Worked example 1
Rank the isoelectronic species O²⁻, F⁻, Na⁺ and Mg²⁺ in order of decreasing radius.
Try it first: Confirm they all have the same electron count before comparing.
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Periodic TrendsIonic radiusContent level: Core 20 min
Ionic Radius and Isoelectronic Series
What you'll be able to do: Compare the size of an ion to its parent atom and rank an isoelectronic series correctly.
Best after: Atomic Radius, Ionization Energy and Electronegativity, Electron Configurations of Ions
Introduction
Ions are not the same size as the atoms they came from, and a set of ions with identical electron counts can still differ widely in size. One rule handles both cases: compare protons per electron.
These are recommended, not required. You can start this lesson at any time.
Learning objectives
- Predict whether an ion is larger or smaller than its parent atom
- Explain cation and anion size changes with Zeff and shell loss
- Identify isoelectronic species
- Rank an isoelectronic series by radius
Lesson
Cations shrink
Sodium loses its single 3s electron to become Na⁺, which empties the n = 3 shell entirely. The ion is left with a neon-like n = 2 outer shell, and the same 11 protons now pull on only 10 electrons. Na⁺ (about 102 pm) is far smaller than Na (about 186 pm).
For main-group metals the cation often loses a whole shell, which is why the size drop is so large.
Anions swell
Chlorine gains an electron to become Cl⁻. No new shell is added, but 17 protons must now hold 18 electrons, so the pull per electron falls and electron-electron repulsion rises. Cl⁻ (about 181 pm) is noticeably larger than Cl (about 99 pm).
Isoelectronic series
Species such as N³⁻, O²⁻, F⁻, Ne, Na⁺, Mg²⁺ and Al³⁺ all have 10 electrons. Their sizes are set purely by nuclear charge: more protons means a tighter grip. Radius therefore decreases as Z increases along the series.
N³⁻ > O²⁻ > F⁻ > Ne > Na⁺ > Mg²⁺ > Al³⁺
Choose a comparison before ranking
For an isoelectronic series, the ions have the same number of electrons, so the one with more protons is smaller. For an atom and its own cation or anion, compare shell loss and electron repulsion as well as proton count. A single proton-to-electron ratio cannot safely rank unrelated species with different occupied shells. Na⁺ is neon-like (outer n = 2), while Cl⁻ is argon-like (outer n = 3); first identify their configurations, then compare. This avoids treating several distinct size effects as one arithmetic rule.
Use the right comparison for the species
The strongest ranking rule is for an isoelectronic series: with the same number of electrons and broadly comparable shells, more protons pull those electrons closer. For a neutral atom and its cation, also ask whether ionization emptied an entire outer shell, as Na → Na⁺ does. For two ions of the same element, the more positive ion is usually smaller because fewer electrons repel one another. Do not use a simple proton-to-electron ratio to rank unrelated ions in different principal shells; Na⁺ and Cl⁻ differ in occupied shell as well as charge. Compare electron configurations first, then nuclear charge.
Check electron count before ranking ions
Isoelectronic ions contain the same number of electrons and fill the same shells. Their radius then depends chiefly on how strongly each nucleus attracts that shared electron arrangement: more protons generally mean a smaller ion. First verify that the ions are actually isoelectronic; comparing charges alone can mislead when electron shells differ.
Same electrons + more protons → smaller radius.
Key ideas
Rule
Cation size
A cation is always smaller than its parent atom.
Rule
Anion size
An anion is always larger than its parent atom.
Definition
Isoelectronic series
A set of atoms and ions with the same number of electrons but different nuclear charges.
Rule
Isoelectronic ranking
Within the series, radius decreases as the number of protons increases.
Worked examples
Worked example 2
Is a chloride anion larger or smaller than a neutral chlorine atom, and why?
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Worked example 3
Compare Fe²⁺ and Fe³⁺ in size, starting from Fe = [Ar] 4s² 3d⁶.
Try it first: Write each ion and compare their electron counts with the same 26-proton nucleus.
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Worked example 4
Order Al³⁺, Mg²⁺, and Na⁺ from largest to smallest radius.
Try it first: Count electrons in each ion before comparing proton counts.
0 of 3 steps revealed.
Common mistakes
Ranking an isoelectronic series by charge magnitude alone.
Why it's wrong: Charge is a symptom. The real driver is proton count relative to a fixed electron count.
Check instead: Order by atomic number: highest Z is smallest.
Saying a cation is smaller because it lost mass.
Why it's wrong: Mass is essentially unchanged. Size drops because a shell is emptied and the remaining electrons feel a higher Zeff.
Check instead: Explain with the electron shell lost and the proton-to-electron ratio.
Assuming anions are smaller because they are more stable.
Why it's wrong: Stability and size are unrelated. Adding electrons always increases repulsion and expands the cloud.
Check instead: Anion larger than atom, cation smaller, every time.
After the lesson · Question bank
Independent practice
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What you should now know
Cations are smaller than their parent atoms and anions are larger. Within an isoelectronic series, the species with the most protons is the smallest, because the same electron cloud is pulled by a stronger nucleus.
- Cations are smaller than their parent atoms, anions are larger
- Isoelectronic radius falls as proton count rises
- Compare protons per electron to settle any size question
- Charge magnitude alone is not a ranking rule
Sources and further reading
- Chemistry 2e, Section 6.5: Periodic Variations in Element PropertiesFlowers, Theopold, Langley, Robinson · OpenStax, Rice University · Chapter 6.5View source
Access for free at openstax.org License