Effective Nuclear Charge
Definition and meaning of Effective Nuclear Charge in chemistry.
Effective nuclear charge (Zeff) is the net positive charge actually experienced by an electron in a multi-electron atom, after accounting for the shielding, or screening, effect of the other electrons. It is calculated as Zeff = Z − S, where Z is the true nuclear charge (atomic number) and S is the shielding constant contributed by intervening electrons.
In more detail
Inner-shell electrons shield outer electrons from the full nuclear attraction almost completely, while electrons in the same shell shield one another only weakly. Because of this, Zeff rises across a period from left to right (added protons are poorly shielded by electrons entering the same shell), causing atomic radius to shrink and ionization energy to increase. Slater's rules give a simple empirical method for estimating S, and thus Zeff, for any electron in an atom.
Key facts
| Symbol | Zeff |
|---|---|
| Formula | Zeff = Z − S |
| Periodic trend | Increases left to right across a period |
| Field | General Chemistry |
For sodium (Z = 11), the valence 3s electron does not feel the full +11 charge because the ten core electrons (1s²2s²2p⁶) shield it. Using Slater's rules, S ≈ 8.8, giving Zeff ≈ 11 − 8.8 = 2.2 for that outermost electron.
Frequently asked questions
How is effective nuclear charge estimated in practice?
Slater's rules provide a set of empirical guidelines for calculating the shielding constant S based on which shell and subshell an electron occupies relative to the others, allowing Zeff to be approximated without complex calculations.
Why does effective nuclear charge increase across a period but atomic radius decrease?
Moving across a period, protons are added to the nucleus while new electrons enter the same principal shell, which shields poorly; the rising Zeff pulls the valence electrons in more tightly, shrinking the atomic radius.