8.3: Ionic Radii

Ionic radius is the measure used to describe the size of an ion. A cation always has fewer electrons and the same number of protons as the parent atom; it is smaller than the atom from which it is derived. For example, the covalent radius of an aluminum atom (1s²2s²2p⁶3s²3p¹) is 118 pm, whereas the ionic radius of an Al³⁺ (1s²2s²2p⁶) is 68 pm. As electrons are removed from the outer valence shell, the remaining core electrons occupying smaller shells experience a greater effective nuclear charge Z_eff and are drawn even closer to the nucleus.

Cations with larger charges are smaller than cations with smaller charges (e.g., V²⁺ has an ionic radius of 79 pm, while that of V³⁺ is 64 pm). Proceeding down the groups of the periodic table, cations of successive elements with the same charge generally have larger radii, corresponding to an increase in the principal quantum number, n.

An anion (negative ion) is formed by the addition of one or more electrons to the valence shell of an atom. This results in a greater repulsion among the electrons and a decrease in Z_eff per electron. Both effects (the increased number of electrons and the decreased Z_eff) cause the radius of an anion to be larger than that of the parent atom. For example, a sulfur atom ([Ne]3s²3p⁴) has a covalent radius of 104 pm, whereas the ionic radius of the sulfide anion ([Ne]3s²3p⁶) is 170 pm. For consecutive elements proceeding down any group, anions have larger principal quantum numbers and, thus, larger radii.

Atoms and ions that have the same electron configuration are said to be isoelectronic. Examples of isoelectronic species are N^3–, O^2–, F^–, Ne, Na⁺, Mg²⁺, and Al³⁺ (1s²2s²2p⁶). Another isoelectronic series is P^3–, S^2–, Cl^–, Ar, K⁺, Ca²⁺, and Sc³⁺ ([Ne]3s²3p⁶). For atoms or ions that are isoelectronic, the number of protons determines the size. The greater the nuclear charge, the smaller the radius in a series of isoelectronic ions and atoms.

This text is adapted from OpenStax Chemistry 2e, Section 6.5: Periodic Variations in Element Properties.

An ionic radius is the radius of a cation or an anion defined by the distance between ions in an ionic compound. Cations are smaller than the parent atom, whereas anions are larger. Similar to atomic radii, ionic radii are determined by the number of electrons, the orbitals holding its valence electrons, and the nuclear charge. 

Consider lithium, which has an electron configuration of a helium core and one outermost 2s electron. The 2s electron is shielded from the nuclear charge by two 1s electrons and contributes to the atomic radius of 152 picometers.

The loss of the outermost 2s electron generates a lithium cation, which has fewer electrons but the same number of protons as the parent atom. The two 1s  electrons are held closer to the nucleus because they experience a greater effective nuclear charge than the 2s electron did. Thus, the ionic radius of the lithium cation is 60 picometers, which is much smaller than the parent atom. 

This trend is generally observed with all metal cations and their parent atoms.

In contrast, anions are larger than their parent atoms. When a fluorine atom accepts an electron, there is an additional outermost electron, but the number of protons, and hence the nuclear charge, remains the same. The increased electron – electron repulsion causes the electrons to spread out more in space. Thus, the fluoride anion has a radius of 136 picometers, which is much larger than the parent atom.

In general, the ionic radius for s and p-block elements increases down the column, as the number of principal energy levels, and hence the number of orbitals, increases. 

What about a group of atoms and ions that have the same number of electrons? They are referred to as an isoelectronic series and can be arranged by increasing atomic number. 

Each member of the isoelectronic series depicted has 18 electrons. However, they differ in the number of protons. The sulfide ion has 16 protons attracting 18 electrons, while the calcium ion has 20 protons attracting the same number of electrons. 

Thus, with more protons, calcium can pull electrons much closer to the nucleus than sulfide can, resulting in the calcium ion being smaller than the sulfide ion. 

The greater the nuclear charge, the smaller the radius, although adding an electron shell disrupts this trend. Nevertheless, sulfide is the biggest and calcium is the smallest ion in this series.