi_0$ below one and changes the slope through $\tau_0$; assuming $\tau_0=1/k_F$ would then give the wrong result. A quencher that itself changes <intersystem crossing> or returns triplet population to the singlet requires a larger kinetic scheme.
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