Periodic Trends: Atomic and Ionic Radius

Atomic radius is half the distance between the nuclei of two bonded atoms of an element, and ionic radius is the size of an ion; atomic radius decreases from left to right across a period and increases down a group, cations are smaller than their atoms and anions are larger. In brief: sodium (166 pm) is larger than chlorine (102 pm) in the same period, cesium (244 pm) is larger than lithium (128 pm) in the same group, Na⁺ (102 pm) is much smaller than Na, and Cl⁻ (181 pm) is much larger than Cl.

The size of atoms and ions affects bond lengths, the structure of crystals, density and reactivity. Atoms do not have a sharp edge, so there are several definitions of radius and the values depend on the method. This article defines the radius, explains the trends with effective nuclear charge and the number of shells, shows data tables, explains the size of ions and isoelectronic series, works through examples that rank sizes and gives some history.

How is atomic radius defined?

The electron cloud of an atom has no sharp boundary, so radius is defined in practice by distances between atoms. For metals, the metallic radius is half the distance between nuclei of neighboring atoms in the solid. For nonmetals that form molecules, the covalent radius is half the length of a single bond between two identical atoms, such as in Cl₂. The van der Waals radius is half the distance between nuclei of two nonbonded atoms that touch, and is larger. Values in tables depend on which definition is used, so compare only values from the same source. The data below are covalent radii in picometers (1 pm = 10⁻¹² m).

How does radius change across a period?

Across a period from left to right, electrons are added to the same shell, but the nuclear charge increases and the electrons do not shield each other well. The effective nuclear charge rises, pulling the electron cloud closer to the nucleus. The atoms become smaller.

The decrease slows near the end of the period, as more electrons in the same subshell repel each other. Noble gases are left out of such comparisons, because their radii are measured in a different way and are not comparable.

How does radius change down a group?

Down a group, each element has one more occupied shell, so the outer electrons are farther from the nucleus. The increase in nuclear charge is mostly offset by shielding from the inner electrons, so the effective nuclear charge changes little. The atoms get larger.

How do ions compare in size with their atoms?

• Cations are smaller than their parent atoms. When electrons are removed, the remaining electrons feel a larger effective nuclear charge, and there is less repulsion between them. Often, the entire outer shell is lost, as in sodium (3s electron removed), which further reduces the size. The more positive the charge, the smaller the ion.
• Anions are larger than their parent atoms. Extra electrons increase electron-electron repulsion while the nuclear charge stays the same, so the electron cloud expands.

What is an isoelectronic series?

Isoelectronic species have the same number of electrons. In such a series, the ion with the larger nuclear charge is smaller, because it holds the same electrons more strongly. The series O²⁻, F⁻, Na⁺, Mg²⁺ and Al³⁺ all have 10 electrons, like neon.

Worked examples

1. Rank by size. Rank Mg, Na, Al and Cl in increasing atomic radius. All are in period 3. Radius decreases from left to right, so the order of size from smallest to largest is Cl (102) < Al (121) < Mg (141) < Na (166).
2. Percent change in size. Na to Na⁺: (166 − 102) ÷ 166 × 100% = 38.6% smaller. Cl to Cl⁻: (181 − 102) ÷ 102 × 100% = 77.5% larger.
3. Isoelectronic ranking. Rank S²⁻, Cl⁻, K⁺ and Ca²⁺. All have 18 electrons, with nuclear charges 16, 17, 19 and 20. The larger the nuclear charge, the smaller the ion: Ca²⁺ (100 pm) < K⁺ (138 pm) < Cl⁻ (181 pm) < S²⁻ (184 pm).
4. Volume change. The volume of a sphere is proportional to r³. The ratio for Na to Na⁺ is (166 ÷ 102)³ = 1.63³ = 4.3, so the atom has about 4.3 times the volume of the ion.
5. Bond length estimate. The covalent radii of carbon (76 pm) and chlorine (102 pm) predict a C–Cl bond length of 76 + 102 = 178 pm, close to the experimental value of about 177 pm.
6. Ionic compound. The distance between Na⁺ and Cl⁻ in the sodium chloride crystal is estimated by 102 + 181 = 283 pm. The measured value is 282 pm.

Are there exceptions?

The trends hold in most cases. Some irregularities arise in the transition metals, where the radius decreases at first and then changes little because the added d electrons shield the outer electrons. After the lanthanides, the elements of period 6 are almost as large as those of period 5 in the same group (for example zirconium and hafnium), because of the lanthanide contraction: the 4f electrons shield poorly, so the nuclear charge increases without a matching increase in size. As a result, hafnium (150 pm) and zirconium (148 pm) are very similar in chemistry.

How was atomic size first measured?

Early estimates of molecular size came from kinetic theory in the 19th century. Johann Loschmidt estimated molecular diameters in 1865. In 1913, William Henry Bragg and William Lawrence Bragg developed X-ray crystallography, which allowed accurate measurement of distances between atoms in crystals and led to tables of ionic radii by Victor Goldschmidt and Linus Pauling in the 1920s. Robert Shannon published a widely used set of ionic radii in 1976, depending on charge and coordination number.

Which mistakes are common?

Mistake 1: Thinking that atoms get larger across a period because there are more electrons

The added electrons are in the same shell and the nuclear charge also grows, so atoms get smaller.

Mistake 2: Saying that all anions are larger than the cations of the same period

Compare ions with the same number of electrons, or consider both the shell and the charge.

Mistake 3: Comparing radii from different definitions

Metallic, covalent, van der Waals and ionic radii are not interchangeable.

Mistake 4: Forgetting that cations lose a shell

A cation like Na⁺ has only 2 occupied shells, compared with 3 in the atom.