Zeff can be calculated by subtracting the magnitude of shielding from the total nuclear charge and the effective nuclear charge of an atom is given by the equation:

where Z is the atomic number (number of protons in nucleus) and S is the shielding constant. The value of Zeff will provide information on how much of a charge an electron actually experiences.

We can see from Equation above that the effective nuclear charge of an atom increases as the number of protons in an atom increases (Figure 1.1). Therefore as we go from left to right on the periodic table the effective nuclear charge of an atom increases in strength and holds the outer electrons closer and tighter to the nucleus. As we will discuss later on in the chapter, this phenomenon can explain the decrease in atomic radii we see as we go across the periodic table as electrons are held closer to the nucleus due to increase in number of protons and increase in effective nuclear charge.

Figure 1.1 : Relationship between the Effective Nuclear Charge Z_eff and the Atomic Number Z for the Outer Electrons of the Elements of the First Three Rows of the Periodic Table. Except for hydrogen, (Zeff is always less than Z, and (Zeff increases from left to right as you go across a row.

The shielding constant can be estimated by totaling the screening by all electrons (n) except the one in question.

where Si is the shielding of the i^th electron.

Electrons that are shielded from the full charge of the nucleus experience an effective nuclear charge (Zeff ) of the nucleus, which is some degree less than the full nuclear charge an electron would feel in a hydrogen atom or hydrogenlike ion.

 Zeff for a specific electron can be estimated is the shielding constants for that electron of all other electrons in species is known. A simple approximation is that all other electrons shield equally and fully: