A novel expansion of the Thomas-Fermi potential for a weakly ionized atom is presented. It is employed in calculating the ionization energies of neutral atoms as they are predicted by an extended version of the Thomas-Fermi model which includes the exchange energy and the leading quantum correction. The ionization energy, I, can be split into a smooth part, I stat , that is here obtained by the statistical treatment, and an oscillatory part, / osc , which represents significant shell effects. The experimental ionization energies of alkaline atoms are well reproduced by / stat , which approaches the constant of 3.15 eV when the atomic number, Z, gets large. It is observed that the amplitude of / osc is proportional to Z −1/3 , so that shell effects are small compared to the smooth part of I (Z ) if Z is sufficiently large (this situation occurs for Z ≿ 10 3 , far beyond the Periodic Table). The study of the systematics of / ( Z ) leads to predictions for the ionization energies of astatine (Z = 85, I ≅ 9.5 eV) and francium (Z = 87, / ≅ 3.9 eV), for which reliable experimental results are not reported.