Abstract
Let Nc denote the maximum number of electrons that can be bound to an atom of nuclear charge z, in the Thomas-Fermi-von Weizsacker theory. It is proved that Nc cannot exceed z by more than one, and thus this theory is in agreement with experimental facts about real atoms. A similar result is proved for molecules, i.e. Nc cannot exceed the total nuclear charge by more than the number of atoms in the molecule.