Atomic radius

Atomic radius, and more generally the size of an atom, is not a precisely defined physical quantity, nor is it constant in all circumstances. The value assigned to the radius of a particular atom will always depend on the definition chosen for "atomic radius", and different definitions are more appropriate for different situations.

The term "atomic radius" itself is problematic: it may be restricted to the size of free atoms, or it may be used as a general term for the different measures of the size of atoms, both bound in molecules and free. In the latter case, which is the approach adopted here, it should also include ionic radius, as the distinction between covalent and ionic bonding is itself somewhat arbitrary.

The atomic radius is determined entirely by the electrons: The size of the atomic nucleus is measured in femtometres, 100,000 times smaller than the cloud of electrons. However the electrons do not have definite positions&mdash;although they are more likely to be in certain regions than others&mdash;and the electron cloud does not have a sharp edge.

Despite (or maybe because of) these difficulties, many different attempts have been made to quantify the size of atoms (and ions), based both on experimental measurements and calculational methods. It is undeniable that atoms do behave as if they were spheres with a radius of 30–300 pm, that atomic size varies in a predictable and explicable manner across the periodic table and that this variation has important consequences for the chemistry of the elements.

Periodic trends in atomic radius
Atomic radius tends to decrease on passing along a period of the periodic table from left to right, and to increase on descending a group. This is, in part, because the distribution of electrons is not completely random. The electrons in an atom are arranged in shells which are, on average, further and further from the nucleus, and which can only hold a certain number of electrons. Each new period of the periodic table corresponds to a new shell which starts to be filled up, and so the outermost electrons are further and further from the nucleus as a group is descended.

The second major effect which determines trends in atomic radius is the charge of the nucleus, which increases with the atomic number, Z. The nucleus is positively charged, and tends to attract the negatively-charged electrons. Passing along a period from left to right, the nuclear charge increases while the electrons are still entering the same shell: the effect is that the physical size of the shell (and hence of the atom) decreases in response.

The increasing nuclear charge is partly counterbalanced by the increasing number of electrons in a phenomenon known as shielding, which is why the size of atoms usually increases as a group is descended. However, there are two occasions where shielding is less effective: in these cases, the atoms are smaller than would otherwise be expected.

Lanthanide contraction
The electrons in the 4f-subshell, which is progressively filled from cerium (Z = 58) to lutetium (Z = 71), are not particularly effective at shielding the increasing nuclear charge from the sub-shells further out. The elements immediately following the lanthanides have atomic radii which are smaller than would be expected and which are almost identical to the atomic radii of the elements immediately above them. Hence hafnium has virtually the same atomic radius (and chemistry) as zirconium, tantalum as niobium etc. The effect of the lanthanide contraction is noticeable up to platinum (Z = 78), after which it is masked by a relativistic effect known as the inert pair effect.

d-Block contraction
The d-block contraction is less pronounced than the lanthanide contraction but arises from a similar cause. In this case, it is the poor shielding capacity of the 3d-electrons which affects the atomic radii and chemistries of the elements immediately following the first row of the transition metals, from gallium (Z = 31) to bromine (Z = 35).

Empirically measured atomic radius
Empirically measured atomic radius in picometres (pm) to an accuracy of about 5 pm

Periodic table of empirically measured atomic radius in picometres (pm) to an accuracy of about 5 pm

See also Periodic table

Reference: J.C. Slater, ''J. Chem. Phys.'' 1964, 41, 3199.

Calculated atomic radius
Calculated atomic radius in picometres (pm)

Periodic table of calculated atomic radius in picometres (pm)

See also Periodic table

Reference: E. Clementi, D.L.Raimondi, and W.P. Reinhardt, ''J. Chem. Phys.'' 1967, 47, 1300.