effective nuclear charge

Meaning: Effective nuclear charge (Zeff) is the net positive charge a valence electron feels from the nucleus. Core electrons repel it and shield it from the full nuclear charge; same-shell electrons shield only slightly. Across a period, protons are added but the new electrons enter the same shell, so Zeff rises and electrons are pulled closer. Down a group, added core electrons offset added protons, so Zeff changes little.

Equation: Zeff = Z − S, where Z is the atomic number (number of protons), S is the shielding constant (roughly the number of core electrons), and both are pure counts. Zeff is expressed in units of the elementary charge e = 1.60 × 10⁻¹⁹ C.

On the MCAT: It explains periodic trends: across a period, atomic radius falls while ionization energy and electronegativity rise. In an isoelectronic series (O²⁻, F⁻, Na⁺, Mg²⁺), more protons means higher Zeff and a smaller radius. A quick estimate is Zeff ≈ number of valence electrons (Na ≈ +1, Cl ≈ +7).

Common confusion: Zeff is not the atomic number. Students say it grows down a group because Z does, but added inner shells cancel most of that gain. The valence-electron shortcut slightly overestimates, because same-shell electrons shield a little.