# Shielding effect

The shielding effect sometimes referred to as atomic shielding or electron shielding describes the attraction between an electron and the nucleus in any atom with more than one electron. The shielding effect can be defined as a reduction in the effective nuclear charge on the electron cloud, due to a difference in the attraction forces on the electrons in the atom. It is a special case of electric-field screening.

## Strength per electron shell

The wider the electron shells are in space, the weaker is the electric interaction between the electrons and the nucleus due to screening. In general we can order the electron shells (s,p,d,f) as such

${\displaystyle S(\mathrm {s} )>S(\mathrm {p} )>S(\mathrm {d} )>S(\mathrm {f} )}$,

where S is the screening strength that a given orbital provides to the rest of the electrons.

## Reason

In hydrogen, or any other atom in group 1A of the periodic table (those with only one valence electron), the force on the electron is just as large as the electromagnetic attraction from the nucleus of the atom. However, when more electrons are involved, each electron (in the nth-shell) experiences not only the electromagnetic attraction from the positive nucleus, but also repulsion forces from other electrons in shells from 1 to n. This causes the net force on electrons in outer shells to be significantly smaller in magnitude; therefore, these electrons are not as strongly bonded to the nucleus as electrons closer to the nucleus. This phenomenon is often referred to as the orbital penetration effect. The shielding theory also contributes to the explanation of why valence-shell electrons are more easily removed from the atom.

The size of the shielding effect is difficult to calculate precisely due to effects from quantum mechanics. As an approximation, we can estimate the effective nuclear charge on each electron by the following:

${\displaystyle Z_{\mathrm {eff} }=Z-\sigma \,}$

Where Z is the number of protons in the nucleus and ${\displaystyle \sigma \,}$ is the average number of electrons between the nucleus and the electron in question. ${\displaystyle \sigma \,}$can be found by using quantum chemistry and the Schrödinger equation, or by using Slater's empirical formulas.

In Rutherford backscattering spectroscopy the correction due to electron screening modifies the Coulomb repulsion between the incident ion and the target nucleus at large distances. It is the repulsion effect caused by the inner electron on the outer electron.