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In a hydrogen atom, the single electron feels the full nuclear charge Z. In multi-electron atoms, inner electrons partially cancel the nuclear attraction for outer electrons through a phenomenon called shielding. Slater's rules quantify this: each electron in the same shell contributes 0.35 to the shielding constant, each electron in the n-1 shell contributes 0.85, and electrons in shells n-2 or lower contribute 1.00. For sodium (Z=11), the outer 3s electron has Zeff = 11 - (2×1.00 + 8×0.85) = 11 - 8.8 = 2.2.
Zeff increases across a period because each added proton increases Z by 1, while electrons added to the same shell shield only 0.35 per electron—a net increase. This explains why fluorine (Zeff ≈ 5.2) holds its electrons much more tightly than lithium (Zeff ≈ 1.3) despite both being in period 2. Higher Zeff contracts the electron cloud, raising ionization energy and electronegativity while decreasing atomic radius.
Down a group, Zeff remains roughly constant or increases slightly because new shells are added and inner electrons provide near-complete shielding. However, the principal quantum number n increases, placing valence electrons farther from the nucleus. This combination—similar Zeff but larger n—results in weaker electron binding down a group, explaining the gradual decrease in ionization energy and the increase in atomic and ionic radii as you descend the periodic table.
Atomic radius, ionization energy, electron affinity, electronegativity, and periodic trends
Explore CategoryZeff = Z - S, where Z is the atomic number and S is the shielding constant calculated using Slater's rules. Each electron group contributes a specific fraction to S based on its shell.
Each new proton adds +1 to Z, but same-shell electrons only shield 0.35 each, so the net Zeff rises by approximately 0.65 per element across a period.
Higher Zeff means the nucleus attracts valence electrons more strongly, requiring more energy to remove them. This is why ionization energy generally increases across a period.
Slater's rules are empirical guidelines for estimating the shielding constant S. Electrons in the same group contribute 0.35, the (n-1) shell contributes 0.85, and inner shells contribute 1.00 to S for s and p electrons.
No. Z is always an integer equal to the number of protons. Zeff is a smaller decimal value reflecting what an outer electron actually experiences after inner electrons partially cancel the nuclear attraction.