Final answer:
The ionic radius of a positive ion is smaller than the atomic radius due to fewer electron repulsions and a higher effective nuclear charge after electron loss. An example is the Al³+ ion, which is significantly smaller than a neutral aluminum atom.
Step-by-step explanation:
The ionic radius of a positive ion, or cation, is typically smaller than the atomic radius of the same element. When an atom forms a cation by losing one or more electrons, several things occur. Firstly, there are fewer electron-electron repulsions within the valence shell, allowing the remaining electrons to be drawn closer to the nucleus. Secondly, the removal of electrons means the remaining electrons experience a higher effective nuclear charge (Zeff). With the same number of protons in the nucleus, fewer electrons mean that the positive charge of the nucleus has a stronger pull on the remaining electron cloud, which causes the ion to be smaller.
For example, an aluminum atom has a covalent radius of 118 pm. When it loses electrons to become an Al³+ ion, its ionic radius decreases to 68 pm due to a higher Zeff and lower repulsion between the fewer electrons.
Furthermore, cations of elements farther down the periodic table are generally larger due to an increase in the principal quantum number, n, which reflects having more electron shells.