Periodic Trends: Effective Nuclear Charge, Size, and Energy

Effective nuclear charge and shielding

An outer electron does not feel the full nuclear charge Z. Electrons closer to the nucleus partly cancel it, and the net pull is described by the effective nuclear charge, Zeff = Z − S, where S is a shielding constant. Core electrons, in lower shells, shield well. Electrons in the same shell shield poorly, because on average they are no closer to the nucleus than the electron in question.

A rough estimate counts only core electrons. Sodium (Z = 11) and chlorine (Z = 17) both have 10 core electrons, so sodium's 3s electron feels about +1 and chlorine's 3p electrons about +7. Slater's rules refine this. For an electron in an ns or np subshell, each other electron in the same ns and np subshells adds 0.35 to S (0.30 within 1s), each electron in shell n − 1 adds 0.85, and each electron in deeper shells adds 1.00.

Worked example 1. For sodium's 3s electron, S = 8(0.85) + 2(1.00) = 8.80, so Zeff = 11 − 8.80 = 2.20. For one of chlorine's 3p electrons, S = 6(0.35) + 8(0.85) + 2(1.00) = 10.90, so Zeff = 17 − 10.90 = 6.10. Across period 3, each added proton is only partly offset by the added same-shell electron, so Zeff rises from left to right while n stays at 3.

Atomic radius and isoelectronic ions

Atomic radius decreases across a period because Zeff increases while the outer electrons stay in the same shell, so they are pulled closer. It increases down a group because each period adds a shell, placing the outer electrons farther out, while Zeff changes comparatively little. The largest atoms are at the lower left of the table and the smallest at the upper right.

A cation is smaller than its parent atom: losing electrons reduces repulsion, and for main-group cations it usually empties the outer shell. An anion is larger than its parent atom, because the added electron increases repulsion while the nuclear charge stays the same.

Worked example 2. Rank N³⁻, O²⁻, F⁻, Na⁺, Mg²⁺, and Al³⁺ by radius. Count electrons first: 7 + 3, 8 + 2, 9 + 1, 11 − 1, 12 − 2, and 13 − 3 all equal 10, so every ion has the neon configuration 1s² 2s² 2p⁶. With identical electron counts, the only difference is nuclear charge, which rises from 7 to 13. More protons pull the same electron cloud tighter, so the order is N³⁻ > O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺.

First ionization energy and its subshell exceptions

The first ionization energy is the energy needed to remove the most loosely held electron from a gaseous atom: X(g) → X⁺(g) + e⁻. It generally increases across a period, as Zeff rises and radius shrinks, and decreases down a group. NIST lists ionization energies in electron volts per atom; multiplying by 96.485 kJ/mol per eV converts them to molar units.

Converted from the NIST Atomic Spectra Database, the period 2 values are Li 520.2, Be 899.5, B 800.6, C 1086.5, N 1402.3, O 1313.9, F 1681.0, and Ne 2080.7 kJ/mol. Two steps go the wrong way. Boron is below beryllium because its outermost electron is in 2p, which is higher in energy and partly shielded by the 2s pair. Oxygen is below nitrogen because its fourth 2p electron must pair in an occupied orbital, and the extra repulsion makes it easier to remove.

The same two dips appear in period 3: aluminum (577.5 kJ/mol) is below magnesium (737.7 kJ/mol), and sulfur (999.6 kJ/mol) is below phosphorus (1011.8 kJ/mol). The repeated pattern shows that it comes from subshell structure, not from one peculiar element.

Successive ionization energies and valence electrons

Each successive ionization energy is larger than the one before, because every electron leaves from an increasingly positive ion. The size of each jump is the useful information. A moderate increase means the next electron comes from the same valence shell; a very large jump means it must come from the core, which is closer to the nucleus and far less shielded.

Worked example 3. NIST gives magnesium's first three ionization energies as 7.646, 15.035, and 80.144 eV. Converting: 7.646 eV × 96.485 kJ/(mol·eV) = 737.7 kJ/mol; 15.035 × 96.485 = 1450.7 kJ/mol; 80.144 × 96.485 = 7732.7 kJ/mol. The ratio IE₂/IE₁ is 1450.7 / 737.7 = 1.97, but IE₃/IE₂ is 7732.7 / 1450.7 = 5.33. The large jump after the second electron shows that magnesium has two valence electrons, [Ne] 3s², and explains why it forms Mg²⁺ but not Mg³⁺ in ordinary chemistry.

Sodium shows the jump one step earlier. Its second ionization energy, 4562.4 kJ/mol, is about 9.2 times its first, 495.8 kJ/mol, because the second electron must come from the 2p core.

Electron affinity and electronegativity

Electron affinity describes the energy change when a gaseous atom gains an electron: X(g) + e⁻ → X⁻(g). Sign conventions differ. Some textbooks, including OpenStax, report the energy change, which is negative when energy is released; others report the energy released as a positive number. Check the convention before comparing values. Apart from the noble gases, atoms toward the right of a period release the most energy, because their high Zeff attracts the incoming electron strongly.

Electron affinity is less regular than ionization energy. Chlorine releases more energy than fluorine, about 349 kJ/mol compared with 328 kJ/mol, based on NIST Chemistry WebBook values of 3.613 and 3.401 eV. The added electron in fluorine's compact 2p subshell meets stronger repulsion. Beryllium, nitrogen, and the noble gases have little or no tendency to form stable gaseous anions, because the added electron would enter a higher subshell or pair in a half-filled one.

Electronegativity is the ability of an atom in a molecule to attract the electrons of a bond. Unlike ionization energy, it is not measured on an isolated atom; it is derived from bond energies or other data, and the Pauling scale is the most widely used. Fluorine is highest, at about 4.0. Electronegativity increases across a period and decreases down a group, so bond polarity falls from H–F through H–Cl and H–Br to H–I.

Common mistakes in explaining periodic trends

Trend questions are usually judged on the explanation, not only the order.

A complete explanation names the comparison (same shell or a different shell), states what happens to Zeff or distance, and connects that change to the force on the electron in question.

• Saying an atom is smaller because it has more electrons. Across a period, electrons enter the same shell; size falls because Zeff rises.
• Explaining a group trend with 'more shells' alone, without noting that Zeff changes little down a group.
• Treating ionization energy as strictly increasing across a period. Check the group 2 to 13 and group 15 to 16 steps.
• Comparing ions by nuclear charge without first checking that they are isoelectronic.
• Mixing electron affinity sign conventions and concluding that the more negative number is the smaller affinity.
• Comparing radii from different tables. Covalent, metallic, and ionic radii are defined differently.
• Explaining with what an atom 'wants'. Atoms have no goals; explain with attraction, distance, and repulsion.