A modified Thomas-Fermi equation proposed previously by the present author is used to derive analytical expressions for the electrostatic potentials of atoms and ions. This equation considers the exponential falloff of electron density at large distances from the nucleus, corresponding to the Hartree asymptote. The expressions obtained satisfy the normalization condition. Expressions are presented for the radii and total energies of atoms and ions. The ions Li** plus , Na** plus , and K** plus are considered as examples.