Subjects and lessons to explore.

Law

General Chemistry I · Periodic Properties

Ionic Radius

5 min read
SourcesReport an error
Want it in plain words first? Jump to Eli explains — the same idea, no jargon.
On this page 7 sections
  1. In 30 seconds
  2. Why this matters
  3. The college version
  4. Eli explains
  5. Key takeaway
  6. Study tools
  7. Sources & references

In 30 seconds

When an atom becomes an ion, its radius changes in a predictable way. Cations (positive ions) are smaller than their parent atoms because they lose valence electrons — reducing electron–electron repulsion and often removing the entire valence shell. Anions (negative ions) are larger than their parent atoms because they gain electrons, increasing repulsion while the nuclear charge stays the same. Within an isoelectronic series (ions with the same number of electrons), size decreases as nuclear charge increases.

Why this matters

Ionic size determines how tightly ions pack in a crystal and therefore the lattice energy and melting point of ionic solids (smaller ions + higher charge → stronger lattice, see the Coulomb's-law note). It also matters in biology: ion channels in cell membranes are selective in part because they are sized to pass, say, K⁺ but not the larger Na⁺, and ion size affects solubility and hydration in water.

The college version

Key Ideas

  • Cation (positive ion): forms by losing electrons. It is smaller than the parent atom.
  • Anion (negative ion): forms by gaining electrons. It is larger than the parent atom.
  • Why cations shrink: fewer electrons → less electron–electron repulsion, and the same nuclear charge now pulls a smaller cloud (valence shell may be lost entirely, e.g., Na → Na⁺ drops the 3s shell).
  • Why anions expand: more electrons → greater repulsion among electrons, but the nuclear charge is unchanged, so the cloud spreads out.
  • Isoelectronic series: a set of ions (and sometimes atoms) with the same electron count. Example: O²⁻, F⁻, Na⁺, Mg²⁺, Al³⁺ all have 10 electrons.
  • Isoelectronic trend: among ions with equal electrons, the one with the highest nuclear charge (Z) is smallest — more protons pull the same number of electrons in tighter.

Equations and Variables

No simple formula gives ionic radii, but the controlling factor is the charge-to-size relationship (same idea that governs Coulomb's law):

  • Zeff = Z − S governs the pull on the electron cloud; higher Z (same electron count) → smaller ion.
  • Qualitatively: for an isoelectronic series, radius ∝ 1/Zeff (more protons = tighter, smaller cloud).

How It Works

  1. A neutral atom has equal numbers of protons and electrons; its radius balances nuclear attraction against electron–electron repulsion.
  2. Removing electrons forms a cation: fewer electrons mean less mutual repulsion, and (for main-group metals) the valence shell is often emptied, leaving a smaller, noble-gas-like core.
  3. Adding electrons forms an anion: the same nucleus must now hold more electrons, so repulsion rises and the cloud expands.
  4. In an isoelectronic series, all species have the same number of electrons; the only difference is the number of protons.
  5. More protons (higher Z) exert a stronger pull on the identical electron cloud, shrinking it — so size falls as Z rises through the series.

Worked Example

1. Which is larger, Cl or Cl⁻? Cl⁻ is larger. Adding one electron to chlorine (Z = 17) increases electron–electron repulsion while the nuclear charge stays at 17, so the anion expands (Cl ≈ 99 pm → Cl⁻ ≈ 181 pm).

2. Which is smaller, Na or Na⁺? Na⁺ is smaller. Sodium loses its only 3s electron, dropping the entire valence shell, so the ion shrinks dramatically (Na ≈ 186 pm → Na⁺ ≈ 102 pm).

3. Rank this isoelectronic series (all 10 electrons) from largest to smallest: O²⁻, F⁻, Na⁺, Mg²⁺, Al³⁺. All have 10 electrons, so size is set by nuclear charge (O = 8, F = 9, Na = 11, Mg = 12, Al = 13). Higher Z → smaller ion: O²⁻ (140 pm) > F⁻ (133 pm) > Na⁺ (102 pm) > Mg²⁺ (72 pm) > Al³⁺ (54 pm).

Common Confusions

  • "Gaining electrons makes an ion smaller." — Wrong: gaining electrons increases repulsion, so anions are larger than their parent atoms.
  • "Cations and anions are both bigger than the parent." — Wrong: only anions expand; cations shrink.
  • "In an isoelectronic series, the biggest ion has the most protons." — Wrong: more protons pull the same electron cloud tighter, so the highest-Z ion is the smallest.
  • "Ionic and atomic radii are interchangeable." — No: a cation is much smaller than its neutral atom, so you cannot use the neutral radius for an ion in bond-length or lattice calculations.
Eli, the EliExplains learning guide

Eli explains

The same idea, in plain words

Explain it like I’m 10

Imagine a fixed magnet (the nucleus) holding a cloud of rubber bands. If you take some rubber bands away (lose electrons to make a cation), the remaining ones pull in tighter, so the bundle shrinks. If you stuff extra rubber bands in (gain electrons to make an anion), they push against each other and the bundle puffs up — but the magnet didn't get any stronger, so it can't hold them as tightly. In an isoelectronic series, everyone has the same number of rubber bands, but a stronger magnet pulls the same bundle in tighter. (The analogy captures repulsion vs. attraction; it omits the quantum shells that disappear when a cation forms.)

Key takeaways

  • Cations are smaller than their parent atoms; anions are larger.
  • Removing electrons decreases repulsion (and may remove a whole shell), shrinking the ion.
  • Adding electrons increases repulsion with no change in nuclear charge, expanding the ion.
  • In an isoelectronic series, size decreases with increasing nuclear charge.
  • Classic 10-electron series (largest → smallest): O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺.
  • Typical radii: Na⁺ 102 pm, Mg²⁺ 72 pm, Al³⁺ 54 pm, O²⁻ 140 pm, F⁻ 133 pm, Cl⁻ 181 pm.
  • Small, highly charged ions (Mg²⁺, Al³⁺) give very strong ionic lattices.
  • Cations smaller than parent; anions larger than parent.
  • Losing electrons → less repulsion (and possibly a lost shell) → smaller ion.
  • Gaining electrons → more repulsion → larger ion.
  • Isoelectronic series: same electron count, size decreases as Z increases.
  • O²⁻ > F⁻ > Na⁺ > Mg²⁺ > Al³⁺ (all 10 electrons).
  • Ionic size feeds directly into lattice energy and melting points.

Keep learning

Ready to build on this? Continue to the next lesson.

Practice General Chemistry I

This lesson has no separate scored set. Practice draws from the subject’s question bank.

Study tools & related lessonsYou’ll learn to · Related

You’ll learn to

  • Explain why cations are smaller than their parent atoms and anions are larger.
  • Define an isoelectronic series and predict size order within one.
  • Use periodic position and charge to compare the sizes of different ions.
  • Connect ionic size to the physical properties of ionic compounds (e.g., lattice energy).

Sources & references

  1. OpenStax, *Chemistry 2e*, "6.5 Periodic Variations in Element Properties."
  2. OpenStax, *Chemistry 2e*, "7.1 Ionic Bonding."
  3. PubChem, "Sodium (Element)."
  4. PubChem, "Chlorine (Element)."

This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.

Educational content only. It is not medical, legal or professional advice. Found an error? Tell us.