Ionic Radius

Ionic radius refers to the effective size of an ion in a crystalline lattice or solution, measured as the distance from the nucleus to the outermost electron shell. Unlike atomic radius, ionic radius depends critically on whether an atom has lost electrons to form a cation or gained electrons to form an anion. These two processes produce dramatically different size outcomes: cations are always smaller than their parent atoms, while anions are always larger. The reason lies in the balance between nuclear charge (protons) and electron–electron repulsion. When an atom loses one or more electrons to become a cation, the same number of protons must now attract a smaller electron cloud, pulling the remaining electrons closer to the nucleus and shrinking the ion. Conversely, when an atom gains electrons to form an anion, the added electrons increase repulsion among the electron cloud without adding any protons, causing the cloud to expand outward. This asymmetry is one of the most important concepts in understanding ionic bonding and crystal structures. Ionic radii are typically reported in picometres (pm) or angstroms (Å), where 1 Å = 100 pm. For example, a sodium atom (Na) has an atomic radius of approximately 186 pm, but the sodium ion (Na⁺) has an ionic radius of only 102 pm — a reduction of nearly 45%. In contrast, a chlorine atom has an atomic radius of about 99 pm, but the chloride ion (Cl⁻) swells to 181 pm. Understanding these trends allows chemists to predict lattice energies, solubility, and the geometry of ionic compounds.

Key takeaways
  • Cations Are Smaller Than Their Parent Atoms
  • Anions Are Larger Than Their Parent Atoms
  • Trends Across a Period
  • Trends Down a Group
  • Isoelectronic Series

Cations Are Smaller Than Their Parent Atoms

When a metal atom loses electrons, it forms a cation with fewer electrons than protons. The nuclear charge (Z) remains unchanged, but the electron–electron repulsion decreases because there are fewer electrons. The effective nuclear charge felt per electron increases, drawing the remaining shells inward. For example, magnesium (Mg, atomic radius ≈ 160 pm) loses two electrons to form Mg²⁺ (ionic radius ≈ 72 pm). The loss of the entire outer 3s shell accounts for the dramatic shrinkage.

Anions Are Larger Than Their Parent Atoms

When a nonmetal atom gains electrons, it forms an anion. The additional electrons enter the existing valence shell, increasing electron–electron repulsion without any increase in nuclear charge. The shielding effect grows, reducing the effective nuclear charge experienced by each electron, and the ion expands. Oxygen (O, atomic radius ≈ 73 pm) gains two electrons to form O²⁻ (ionic radius ≈ 140 pm), nearly doubling in size.

Moving left to right across a period, ionic radii of isoelectronic species (ions with the same electron configuration) decrease with increasing atomic number. This occurs because each successive element has one more proton, pulling the same number of electrons more tightly. For the isoelectronic series with 10 electrons (neon configuration): O²⁻ (140 pm) > F⁻ (133 pm) > Ne (38 pm, neutral) > Na⁺ (102 pm) > Mg²⁺ (72 pm) > Al³⁺ (53 pm). The greater the nuclear charge for the same electron count, the smaller the ion.

Moving down a group, ionic radii increase because each successive period adds a new electron shell farther from the nucleus. For example, the Group 1 cation radii increase: Li⁺ (76 pm) < Na⁺ (102 pm) < K⁺ (138 pm) < Rb⁺ (152 pm) < Cs⁺ (167 pm). Similarly, halide anion radii increase: F⁻ (133 pm) < Cl⁻ (181 pm) < Br⁻ (196 pm) < I⁻ (220 pm). The added principal quantum shells dominate over the increased nuclear charge.

Isoelectronic Series

An isoelectronic series is a group of ions or atoms that all have the same number of electrons but different nuclear charges. Comparing isoelectronic species isolates the effect of nuclear charge alone. For the 18-electron (argon configuration) isoelectronic series: S²⁻ (184 pm) > Cl⁻ (181 pm) > Ar (neutral, ~71 pm) > K⁺ (138 pm) > Ca²⁺ (100 pm) > Sc³⁺ (74.5 pm). As the atomic number Z increases across this series, the ionic radius decreases because more protons exert a stronger pull on the same 18 electrons.

The Key Equation

Zeff=Z−σZ_{\text{eff}} = Z - \sigma
  • Z_{\text{eff}} — Effective nuclear charge (dimensionless (in units of elementary charge)): The net positive charge experienced by a valence electron after accounting for shielding by inner electrons. Higher Z_eff pulls electrons closer, reducing ionic radius.
  • Z — Atomic number (dimensionless): The total number of protons in the nucleus; determines the strength of the attractive force on all electrons.
  • \sigma — Shielding constant (dimensionless): The degree to which inner-shell electrons shield outer electrons from the full nuclear charge. Estimated using Slater's rules. Larger σ means more shielding and a larger ionic radius.

Worked Example

Problem. Arrange the following species in order of increasing ionic radius: Na⁺, F⁻, Mg²⁺, O²⁻. All four are isoelectronic with 10 electrons (neon configuration). Justify your answer using nuclear charge.

r(Mg2+)<r(Na+)<r(F−)<r(O2−)r(\text{Mg}^{2+}) < r(\text{Na}^+) < r(\text{F}^-) < r(\text{O}^{2-})

Answer. Increasing ionic radius: Mg²⁺ < Na⁺ < F⁻ < O²⁻

Figure
Diagram
Ionic Radius: Isoelectronic Series (10 electrons, Ne configuration)O²⁻Z=8r ≈ 140 pmF⁻Z=9r ≈ 133 pmNa⁺Z=11r ≈ 102 pmMg²⁺Z=12r ≈ 72 pm← Increasing nuclear charge (Z) → Decreasing ionic radius● = anions (larger)● = cations (smaller)All species have 10 electrons; radius decreases as Z increases
Origins · 1 minLinus Pauling and how this was discovered
LP
Linus Pauling
1901–1994 · American

Linus Pauling made foundational contributions to our understanding of chemical bonding, electronegativity, and ionic radii. In his landmark 1927 work and in his book 'The Nature of the Chemical Bond' (1939), Pauling derived a self-consistent set of ionic radii from X-ray crystallographic data by assuming that the sum of cation and anion radii equals the observed bond length in a crystal. His ionic radii values (known as Pauling radii) are still widely taught and used today. He also developed Slater's rules (alongside John C. Slater) to estimate shielding constants, directly linking Z_eff to ionic size. Pauling is one of only four people to have won two Nobel Prizes — Chemistry (1954) for his work on chemical bonding, and Peace (1962) for his nuclear weapons activism.

  • Atomic Radius — Ionic radius is derived from atomic radius; understanding how atomic size changes across the periodic table is essential before comparing it to ionic size after electron gain or loss.
  • Ionization Energy — Ionization energy determines how easily an atom loses electrons to form a cation, directly linking to why cations are smaller and how ionic radius trends relate to energy changes.
  • Electronegativity — Electronegativity governs which atoms gain electrons (forming larger anions) and which lose them (forming smaller cations), connecting ionic radius trends to bond polarity and ionic character.
  • Lattice Energy — Ionic radius directly determines lattice energy through Coulomb's law: smaller ions pack more closely together, resulting in stronger electrostatic attractions and higher lattice energies.
  • Effective Nuclear Charge — Z_eff is the fundamental quantity that explains why isoelectronic ions differ in size — the core mechanism behind ionic radius trends across periods.