How big is an atom?
An atom has no sharp edge: its electron cloud just gets thinner and thinner farther out. So how do you measure its size? Chemists measure the distance between the nuclei of two bonded atoms and work out each atom’s radius from it. The radius worked out from covalently bonded atoms is the covalent radius共价半径; the one from metal crystals is the metallic radius. Different methods and different tables can disagree by tens of picometers (1 pm = 10⁻¹² m), so compare sizes using a single table. All atomic radii on this site are covalent radii from one table (Cordero and coworkers, 2008).
Trends in atomic radius
Lesson 1.4.5 showed two trends, and lesson 2.3.2 gave them one explanation:
- Atomic radius decreases across a period. The atoms have the same number of energy levels, but Zeff increases, pulling the outer electrons closer. Period 3 runs from Na at 166 pm to Cl at 102 pm.
- Atomic radius increases down a group. Each step down adds an energy level, so the outer electrons are farther from the nucleus, and that outweighs the extra nuclear charge. Group 1 runs from Li at 128 pm to Cs at 244 pm.
- Across the transition metals, the radius changes little. The added electrons go into the inner (n−1)d sublevel, where they shield the added nuclear charge, so the outer ns electrons feel about the same pull.
Ionic radius
When an atom gains or loses electrons, its size changes a lot:
- A cation is smaller than its parent atom. When sodium loses its 3s electron, the whole third energy level is empty, leaving only the 2, 8 levels: Na is 166 pm, but Na⁺ is only 102 pm. With fewer electrons there is also less electron–electron repulsion, so the 11 protons pull the remaining electrons in tighter.
- An anion is larger than its parent atom. When chlorine gains an electron, its nuclear charge is still +17, but it now has 18 electrons instead of 17. The extra electron–electron repulsion makes the electron cloud spread out: Cl is 102 pm, and Cl⁻ is 181 pm.
- For ions with the same electron configuration, the larger the nuclear charge, the smaller the ion. N³⁻, O²⁻, F⁻, Na⁺, Mg²⁺, and Al³⁺ all have 10 electrons arranged like neon (1s²2s²2p⁶). Atoms and ions with the same number of electrons are isoelectronic等电子粒子. With the same electrons and a nuclear charge rising from +7 to +13, the pull keeps getting stronger: N³⁻ is the largest at 146 pm, and Al³⁺ is the smallest at 54 pm.
Ionic radii are measured in ionic crystals, a different method from covalent radii, so comparisons between an atom and an ion are only rough. The conclusions above still hold.
To compare sizes, think in this order: first count energy levels (more levels, larger); if they’re equal, compare nuclear charge (more protons, smaller); if that’s equal too (the same element), compare electrons (more electrons, larger).
Switch between the sets of atoms and ions and watch how the circles change; click a circle to see its nuclear charge, electrons, and energy levels:
Example 1: Ranking isoelectronic ions
Rank S²⁻, Cl⁻, K⁺, and Ca²⁺ from largest to smallest.
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Count the electrons. Electrons = atomic number − ionic charge:
Ion Electrons Nuclear charge S²⁻ 16 + 2 = 18 +16 Cl⁻ 17 + 1 = 18 +17 K⁺ 19 − 1 = 18 +19 Ca²⁺ 20 − 2 = 18 +20 All have 18 electrons, arranged like argon, in the same number of shells.
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Compare nuclear charges. With the same electrons, a larger nuclear charge pulls those 18 electrons in harder, giving a smaller radius.
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Conclusion. S²⁻ > Cl⁻ > K⁺ > Ca²⁺.
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Check with data. The ionic radii are 184, 181, 138, and 100 pm.
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A common mistake. Assuming the cations, with larger atomic numbers, are larger. For isoelectronic ions, the larger the nuclear charge, the smaller the ion.
Example 2: Three comparisons
In each pair, which is larger? (1) Li⁺ or Na⁺; (2) F⁻ or Na⁺; (3) Cl or Cl⁻.
