The widely used relation alpha; = alpha(0)+Deltaalpha for the electric polarizability, where Deltaalpha is proportional to the r.m.s. charge radius of the system, is revisited within a simple model of two spinless particles bound electromagnetically. A complete set of the relativistic corrections to alpha(0) following from the Breit Hamiltonian is obtained. It is shown that these corrections modify the result for alpha; in comparison to that obtained with alpha(0) taken in the nonrelativistic approximation. We propose that the same situation can take place in the more complicated case of hadrons. Special attention is devoted to the correct definition of the center-of-mass coordinates which are found to be very important.