Effective Nuclear Charge (\(Z_{eff}\)) represents the net positive attraction experienced by an electron in a multi-electron atom. This concept is fundamental to understanding how atoms interact and exhibit their characteristic chemical behavior. Although the atomic nucleus contains a specific number of protons, the outermost electrons do not feel the full force of that positive charge. \(Z_{eff}\) is therefore a more accurate measure of the nucleus’s effective pulling power, driving properties like atomic size and ionization energy.
Defining Effective Nuclear Charge and Shielding
The actual nuclear charge (\(Z\)) is the atomic number—the total count of protons within the nucleus. In a single-electron atom, like hydrogen, the electron feels the full attractive force, so \(Z_{eff}\) equals \(Z\). In multi-electron atoms, however, outer electrons are attracted to the nucleus but repelled by the negative charge of the inner-shell electrons.
This repulsion is known as the shielding or screening effect (\(S\)). Inner core electrons form a negative cloud that partially blocks the nucleus’s attractive force from reaching the outermost, or valence, electrons. Consequently, \(Z_{eff}\) is always less than \(Z\), described by the formula \(Z_{eff} = Z – S\).
The Driving Factor: Increasing Across a Period
The most significant increase in effective nuclear charge occurs when moving from left to right across a period (row) on the periodic table. Moving across a period, the atomic number (\(Z\)) increases by one for each successive element, adding an additional proton to the nucleus. This steady increase in positive charge is the primary reason for the rising \(Z_{eff}\).
The new electron being added enters the same principal quantum shell, not a new inner shell. For example, in the third period, electrons are all added to the \(n=3\) shell. Since electrons in the same shell do not shield each other effectively, the shielding constant (\(S\)) remains relatively stable.
The dramatic increase in \(Z\) therefore outweighs the minimal change in \(S\), resulting in a substantial net increase in \(Z_{eff}\). For instance, in the third period, the calculated \(Z_{eff}\) rises from approximately 2.2 for Sodium (Na) to about 6.8 for Argon (Ar).
The Effect of Moving Down a Group
The trend for effective nuclear charge is much less pronounced when moving down a group (column) on the periodic table. Moving downward, the number of protons (\(Z\)) increases significantly, but a new, larger electron shell is also introduced. This new shell places the valence electrons farther away from the nucleus.
The core electrons fill these newly added inner shells, substantially increasing the shielding constant (\(S\)). This greater number of inner electrons screens the nucleus much more efficiently from the outermost valence electrons. While \(Z\) increases, the shielding effect \(S\) increases at a similar rate.
These two opposing factors largely counterbalance each other, meaning the \(Z_{eff}\) experienced by the outermost electrons remains nearly constant or shows only a very slight increase down a group. The size increase observed down a group is due primarily to the addition of a new, distant electron shell.
How Increasing Effective Nuclear Charge Influences Atomic Properties
The strong increase in effective nuclear charge across a period has direct consequences for the atom’s physical and chemical properties. A higher \(Z_{eff}\) signifies a greater inward pull on the valence electrons, causing the atomic radius to decrease from left to right across the periodic table.
Ionization Energy
The increased attraction means that valence electrons are held more tightly by the nucleus. This tighter hold requires a greater input of energy to remove an electron from the atom. Consequently, the ionization energy, the energy required to detach an electron, increases significantly across a period.
Electron Affinity
A high effective nuclear charge also increases an atom’s propensity to attract an additional electron. Atoms with a greater \(Z_{eff}\) have a stronger desire to pull in negative charge, resulting in a more favorable electron affinity. This stronger grip dictates how an element will bond and react with other substances.