In atoms and ions with only one electron, the total force experienced by an orbiting electron is equal to the electromagnetic attractive force that the nucleus exerts on this electron. When there are more electrons orbiting the nucleus, each electron experiences this nuclear electromagnetic attraction in addition to repulsion forces by the surrounding electrons. The magnitude of this repulsive force depends on the number of electrons, so as the number of filled electron shells increases, the net force on the outermost electrons decreases. These outer shell electrons are not as strongly bonded to the nucleus as the electrons in inner shells, explaining why valence-shell electrons are more easily removed from an atom than inner shell ones.
A larger number of orbiting electrons results in more complex repulsive interactions between these electrons, making the quantitative assessment of the repulsive force resulting from the shielding effect difficult. Techniques to determine the shielding effect include numerical solutions of the Schrodinger wave equation, using Slater empirical formulas or inferring the effect using the Rutherford backscattering spectrometry.
