The effective nuclear charge, also known as Zeff, is a measure of the effective nuclear charge felt by an electron in an atom. It is a measure of how strongly the nucleus attracts the electron and is an important factor in determining the chemical properties of atoms. Zeff values are related to the number of electrons in the shell, the nuclear charge, and the shielding effect of inner electrons. Understanding Zeff is crucial to predicting the behavior of atoms in molecules.

The following trends are indirectly proportional to the effective nuclear charge, Zeff:

• Atomic size increases with increasing nuclear charge.
• Atomic ionization energy decreases with increasing nuclear charge.
• Atomic electron affinity increases with decreasing nuclear charge.
• Atomic electronegativity decreases with increasing nuclear charge.

Atomic size increases with increasing nuclear charge because Zeff increases with nuclear charge, which means more electrons are attracted to the nucleus. For example, as the nuclear charge increases from 5 to 8, the effective nuclear charge experienced by the outermost electrons increases from 4.8 to 7.9. Thus, electrons are more strongly attracted to the nucleus, causing the atomic radius to decrease.

Atomic ionization energy decreases with increasing nuclear charge because Zeff increases with nuclear charge, meaning that the electrons in the outermost shell experience a greater effective nuclear charge. This makes it easier to remove electrons from the outermost shell, thus reducing the ionization energy.

Atomic electron affinity increases with decreasing nuclear charge because Zeff decreases as the nuclear charge decreases, meaning that electrons in the outermost shell experience a weaker effective nuclear charge. This makes it easier to add electrons to the outermost shell, thus increasing the electron affinity.

Atomic electronegativity decreases with increasing nuclear charge because Zeff increases with nuclear charge, meaning that electrons in the outermost shell experience a greater effective nuclear charge. Thus, the atom tends to attract electrons more strongly, reducing its electronegativity.

In summary, the trends of atomic size, ionization energy, electron affinity, and electronegativity are all indirectly proportional to the effective nuclear charge, Zeff. Understanding Zeff and its relationship to these trends is essential for predicting the behavior of atoms in molecules.