  Recently, we have proposed the existence of a universal relation between the
maximal electric charge and total mass of any weakly self-gravitating object:
$Z\leq Z^*={\alpha}^{-1/3}A^{2/3}$, where $Z$ is the number of protons, $A$ is
the total baryon (mass) number, and $\alpha=e^2/\hbar c$ is the fine-structure
constant. Motivated by this novel bound, we explore the $(Z,A)$-relation of
atomic nuclei as deduced from the Weizs\"acker semi-empirical mass formula. It
is shown that {\it all} nuclei, including the meta-stable maximally charged
ones, conform to the upper bound. Moreover, we suggest that the new charge-mass
bound places an interesting constraint on the value of the fine-structure
constant: $\alpha\gtrsim 1/323$.
