Periodic Variations in Element Properties

Core Concepts

Effective nuclear charge: the engine of the trends

A valence electron does not feel the full nuclear charge Z; core electrons between it and the nucleus partly cancel it. The net charge felt is:

Z_eff = Z - S

where S is the shielding constant. Two facts drive everything: (1) core electrons shield very effectively — a 3s electron in sodium feels roughly Z_eff ≈ +1, not +11; (2) same-shell electrons shield poorly — each new proton across a period adds no shielding, so Z_eff climbs steadily left to right. This rising Z_eff drives nearly every trend in this topic.

Atomic radius: shrink across, grow down

The atomic radius (usually half the distance between bonded atoms) reflects how far the outermost electrons sit from the nucleus. Across a period, Z_eff rises while the shell number stays the same, pulling the electron cloud in — radii decrease (Na > Mg > Al > ... > Cl). Down a group, each step adds a shell, and the distance gain beats the modest shielding increase — radii increase (Li < Na < K < Rb < Cs). Largest atoms: bottom left (Fr, Cs); smallest: top right (F, He).

Ionization energy: the cost of removing an electron

First ionization energy (IE₁) is the energy required to remove the outermost electron from a neutral gaseous atom. It increases across a period — more protons, tighter grip — and decreases down a group — bigger atom, farther electron. Two wrinkles: (1) successive IEs grow, and jump enormously once core electrons start being removed — the IE₂ → IE₃ jump in magnesium reveals its two valence electrons; (2) small dips occur — boron's IE₁ is lower than beryllium's because its outer electron sits in a higher-energy 2p orbital, and oxygen's is lower than nitrogen's because its extra electron must pair in a 2p orbital. The same logic gives the Mg→Al and P→S dips.

Electron affinity: the payoff for adding an electron

Electron affinity (EA) is the energy change when a neutral gaseous atom gains an electron: X(g) + e^- → X^-(g), reported as the negative of that change, so a more negative EA means a more favorable (more exothermic) gain. Halogens have the most negative EAs — one electron completes their octet — while noble gases have EA near zero or positive (no room in the valence shell). Across a period EA generally becomes more negative (chlorine, not fluorine, is the extreme, because fluorine's small size causes repulsion in F⁻); down a group it becomes less negative (the added electron enters a larger, more diffuse orbital).

Electronegativity: the tug-of-war for bonding electrons

Electronegativity is a dimensionless measure of how strongly an atom attracts electrons in a chemical bond. On the Pauling scale, values run from about 0.7 (Cs, Fr) to 3.98 (F), increasing across a period and decreasing down a group — the same Z_eff logic applied to bonded electrons. Fluorine (3.98) leads; oxygen (3.44), chlorine (3.16), and nitrogen (3.04) follow. The difference between bonded atoms (ΔEN) classifies bonds by a commonly taught guideline: ΔEN < 0.4 — nonpolar covalent; 0.4 to about 1.7 — polar covalent; > 1.7 (some texts use 2.0) — largely ionic. These cutoffs are heuristics, not laws — bonds fall on a continuum.

Ionic radius: cations shrink, anions swell

Ions are not the size of their parent atoms. Cations lose their outermost shell (or lose electrons with the nuclear charge unchanged), so they are much smaller — Na (186 pm) → Na⁺ (102 pm). Anions gain electrons with no increase in nuclear charge, so the cloud expands — Cl (99 pm) → Cl⁻ (181 pm). Across a period, ions of the same charge shrink as Z rises (Mg²⁺ < Na⁺). In an isoelectronic series — ions with the same electron count, like O²⁻, F⁻, Na⁺, Mg²⁺, Al³⁺ — radius decreases steadily as nuclear charge increases: more protons pulling the same electrons.

Common Confusions