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B. Matter, Chemical Trends, and Chemical Bonding · Matter, Chemical Trends, and Chemical Bonding

Trends in Atomic and Ionic Radius

B2.1 B3.3 B2.2About 65 minutes
Learning goals
  • I can describe how atomic radius is measured.
  • I can describe and explain the trends in atomic radius across a period and down a group.
  • I can explain why cations are smaller and anions larger than their atoms.
  • I can rank atoms and isoelectronic ions by size.

Words to know

atomic radius
A measure of the size of an atom, usually half the distance between the nuclei of two bonded identical atoms.
covalent radius
Half the distance between the nuclei of two identical atoms joined by a covalent bond.
picometre (pm)
10⁻¹² m, a common unit for atomic and ionic sizes.
ionic radius
The radius of an ion, measured in ionic crystals.
cation / anion
A positively charged ion (lost electrons) / a negatively charged ion (gained electrons).
isoelectronic
Having the same number of electrons (and the same electron arrangement).

How big is an atom?

A caesium atom is the largest atom in the first six periods, and its radius is only about 0.000 000 000 24 m. That is 244 picometres (1 pm = 10⁻¹² m). Lined up side by side, about 40 million caesium atoms would fit across a 2 cm button.

Atoms do not have hard edges; the electron cloud just fades out. So how can we measure a radius at all? And why are some atoms more than four times wider than others? Effective nuclear charge, from the last lesson, gives the answer.

Measuring atomic radius

Chemists measure the distance between the nuclei of two atoms that are bonded together. For two identical atoms joined by a covalent bond, the covalent radius is half the distance between the two nuclei. In Cl₂, the nuclei are 198 pm apart, so the radius of chlorine is about 99 to 102 pm (different methods and tables give slightly different values). For metals, chemists use half the distance between neighbouring atoms in the solid.

Atomic radius is a general name for these measurements. Always compare values from the same table, because different methods give slightly different numbers.

The trends

Across a period, atomic radius decreases. Each step to the right adds one proton and one electron, but the electron goes into the same shell. The core electrons stay the same, so Zeff increases and the whole electron cloud is pulled in closer.

Down a group, atomic radius increases. Each step down adds a new shell of electrons, farther from the nucleus. Zeff stays about the same, so the extra shell wins and the atom gets bigger.

So the smallest atoms are at the top right of the table (fluorine, and the noble gases helium and neon) and the largest are at the bottom left (caesium and francium).

Period 2Period 3128Li96Be84B76C71N66O57F166Na141Mg121Al111Si107P105S102Clcovalent radius (pm); radius decreases across each period
Atomic (covalent) radii in picometres. In both periods the radius shrinks from left to right as the effective nuclear charge grows.
Li128 pmNa166 pmK203 pmRb220 pmCs244 pmGroup 1: radius increases down the group (drawn to scale)
Down group 1, each atom has one more electron shell than the one above it, so the atoms get bigger.

Ionic radius

When atoms gain or lose electrons to form ions, their size changes a lot.

  • Cations (positive ions) are smaller than their atoms. A sodium atom (2, 8, 1) loses its only valence electron. Na⁺ (2, 8) has lost its whole outer shell, and now 11 protons pull on just 10 electrons. Na⁺ is much smaller than Na.
  • Anions (negative ions) are larger than their atoms. A chlorine atom (2, 8, 7) gains an electron to become Cl⁻ (2, 8, 8). The same 17 protons now hold 18 electrons, and the extra electron increases the repulsion between electrons in the outer shell. The cloud spreads out, so Cl⁻ is much larger than Cl.

Within a group, ions with the same charge also get larger going down: Li⁺ < Na⁺ < K⁺ and F⁻ < Cl⁻ < Br⁻.

NaNa atom 166 pmNa⁺Na⁺ ion 102 pmloses 1 e⁻: smallerClCl atom 102 pmCl⁻Cl⁻ ion 181 pmgains 1 e⁻: larger
Drawn to scale. Losing an electron shell makes Na⁺ much smaller than Na. Gaining an electron makes Cl⁻ much larger than Cl.

Isoelectronic ions

O²⁻, F⁻, Na⁺, Mg²⁺ and Al³⁺ all have 10 electrons in the arrangement 2, 8. Particles with the same number of electrons are isoelectronic. Which is biggest? The only difference is the number of protons: 8, 9, 11, 12 and 13. More protons pull the same 10 electrons in more tightly, so

O²⁻ (140 pm) > F⁻ (133 pm) > Na⁺ (102 pm) > Mg²⁺ (72 pm) > Al³⁺ (54 pm)

In an isoelectronic series, the more protons, the smaller the ion.

ParticleProtonsElectronsRadius (pm, approx.)
Na atom1111166
Na⁺1110102
Mg²⁺121072
Cl atom1717102
Cl⁻1718181
S²⁻1618184
Some atomic and ionic radii. Ionic radii are for ions in crystals.
Worked example

Example 1: Ranking atoms by size

Arrange these atoms from smallest to largest: K, Mg, S, Na. Explain.

