Question

(a) Because an exact outer boundary cannot be measured or even calculated for an atom, how are atomic radii determined? (b) What is the difference between a bonding radius and a nonbonding radius? (c) For a given element, which one is larger?

Short answer

(a) Atomic radii are determined by observing bond lengths, which are the distances between two bonded atoms, and estimating the atomic radius as half of this distance. (b) The bonding radius is the distance between the nuclei of two bonded atoms, while the nonbonding radius (van der Waals radius) is the distance between the nuclei of nearby but non-bonded atoms. (c) For a given element, the nonbonding radius is generally larger than the bonding radius, as the electron cloud of bonded atoms overlaps and brings them closer together, while van der Waals forces cause nonbonded atoms to have a more diffuse electron cloud and greater distance between them.

Step-by-step solution

Determining atomic radii

Since atoms are not solid spheres and their electrons are distributed in a diffuse cloud, it is impossible to measure or calculate an exact atomic radius. However, atomic radii can be determined by observing the distance (called bond lengths) between two atoms that are bonded together. Then the atomic radius can be estimated as half of this distance.

Bonding radius and nonbonding radius

The bonding radius refers to the distance between the two nuclei of atoms involved in a single bond. This radius lies between the two atomic nuclei, which are bonded together. On the other hand, the nonbonding radius, also known as the van der Waals radius, describes the distance between the nuclei of nearby but non-bonded atoms. This radius is associated with weaker van der Waals forces between neutral atoms.

Comparing the bonding and nonbonding radii

For a given element, the nonbonding radius (van der Waals radius) is generally larger than the bonding radius. This is because, in a chemical bond, the electron cloud of the bonded atoms overlaps, which causes the atoms to be closer together. In contrast, van der Waals forces between nonbonded atoms arise from temporary charge fluctuations, resulting in a more diffuse electron cloud and a greater distance between the atoms.