Negatively charged ions are mainly stabilized through the electron correlation effect. A measure of the stability of a negative ion is the electron affinity, which the energy gain by attaching an electron to a neutral atom. This fundamental quantity is, due to the almost general lack of bound excited states, the only atomic property that can be determined with high accuracy for negative ions. We will present the results of the first laser photodetachment studies of radioactive negative ions at CERN-ISOLDE. The photodetachment threshold for the radiogenic iodine isotope 128I was measured successfully, demonstrating the performance of the upgraded GANDALPH experimental beam line. The first detection of photo-detached astatine atoms marks a milestone towards the determination of the EA of this radioactive element.