We investigate the possibility of detecting the Podolsky generalized electrodynamics constant a. First we analyze an ion interferometry apparatus proposed by B. Neyenhuis et al. (Phys. Rev. Lett. 99, 200401 (2007)), who looked for deviations from Coulomb's inverse-square law in the context of Proca model. Our results show that this experiment has not enough precision for measurements of a. In order to set up bounds for a, we investigate the influence of Podolsky's electrostatic potential on the ground state of the Hydrogen atom. The value of the ground state energy of the Hydrogen atom requires Podolsky's constant to be smaller than 5.6 fm, or in energy scales larger than 35.51 MeV.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)