We use 42 different charged nanoparticles generated by electrospray ionization and a differential mobility analyzer of unusual resolving power, as well as a condensation chamber of the turbulent-mixing type to study the dependence between the diameter, charge state, and critical supersaturation of embryos promoting heterogeneous nucleation. The nanoparticles investigated have diameters ranging from 0.43 to 6.51 nm, and positive charge states varying between 1 and 5 elementary units. We find that the critical supersaturation of small singly charged ions (mobility diameters bellow 1.01 nm) is independent of their size and its value coincides with the result anticipated by Thompson in his theory of ion-induced nucleation. On the other hand, the supersaturation required to activate multiply charged embryos is consistently higher than Thomson's prediction. In fact, the reduction of the critical supersaturation induced by electrification is much smaller than expected for large and multiply charged embryos, and their critical radius is estimated better by Kelvin's criterion. We speculate that this discrepancy is due to the geometrical differences between the actual nucleation sites and the idealized embryo considered in Thomson's model.