Shielding effect

The shielding effect describes the decrease in attraction between an electron and the nucleus in any atom with more than one electron shell. It is also referred to as the screening effect or atomic shielding.

Cause
In a single electron system such as hydrogen, the net force on the electron is just as large as the electric attraction from the nucleus.

But when more electrons are involved, each electron (in the n-shell) feels 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 explains 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:


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

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