Atomic and ionic radii.

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According to quantum theory, the orbitals of an atom extend in principle to infinity and so there is no definite size to an atom - rather there is a probability of locating an outer electron at a certain distance from the nucleus. It is necessary therefore to make some arbitrary decision as to where the boundary of atom lies: the radius of the atom.

Usually for metallic elements, the metallic radius is the value quoted for atomic radius:

The metallic radius is half the distance between the centres of neighbouring atoms in a metal.

For example, the metallic radius of the element lithium is 1.52 x 10^-10m. A variety of units have been used to express these small distances, although most contemporary authors would use nanometres, nm, 10^-9m. Picometres and Ångstroms are also used and are compared in the table below:

Unit	Symbol	Factor	Value for Lithium atom, Li
metres	m	1	1.52 x 10-10m
nanometres	nm	x 10-9m	0.152 nm
picometres	pm	x 10-12m	152 pm
Ångstroms	Å	x 10-10m	1.52 Å

For non-metallic elements, the covalent radius is the value quoted for atomic radius:

The covalent radius is half the internuclear distance between two atoms of element joined by a single covalent bond.

The atomic radii decrease across period 2 and period 3 since as nuclear charge increases and electrons are added to the same shell, the electrons are attracted more strongly. In any period, the alkali metals have the largest atoms and this is reflected in their low densities.

Atomic radii increase down any group because although the nuclear charge increases considerably, the extra electrons are entering shells further from the nucleus.

For some elements metallic and covalent radii can be compared. For example, in the case of lithium, the covalent radius of the vapour phase Li₂ molecules (covalent bonding) can be compared with element atoms in the solid state (metallic bonding).

Measurement	Radius (nm)
metallic radius	0.153
covalent radius	0.123

The covalent radius is the smaller of the two and this is expected as, in the molecule, the atoms are pulled together by their attraction for the electrons shared in the bond between them. In the metal however, valency electrons are delocalised throughout the lattice and consequently a more open structure is present giving a larger value for the radius.

Like the atomic radii, ionic radii are determined by measuring the distance between adjacent nuclei. However, for ions this gives the sum of the ionic radii for an anion/cation pair and so in practice the radius of the oxide anion, O^2-, at 0.146 nm is used as a reference point from which to calculate other ionic radii.

The ionic radius of an element is its share of the distance between adjacent ions in an ionic solid.

For example, the distance between the magnesium cation and the oxide anion in magnesium oxide is 0.211 nm, the radius of the Mg²⁺ ion is calculated from 0.205 nm - 0.146 nm = 0.065 nm.

The size of an ion also varies somewhat with its environment so average values for ionic radii are often quoted.

One way in which the ionic radii of the elements can be compared is to compare ions that are isoelectronic: that is, ions which have identical electron configurations. The table below compares the electron configurations of element atoms and their isoelectronic ions across period 3.

Cations

Element	Sodium	Magnesium	Aluminium
Electron configuration of atom	[Ne] 3s1	[Ne] 3s2	[Ne] 3s2 3p1
Ion	Na+	Mg2+	Al3+
Electron configuration of ion	[Ne]	[Ne]	[Ne]

Anions

Element	Silicon	Phosphorus	Sulphur	Chlorine
Electron configuration of atom	[Ne] 3s2 3p2	[Ne] 3s2 3p3	[Ne] 3s2 3p4	[Ne] 3s2 3p5
Ion	Si4-	P3-	S2-	Cl-
Electron configuration of ion	[Ar]	[Ar]	[Ar]	[Ar]

Comparison of the electron configurations of element atoms and their isoelectronic ions across period 3 leads to the following conclusions:

cations are always smaller than their parent element atoms, because the atom loses one or more electrons to form the cation and exposes its core which is generally much smaller than than the parent atom. anions are always larger than their parent element atoms, because the atom gains one or more electrons to form the anion. The increased number of electrons in the valence shell increases the repulsive effects that the electrons exert on one another, thus increasing the radius. the trend in ionic radii across period 3 shows a decrease for the cations of Na, Mg, and Al as not only do the atomic radii of the parent element atoms decrease across the period, but the [Ne] core that is exposed when the ions form is attracted progessively more strongly by the increasing nuclear charge. the trend in ionic radii across period 3 shows a decrease for the anions of Si, P, S, and Cl as each ion has an electron configuration isoelectronic with argon but a progessively larger nuclear charge exerting a greater electrostatic force of attraction on the valence shell electrons. the trend in ionic radii down a group shows an increase for the same reasons as atomic radii increase down a group.

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