Effective Nuclear Charge measures the net positive charge of nucleus acting on an electron in a multi electron system. It is different from the actual nuclear charge acting between two charged species. This is because there is electron present between nucleus and the electrons in the valence shell which cause repulsion among them countering the attraction of nucleus and electron.

In atomic physics and chemistry, the effective nuclear charge is important in deeper understanding of atomic structure and periodic trends. This article will explore what an effective nuclear charge means, calculate the effective nuclear charge, Slater’s rules, the values of effective nuclear charge, and its trends.

What is Effective Nuclear Charge?

Effective Nuclear Charge is the net positive charge experienced by an electron in a multi-electron atom. The term Effective indicates that the shielding effect of electron prevent electrons from getting completely affected by the nuclear charge. Another name for Effective Nuclear charge is Core Charge. Effective Nuclear Charge is denoted by Z_eff or Z*

Shielding Effect

To understand Effective Nuclear Charge, first, we need to understand why every electron in an atom does not feel the same nuclear charge. It is because, in a multi-electron atom, electrons occupy various orbitals or shells inside the atom, where each shell is situated at different levels from the nucleus. The electrons that are present in the innermost shells repel the electrons that are present in the outer shells. This phenomenon of shielding or screening the outermost electrons from fully experiencing the attraction force of protons in the nucleus by the inner electrons is known as the Shielding effect. This shielding arises between electrons in different shells due to electrostatic repulsion between negatively charged electrons.

Effective Nuclear Charge Formula

To calculate effective charge two parameters we need to consider following two factors:

• The total number of protons present in the nucleus (original nuclear charge), which is given by the atomic number (Z) of that element.
• The shielding constant, which accounts for the repulsion between electrons.

Therefore, the mathematical expression for Effective Nuclear Charge is :

Z_eff = Z – S

where,

• Zeff is Effective Nuclear Charge
• Z is Number of Proton(Atomic Number)
• S is Number of electrons between Nucleus and the electron for which we have to calculate Z_eff

Slater’s Rules

Slater’s Rule is a set of rules used to calculate the effective nuclear charge, where we assign screening constants to each electron in an atom based on its principal quantum number (n) and azimuthal quantum number (l), i.e., the type of orbital (s, p, d, f). Electrons are arranged into groups based on their principal quantum number (n), representing the electron’s energy level. Within each energy level, electrons are further organized into subgroups based on their azimuthal quantum number (l), which describes the shape of the orbital. Here, we consider electrons in s and p orbitals together as they have similar energies. The considerations of Slater’s Rule are mentioned below:

• Electrons that are present in the same group contribute a shielding constant of 0.35. Here, an exception exists for the electron in the [1s] group, where the contribution is 0.30.
• Each electron with a principal quantum number (n-1) contributes a value of 0.85 to the shielding constant.
• Each electron with a principal quantum number less than or equal to (n-2) contributes a value of 1.00 to the shielding constant.
• Each electron with a principal quantum number less than (n) and electrons with a principal quantum number n and an azimuthal quantum number less than (l) contributes a value of 1.00 to the shielding constant because those electrons are closer to the nucleus.

Let’s look at an example of an Iron atom with a nuclear charge of 26 and an electronic configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶ 4s².