A model for fluorescence quenching with exponential distance dependence is developed and applied to external heavy-atom quenching. The systems studied are C-70-bromobenzene and phenanthrene-iodide, in liquid solutions at room temperature and in rigid glasses at 77 K. The predicted parameter correlation is observed in the two systems, which correspond to two extreme and opposite situations, strong and weak quenching. A detailed analysis of the fitted parameters allows the determination of the effective Bohr radii L and of the intrinsic unimolecular rate constants for quenching at contact, k(0). The unusually high value of L for the C-70-bromobenzene pair is tentatively attributed to the extended size of the external part of the pi orbitals of the fullerene. The room temperature quenching rate constant computed with the determined low-temperature parameters is shown to be in good agreement with the experimental one for both systems studied. (C) 2003 American Institute of Physics.