- The order of comparison. First compare shells (more shells, larger); with the same shells, compare nuclear charge (larger charge, smaller); for the same element, compare electrons (more electrons, larger).
- Li⁺ and Na⁺: different shells. Li⁺ has 1 shell (2) and Na⁺ has 2 (2, 8): Na⁺ > Li⁺ (102 pm vs 76 pm).
- F⁻ and Na⁺: same shells, compare nuclear charge. Both are 2, 8; the nuclear charges are +9 for F and +11 for Na: F⁻ > Na⁺ (133 pm vs 102 pm).
- Cl and Cl⁻: same element, compare electrons. Both have a nuclear charge of +17, but Cl⁻ has one more electron and more repulsion: Cl⁻ > Cl (181 pm vs 102 pm).
- Na or Na⁺
Na⁺ has lost its entire third energy level, so it is much smaller than the sodium atom.
- Cl or Cl⁻
The nuclear charge is the same, but Cl⁻ has one more electron, so there is more repulsion and the ion is larger.
- Mg²⁺ or Na⁺
Both have 10 electrons. Sodium's nuclear charge (+11) is smaller than magnesium's (+12), so Na⁺ is larger.
- O²⁻ or F⁻
Both have 10 electrons. Oxygen's nuclear charge (+8) is smaller than fluorine's (+9), so O²⁻ is larger.
- K⁺ or Na⁺
K⁺ has 3 energy levels (2, 8, 8); Na⁺ has only 2.
- S²⁻ or O²⁻
They're in the same group, and S²⁻ has one more energy level.
- Al³⁺ or Mg²⁺
Both have 10 electrons. Aluminum's larger nuclear charge makes Al³⁺ smaller, so Mg²⁺ is larger.
- Cl⁻ or K⁺
Both have 18 electrons. Chlorine's nuclear charge (+17) is smaller than potassium's (+19), so Cl⁻ is larger.
- Li or Be
Atomic radius decreases across a period, and lithium is to the left of beryllium.
Common mistakes
Mistake 1: “An anion is negative, so the nucleus holds it more tightly and it’s smaller than the atom.” The nuclear charge hasn’t changed, but there are more electrons, so electron–electron repulsion increases and the cloud spreads out. An anion is always larger than its parent atom.
Mistake 2: “Ions with the same number of electrons are the same size.” Isoelectronic species have the same electrons and the same configuration, but different nuclear charges. The more protons pulling on the same electrons, the smaller the particle: O²⁻ is 140 pm, but Mg²⁺ is only 72 pm.
Mistake 3: “Two books give different radii for sodium, so one of them is wrong.” Atomic radius has several definitions, including the covalent radius and the metallic radius, each measured differently. Sodium’s covalent radius is 166 pm and its metallic radius is 186 pm; both are correct. As long as you compare values from one table, the trends are the same.
Quick check
Which of these has the smallest radius?
All four have 10 electrons. Magnesium has the largest nuclear charge (+12), so it pulls hardest, and Mg²⁺ is the smallest.
Which statement about atomic and ionic radii is correct?
Across a period, the energy levels stay the same and Zeff increases, so atomic radius decreases. Radius increases down a group, and cations are smaller than their atoms. More electrons doesn't always mean larger: a lithium atom has only 3 electrons but is larger than a chlorine atom with 17 (128 pm versus 102 pm).
Summary
- Atomic radius decreases across a period (Zeff increases) and increases down a group (more energy levels).
- A cation is smaller than its parent atom (it loses its outer level); an anion is larger (more electrons, more repulsion).
- Among isoelectronic species, the larger the nuclear charge, the smaller the particle. To compare sizes, look at energy levels first, then nuclear charge, then the number of electrons.
On to AP (for later)
AP U1.7 often asks you to explain why Cl⁻ is larger than Cl, or why Mg²⁺ is smaller than Na⁺. A full-credit answer uses Coulomb’s law. For the first, say that the nuclear charge is the same but there are more electrons, so electron–electron repulsion is greater. For the second, say that the ions have the same number of electrons, but Mg²⁺ has more protons and so attracts them more strongly.