We study wurtzite GaN/AlN quantum dots (QDs) by time-resolved photoluminescence. The properties of nitride based nano-objects are significantly affected by strong built-in electric fields existing in this crystalline phase. These fields induce a spatial separation of electrons and holes in the quantum dot, a Stark shift of the transition energy, and they slow their radiative recombination down to tens of microseconds of decay time for the largest quantum dots. Such long decay times are responsible for the screening of internal fields by using moderate excitation intensities, thus modifying drastically both the energy and the rate of photon emission. Consequently it is difficult to perform spectroscopic studies of these QDs in the regime where a single electron-hole (e-h) pair is present at the most in each dot. Using a pulsed laser excitation, we study the time-resolved dynamics of carrier recombinations, waiting for complete recombination of all electron-hole pairs in the dots. We clearly exhibit the conditions where no screening of the internal electric field occurs. We especially obtain the transition energy and the mono-exponential decay, i.e the radiative recombination time, of the last e-h pair present in the dot, for a wide range of QD sizes. These results are analyzed within an envelope function model for the electron and hole confinement. The effective electric field, averaged over the strain distribution in the dots, is determined to be of 9.0 ± 0.5 MV/cm.