Describe the relationship between: $$ \begin{array}{l}{\text { a. the radius of a cation and the radius of the atom from which it is formed }} \\ {\text { b. the radius of an anion and the radius of the atom from which it is formed }}\end{array} $$

When an atom loses one or more electrons, it is transformed into what is known as a cation. This process, called ionization, occurs for various reasons, such as chemical reactions where atoms aim to achieve stable electronic configurations similar to noble gases.

During the formation of a cation, the loss of negatively charged electrons means the balance of charges in the atom shifts. The remaining electrons now feel a more potent pull from the positively charged nucleus because there's less repulsion between them, as there are fewer electrons pushing against each other.

This increased attraction by the nucleus causes the electron cloud to draw in tighter, and consequently, the atomic radius—to put it simply, the size of the atom—decreases. A heightened effective nuclear charge (a term that reflects the net positive charge experienced by electrons) underpins this shrinkage.

The opposite of cation formation is when an atom gains electrons and becomes an anion. This addition happens for similar reasons of stability, with the atom seeking to complete its outer electron shell, mirroring the nearest noble gas configuration.

Once electrons are added to an atom, they naturally repel each other because like charges repel according to fundamental principles of electricity. This electrostatic repulsion among added electrons forces the electron cloud to occupy more space. As a result, the atomic radius, or the atom's size, increases. This process is aided by the fact that with more electrons, the shielding effect—where inner electrons block the outer electrons from the pull of the nucleus—also gets stronger, contributing to an increase in size.

The term ionic radius refers to the measure of an atom's size when it has gained or lost electrons and is in the form of an ion. In a cation, the ionic radius is smaller than that of its neutral atom due to a smaller electron cloud. Conversely, an anion has a larger ionic radius because the additional electrons increase the size of the electron cloud.

It's important to note that ionic radius is not a fixed value but varies based on the ion's environment, like the type of ions surrounding it and the crystalline structure it forms part of, if any. Moreover, the ionic radius affects how ions bond with each other, playing a crucial role in determining the strengths of ionic bonds and the physical properties of ionic compounds.

The concept of electrostatic repulsion is pivotal in chemistry, especially when exploring the structure and behavior of atoms and ions. As mentioned, it describes the force that pushes apart particles with the same charge—in this case, electrons.

In a neutral atom, electrons are arranged such that this repulsion is minimized, but there's always some level of repulsion affecting the atom's size. When electrons are added (in an anion), the repulsion increases, leading to a larger atomic radius. But in the case of a cation, when electrons are removed, the decreased repulsion allows the remaining electrons to be held closer to the nucleus by its charge, leading to a smaller atomic radius.

Electrostatic repulsion is a fundamental force that helps determine the spacing between ions in an ionic lattice and influences properties such as melting points, boiling points, and solubility of compounds.