# Effective Nuclear Charge

## Effective Nuclear Charge:

Coulomb’s law of attraction states that the interaction of two electrical charges depends on the magnitude of the charges and the distance between. Therefore the attraction between an electron and the nucleus depends on the magnitude of the overall nuclear charge acting on the electron and the distance between the nucleus and the electron. In many electron atoms, the electrons are attracted to the nucleus and then repelled by the other electrons at the same time. Despite the difficulty in analyzing the situation due to the electron-electron repulsions, the energy of the electron can be calculated by observing how the electron interacts with the nucleus and other electrons. This creates the ability to for us to treat each electron as if it were moving in an electric field (the nucleus and the surrounding electrons). The electric field of electrons is the same as the charge of the electric field of the nucleus, which is called the effective nuclear charge. The effective nuclear charge, Zeff, is the net positive charge experienced by an electron in many-electron atoms; this is not a full nuclear charge because the nucleus is protected by some shielding from the other electrons.

### Equation:

• Zeff = Z – S
• Zeff = Effective nuclear charge.
• Z = the number of protons in the nucleus.
• S = the average number of electrons between the nucleus and the electron being analyzed (total number of core electrons).

### Other Important Info:

The effective nuclear charge on an atom determines many of its properties, such as the screening, or shielding of an atom’s valence electrons. As a result, the effective nuclear charge experienced by the outer electrons is determined primarily by the difference between the charge on the nucleus and the charge of the core electrons.

It is also important to note that the effective nuclear charge of an atom increases across the periods of the periodic table, and increases going down a family. However, the effective nuclear charge changes far less down a family then it does across a period. It increases downward along the periodic table for the following reasons:
• Increase in the number of protons = Increase in the force of electrostatic attraction.
• Increase in the distance between the nucleus and electrons = Decrease in the force of electrostatic attraction.
• Increase in the number of electrons

This event is named as “effective” because of the shielding effect core negative electrons have on higher valence electrons which prevents the higher electrons from experiencing the full effect of the nuclear charge.

### Source of Information:

Pg. 239 - 241 of Chemistry: The Central Science by Brown, LeMay, and Bursten