The atomic radii of the isotopes of an element are identical to one another. However, the atomic radii of the ions of an element are significantly different from the atomic radii of the neutral atom of the element. Explain.

Isotopes refer to the different forms of an element's atoms that share the same number of protons but have varying numbers of neutrons. From a chemistry standpoint, this small internal discrepancy does not influence the electron cloud—the area surrounding the nucleus where electrons are likely to be found. Since the electron configuration in isotopes of the same element remains unchanged, so does the atomic radius.

Take oxygen as an example; it can exist as ¹⁶O, ¹⁷O, and ¹⁸O. The superscript represents the mass number (sum of protons and neutrons), which varies among these isotopes. However, their atomic radii remain constant because each isotope houses eight electrons forming the same electronic architecture. This is crucial in understanding why physical properties like atomic radii do not waver amongst isotopes.

Moving on to ions, these are atoms that have taken on a charge due to the loss or gain of electrons, fundamentally altering their electron configurations. A cation, possessing a positive charge, arises when an atom loses one or more electrons. As a result, the 'vacancy' left by the absent electrons decreases the electron-electron repulsion in the atom, and the decreased shielding effect allows the remaining electrons and nucleus to draw closer. This contraction results in a smaller atomic radius compared to its neutral counterpart.

Conversely, an anion, which holds a negative charge, is produced when an atom gains additional electrons. This increment in the electron count increases the repulsion amongst them and causes the electron cloud to expand. Consequently, the atomic radius of an anion is larger than that of the corresponding neutral atom. The process of ionization, hence, is a transformative one that significantly alters the atomic radii of the resultant ions when compared to the neutral atoms.

Lastly, electron configuration is a term that depicts the distribution of electrons in an atom's orbitals. It is the fundamental feature that impacts atomic radii. During the ionization process, when the configuration of electrons changes, the resulting adjustment in the electrostatic forces within the atom directly influences the size of the electron cloud and thus the atomic radius.

For example, the removal of an electron during the formation of a cation can result in a valence shell being completely stripped away, which significantly reduces the atomic radius. On the other hand, when an electron is added to form an anion, the addition often occurs in a new valence shell, thus increasing the radius. Electron configuration not only affects the chemical properties of atoms and ions but is also the key to understanding trends in atomic size across the periodic table.