ionic radius
If ions are charged balls, how big is each ball? That apparently simple question hides a real difficulty: an ion has no sharp edge — its electron cloud just fades away — and in a crystal you can only measure the distance between two ion centres, not where one ion stops and the next begins. The ionic radius is chemistry's practical answer: a self-consistent set of sizes assigned to ions so that, added together, they reproduce the measured distances in real crystals.
The trick is to divide the experimentally measured cation-to-anion distance between the two ions in a sensible way. Modern tables (Shannon's) do this carefully across thousands of compounds, anchored by a reasonable estimate for one reference ion. The results follow clear and useful trends: cations are smaller than their parent atoms (losing electrons, sometimes a whole shell, shrinks them, and Na+ is much smaller than Na); anions are larger than their parent atoms (added electrons spread out under reduced nuclear pull); for a series of ions with the same number of electrons (isoelectronic, like O2-, F-, Na+, Mg2+) size shrinks as nuclear charge rises; and radius grows down a group as new shells are added. Critically, ionic radius is not a fixed property of an ion — it grows with coordination number, because an ion squeezed by six neighbours is held more tightly than the same ion surrounded by eight.
Ionic radii are the working currency of structural inorganic chemistry. They feed the radius-ratio rules that predict structure, set the inter-ionic distance in the Born-Lande equation for lattice energy, and explain why one cation substitutes for another in a mineral (similar radii substitute freely). The dependence on coordination number is the honest caveat that beginners miss: quoting a single radius for an ion is shorthand, and serious work always specifies the coordination, because the same ion is genuinely a different size in a four-, six-, or eight-coordinate site.
The ion Fe3+ has a Shannon radius of about 55 pm in a four-coordinate (tetrahedral) site but about 65 pm in a six-coordinate (octahedral) one. The same ion is genuinely larger when it has more neighbours pushing it outward — which is why a radius quoted without its coordination number is incomplete.
Ionic radius rises with coordination number — Fe3+ is larger in a six-coordinate site than a four-coordinate one.
There is no absolute ionic radius — values depend on the reference ion chosen and, importantly, on coordination number. Always treat a tabulated radius as a coordination-specific, self-consistent figure, not a fundamental size.