Final answer:
The cation of a particular element has the smallest radius because it has fewer electrons than the neutral atom, leading to decreased electron repulsions and an increased effective nuclear charge.
Step-by-step explanation:
For a particular element, the species that has the smallest radius is the cation. This occurs because when a neutral atom loses one or more electrons to become a cation, it results in two major effects:
- There are fewer electron-electron repulsions within the same principal shell since there are fewer electrons.
- The effective nuclear charge (Zeff) that the remaining electrons feel increases because the number of protons remains the same while the number of electrons has decreased.
For example, looking at aluminum (Al), the covalent radius of an Al atom is 118 pm, whereas the ionic radius of an Al3+ cation (having lost its 3p electron) is only 68 pm. The removal of electrons from the valence shell lets the remaining core electrons that occupy smaller shells be even more attracted to the nucleus due to an increased Zeff. Consequently, the atomic radius of a cation is always smaller compared to its neutral parent atom.