  1. Na, Mg and S are all in period 3; K is in period 4 (one more shell), so K is largest.
  2. Across period 3 the radius decreases: Na > Mg > S, because Zeff increases (Na +1, Mg +2, S +6).
  3. Put it together, smallest first.

S < Mg < Na < K

Worked example

Example 2: Ion versus atom

Explain why the radius of the calcium ion, Ca²⁺ (100 pm), is so much smaller than the calcium atom (176 pm).

  1. Calcium is 2, 8, 8, 2. To form Ca²⁺ it loses its two valence electrons, leaving 2, 8, 8.
  2. The entire fourth shell is gone, so the outermost electrons are now in shell 3, closer to the nucleus.
  3. Also, 20 protons now pull on only 18 electrons, so each electron is pulled in more strongly.

Ca²⁺ is smaller because it has one fewer shell and more protons than electrons.

Worked example

Example 3: An isoelectronic series

Rank S²⁻, Cl⁻, K⁺ and Ca²⁺ from largest to smallest.

  1. Count electrons: S²⁻ 16 + 2 = 18; Cl⁻ 17 + 1 = 18; K⁺ 19 − 1 = 18; Ca²⁺ 20 − 2 = 18. All are isoelectronic (2, 8, 8).
  2. Count protons: 16, 17, 19, 20.
  3. More protons pull the 18 electrons in tighter, so the fewest protons gives the largest ion.

S²⁻ > Cl⁻ > K⁺ > Ca²⁺

Just for fun

Riddle: What gets bigger when it takes something, and smaller when it gives something away?

An atom turning into an ion! Gain an electron and it grows; lose one and it shrinks.

Hands-on activity

A scale model of atom sizes

You need: paper or thin cardboard, a ruler, a pencil, a drawing compass (or cups and lids of different sizes to trace) and scissors (a grown-up can help with cutting).

Scale: 1 cm on paper = 40 pm.

  1. Calculate the paper radius for each atom: Li 128 pm → 3.2 cm; Na 166 pm → 4.2 cm; K 203 pm → 5.1 cm; F 57 pm → 1.4 cm; Cl 102 pm → 2.6 cm; C 76 pm → 1.9 cm; O 66 pm → 1.7 cm.
  2. Draw and cut out a circle for each, and label it.
  3. Arrange them in their positions on a sketch of the periodic table (Li, C, O, F in one row; Na and Cl below Li and F; K below Na).
  4. Now make Na⁺ (102 pm → 2.6 cm) and Cl⁻ (181 pm → 4.5 cm). Place each ion next to its atom.

What to look for: circles shrink to the right and grow downward. Na⁺ is about the same size as a Cl atom, while Cl⁻ is bigger than an Na atom. Ask: which direction across the table makes atoms smaller, and why?

Your turn

1

Define covalent radius.

2

Which is larger, and why: (a) N or P? (b) N or F?

3

Arrange in order of increasing radius: Al, Cl, Na, P.

4

Explain why K⁺ is smaller than K.

5

Explain why O²⁻ is larger than O.

6

Rank F⁻, Mg²⁺, Na⁺ from largest to smallest.

More practice: warm-up

1

What unit is usually used for atomic radius?

2

Does atomic radius increase or decrease down a group?

3

Which corner of the periodic table has the smallest atoms?

4

Is a cation larger or smaller than its atom?

5

What does isoelectronic mean?

More practice: on your own

1

Use Zeff to explain why the radius of Li (128 pm) is about twice that of F (57 pm).

2

Predict which is larger, Br or Se, and justify.

3

A student says, "Cl⁻ is larger than Cl because it has more protons." Correct the student.

4

Order these from smallest to largest: Mg, Mg²⁺, Ca.

5

Why is it better to compare radii from the same table?

Challenge

1

The radii of N³⁻, O²⁻ and F⁻ decrease in that order, but the radii of N, O and F atoms also decrease in that order. Give the different reasons for each trend.

2

Na⁺ (102 pm) and F⁻ (133 pm) are isoelectronic. Na⁺ has 2 more protons than F⁻. Use the data to argue whether nuclear charge has a large or small effect on size.

3

Lithium's radius is 128 pm and sodium's is 166 pm. The radius of Na⁺ is 102 pm. Explain why Na⁺ is smaller than a lithium atom even though sodium is below lithium in the table.

Check your understanding

Quiz

1.

Which atom has the largest radius?

2.

Atomic radius decreases across a period mainly because

3.

Which statement is correct?

4.

Which ion is the largest?

5.

Moving down group 17 from F to I, atomic radius

6.

Covalent radius is defined as

For parents and teachers

Big idea: Atomic radius is one of the periodic properties named in expectation B2.1, and explaining its trend with electron arrangement is part of B3.3. Radius decreases across a period (Zeff increases) and increases down a group (new shells). Ions: cations shrink, anions grow.

How to help: The paper-circle model makes the trends visible. Ask your teen to point to where an element sits and predict its size before looking at the number.

Common difficulties:

  • Expecting atoms to get bigger to the right because they have more electrons. Extra electrons in the same shell are pulled in more strongly by the extra protons.
  • Thinking an anion is bigger because it has more protons; it has more electrons.
  • In isoelectronic series, ranking by charge instead of by protons. Rule: same electrons, more protons, smaller.