Potassium chloride (KCl) is a molecule formed by an ionic bond. At equilibrium separation the atoms are \(r_{0}=0.279 \mathrm{nm}\) apart. Determine the electrostatic potential energy of the atoms.

An ionic bond is a type of chemical bond where one atom, typically a metal, loses an electron to become a positively charged ion, while another atom, usually a non-metal, gains that electron to become a negatively charged ion. In our example of potassium chloride (KCl), potassium (K) gives up an electron to chlorine (Cl), resulting in a K+ ion and a Cl- ion. These ions are held together by the electrostatic attraction between their opposite charges.

This kind of bond is usually formed between elements with a large difference in electronegativities, which is the tendency of an atom to attract electrons. In an ionic bond, the metal atom becomes a cation due to the loss of its valence electron, and the non-metal becomes an anion due to the gain of an electron, leading to a robust compound that has a characteristic crystal lattice structure, high melting and boiling points, and is often soluble in water.

Coulomb's law is critical for understanding the forces involved in an ionic bond. It quantifies the electrostatic force between two charges as directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Mathematically, it is expressed as:
\[ F = k \frac{|q_1 q_2|}{r^2} \]
where \( F \) is the electrostatic force, \( q_1 \) and \( q_2 \) are the magnitudes of the charges, \( r \) is the distance between the charges, and \( k \) is Coulomb's constant. When we consider the context of ionic bonds, Coulomb's law helps us comprehend the energy required to separate the ions to an infinite distance, providing an insight into the bond strength and the system's stability.

Elementary charge is the smallest unit of electric charge that is considered indivisible in classical electromagnetism, denoted as \( e \). Its value is approximately \( 1.60217663 \times 10^{-19} \) coulombs (C). This fundamental charge defines the charge on a single proton (positive) or a single electron (negative).

In ionic compounds such as KCl, the transfer of electrons results in ions carrying a charge that is an integer multiple of the elementary charge. Understanding elementary charge is paramount, as it is utilized when calculating electrostatic potential energy, where the charges of the ions are integral multiples of \( e \), leading to a precise determination of energy using Coulomb's law in the context of ionic compounds.