Atomic Radius and Ionic Radius — Definition

Definition

Imagine an atom as a tiny sphere, with a nucleus at its center and electrons whizzing around it in various shells. Defining the exact 'edge' of this sphere is tricky because the electron cloud doesn't have a sharp boundary; it just fades away. So, we can't simply measure the radius of a single, isolated atom directly. Instead, we define atomic radius based on how atoms interact with each other.

There are a few ways to define atomic radius:

1
Covalent Radius: — This is used for non-metallic elements that form covalent bonds. If you take two identical atoms (like two chlorine atoms, Cl-Cl) bonded together, the covalent radius is half the distance between their nuclei. For example, if the distance between the two chlorine nuclei is 198 picometers (pm), then the covalent radius of chlorine is $198/2 = 99\,\text{pm}$. This is a good measure for atoms in molecules.

1
Metallic Radius: — This applies to metals. In a metallic crystal, metal atoms are packed closely together in a lattice. The metallic radius is defined as half the internuclear distance between two adjacent metal atoms in the metallic crystal lattice. For instance, if two copper atoms in a copper crystal are 256 pm apart, the metallic radius of copper is $256/2 = 128\,\text{pm}$. Metallic radii are generally larger than covalent radii for the same element because metallic bonds are often less 'tight' than covalent bonds, and the electron cloud is delocalized.

1
Van der Waals Radius: — This is used for elements that don't typically form chemical bonds with each other, like noble gases, or for non-bonded atoms in molecules. It's half the internuclear distance between two identical non-bonded atoms of adjacent molecules that are just touching each other. For example, in solid chlorine, there are Cl-Cl molecules. The van der Waals radius is half the distance between the nuclei of two chlorine atoms belonging to *different* Cl-Cl molecules that are in closest contact. Van der Waals radii are always significantly larger than covalent radii because they represent the distance at which repulsive forces between electron clouds balance attractive forces, without actual bond formation.

Ionic Radius is similar but applies to ions (atoms that have gained or lost electrons). When an atom loses electrons, it forms a positive ion called a cation. When it gains electrons, it forms a negative ion called an anion.

The ionic radius is the effective distance from the nucleus to the outermost electron shell of an ion in an ionic crystal. Cations are always smaller than their parent atoms because they have fewer electrons (often losing the outermost shell) and the remaining electrons are pulled more strongly by the same nuclear charge.

Anions are always larger than their parent atoms because they have gained electrons, leading to increased electron-electron repulsion and a larger electron cloud, while the nuclear charge remains the same.