Question

What is effective nuclear charge (Zeff) and how does it influence the atomic radius trend

Answer 1

Atomic radius is generally stated as being the total distance from an atom’s nucleus to the outermost orbital of electron. In simpler terms, it can be defined as something similar to the radius of a circle, where the center of the circle is the nucleus and the outer edge of the circle is the outermost orbital of electron. As you move across or down the periodic table, trends emerge that help explain how atomic radii change.

The effective nuclear charge (Z _eff) of an atom is the net positive charge felt by the valence electron. Some positive charge is shielded by the core electrons therefore the total positive charge is not felt by the valence electron. A detailed description of shielding and effective nuclear charge can be found here. Zeff greatly affects the atomic size of an atom. So as the Z_eff decreases, the atomic radius will grow as a result because there is more screening of the electrons from the nucleus, which decreases the attraction between the nucleus and the electron. Since Z_eff decreases going down a group and right to left across the periodic table, the atomic radius will increase going down a group and right to left across the periodic table.

There is relation between effective nuclear charge and atomic radius

F_eff = k Z_effe²/r²

Z_eff is effective nuclear charge

e is the charge of an electron or proton

r is the radius or distance between the proton and the electron