Indicate which one of the two species in each of the following pairs is smaller: (a) \(\mathrm{Cl}\) or \(\mathrm{Cl}^{-} ;\) (b) Na or \(\mathrm{Na}^{+}\); (c) \(\mathrm{O}^{2-}\) or \(\mathrm{S}^{2-}\) (d) \(\mathrm{Mg}^{2+}\) or \(\mathrm{Al}^{3+}\) (e) \(\mathrm{Au}^{+}\) or \(\mathrm{Au}^{3+}\)

Understanding electron-electron repulsion is crucial when exploring atomic and ionic sizes. In an atom or ion, electrons are negatively charged and repel each other. This repulsion can influence the size of the electron cloud surrounding the nucleus.

For example, let's take chlorine (Cl) and its ion (Cl⁻). When chlorine gains an electron to become Cl⁻, there is an increase in the electron population around the nucleus. This causes an increased repulsion among the electrons, resulting in a larger atomic radius compared to the neutral chlorine atom.

Conversely, when an atom loses an electron to become a cation, like sodium (Na) to Na⁺, electron repulsion decreases because there are fewer electrons to push against each other. The reduction in repulsion allows the remaining electrons to be drawn closer to the nucleus, leading to a decrease in the ionic radius.

The concept of energy levels in atoms plays a significant role in determining atomic and ionic sizes. Energy levels, also known as electron shells, are the regions surrounding the nucleus where electrons are likely to be found. Each subsequent energy level is located farther from the nucleus, and therefore, atoms with more energy levels will have a larger radius.

When comparing ions like the oxide ion (O²⁻) and the sulfide ion (S²⁻), we should consider the energy levels in each ion. Sulfur is located below oxygen in the periodic table, indicating it has more energy levels. Consequently, despite both ions having the same charge, S²⁻ has a larger atomic radius than O²⁻ because its outermost electrons are located in a higher energy level farther away from the nucleus.

The ionic charge is pivotal in determining the size of an ion. Generally, as the ionic charge increases, the atomic radius decreases. This happens because a higher positive charge on the nucleus (due to the loss of electrons) strengthens the nucleus's ability to attract the remaining electrons more tightly towards it.

For instance, when comparing magnesium ion (Mg²⁺) with aluminum ion (Al³⁺), we see that Al³⁺ is smaller despite both having the same number of energy levels. The additional positive charge in Al³⁺ draws the electrons in closer, effectively reducing the radius. Similarly, looking at gold ions, Au⁺ and Au³⁺, the Au³⁺ ion has a higher positive charge, leading to a smaller size than the Au⁺ ion because the increased charge causes a greater pull on the electrons.