D4.6 Ionic Radii

Ionic radius is the radius of a sphere representing a cation or an anion; it can be determined from structures of ionic crystals.

Cations have fewer electrons than the uncharged atoms from which they are derived. Hence, there is less electron-electron repulsion (that is, larger Z_eff), which makes a cation’s radius smaller than the corresponding neutral atom’s radius. For example, the atomic radius of Al ([Ne]3s²3p¹) is 143 pm, which is more than twice as large as the 68 pm ionic radius of Al³⁺ ([Ne]). Often, as in the case of Al, formation of a cation involves removal of all electrons from the outermost shell of an atom, which means the remaining electrons are in smaller shells—another reason why cations are smaller than the neutral atoms from which they form.

For the same element, cations with larger positive charges are smaller than cations with smaller charges. For example, V²⁺ has an ionic radius of 93 pm, while that of V³⁺ is 78 pm. (A neutral V atom has an atomic radius of 135 pm.)

Anions have more electrons and therefore greater electron-electron repulsion (that is, smaller Z_eff) than the neutral atoms from which they are derived. Thus, an anion’s radius is larger than the neutral atom’s radius. For example, the ionic radius of S^2- ([Ne]3s²3p⁶) is 170 pm, larger than the 104 pm atomic radius of S ([Ne]3s²3p⁴).

Periodic trends in radii of a set of anions (or cations) with the same charge are similar to the atomic-radius trends. For instance, proceeding down a group, radii of 1+ cations generally increase as atomic number increases, corresponding to the increase in the principal quantum number, n.

For isoelectronic species (ions or atoms with the same electron configuration), the greater the nuclear charge (number of protons), the smaller the atomic/ionic radius. This implies that isoelectronic anions are larger than isoelectronic neutral atoms which are larger than isoelectronic cations.