Explain why anions are always larger than the atoms from which they are derived, whereas cations are always smaller than the atoms from which they are derived. (Hint: Consider the electrostatic attraction between protons and electrons.)

Understanding the difference between anions and cations is crucial for comprehending why their sizes differ. Anions are atoms that have gained one or more electrons, thus they possess a negative charge. This gain in negative charge increases the electron-electron repulsion within the electron cloud, causing it to expand outwardly. As a result, anions are always larger compared to the neutral atoms they originate from.

Cations, in contrast, form when an atom loses one or more electrons. This loss leads to a positively charged ion with reduced electron-electron repulsion, allowing the remaining electrons to be pulled closer to the nucleus due to the unchanged positive charge of the protons. Consequently, the size of cations is always smaller than their corresponding neutral atoms. This size variation is significant in understanding ionic compounds and their properties.

Electrostatic attraction plays a pivotal role in determining the size of ions. It is the force that exists between particles with opposite charges—they attract each other. In the context of atomic particles, positively charged protons in the nucleus attract the negatively charged electrons. When an electron is added to an atom (forming an anion), the increased electron count heightens the repulsion force among electrons, but the overall electrostatic attraction with the protons prevents the electron cloud from dispersing entirely and thus only an expansion is observed.

Conversely, when an atom loses an electron to become a cation, the reduced number of electrons diminishes the repulsion forces, and the electrostatic attraction from the protons brings the remaining electrons even closer to the nucleus, resulting in a smaller ion.

In any atom, electrons repel one another because they carry the same negative charge. This fundamental aspect of electron behavior—referred to as electron-electron repulsion—affects the shaping of the electron cloud that surrounds the nucleus. When anions form by gaining extra electrons, this results in an increased repulsion among the electrons which spreads the electron cloud, as each electron tries to maintain a distance from the others, within the confines set by electrostatic attraction.

This repulsion also helps to explain the smaller size of cations. When an electron is lost, the repulsion among the remaining electrons decreases which enables them to draw closer together. For students, grasping this concept is essential for predicting the behavior of ions in different chemical reactions and their resultant structures.

To fully grasp why anions are larger and cations are smaller than their parent atoms, a solid understanding of atomic structure is indispensable. Atoms consist of a nucleus containing protons and neutrons, surrounded by electrons that are distributed in regions known as electron shells or energy levels. The configuration of these electrons is governed by quantum mechanical principles, which define not only the distribution but also the energy and distance of electrons from the nucleus.

Anions have additional electrons placed in their outer shells, which increases the average distance between the outermost electrons and the nucleus due to repulsion, thereby expanding the atom's radius. Cations, having lost outer electrons, have fewer electron shells or a reduced electron cloud, which decreases that average distance, resulting in a smaller atomic radius. This relationship between atomic structure and ion size is a cornerstone of chemical bonding theory and helps to elucidate the properties of substances, from their physical state to their reactivity.