Rubidium chloride has the rock salt structure. Cations and anions are in contact along the edge of the unit cell, which is \(658 \mathrm{pm}\) long. The radius of the chloride ion is \(181 \mathrm{pm}\). What is the radius of the \(\mathrm{Rb}^{+}\) ion?

The term 'rock salt structure' typifies a specific type of crystalline arrangement. In chemistry, we often turn to the common table salt, sodium chloride, as a classic example. Correspondingly, rubidium chloride (\r\br\br\(RbCl\) embraces this same architecture. Just like its culinary counterpart, \r\br\br\(RbCl\) forms a face-centered cubic lattice. Here, each positively charged rubidium ion (\r\br\br\(Rb^+\)) is symmetrically surrounded by six chloride ions (\r\br\br\(Cl^-\)), which are also anions (negatively charged). Conversely, each chloride ion is surrounded by six rubidium ions in return, establishing a harmonious octahedral coordination. This intricate dance of ions creates a very stable and rigid structure. \r\br\brTo picture this, imagine a cube where an ion sits at each corner and in the center of each face. The cations and anions alternate positions in the cube, ensuring electrostatic equilibrium, which is fundamental to the material's stability. This is what is fundamentally referred to as the rock salt structure—an endearing relationship between opposed charges that continues indefinitely in all three-dimensional directions in a crystal.

When studying crystalline substances like rubidium chloride, the 'unit cell' is a term you'll frequently encounter. It's the smallest division of the crystal lattice that still preserves the overall symmetry of the entire crystal. In other words, it’s like the fundamental building block or 'brick' for the structure. Considering our focus on \r\br\br\(RbCl\), with its rock salt structure, calculating the dimensions of this unit cell becomes an insightful journey into the microscopic world of materials. \r\br\brFor our particular problem, we measure the unit cell edge length, or simply the 'edge,' which is a primary indicator of the overall lattice size. The edge length can be thought of as the total length of an ion's radius plus the radius of an ion of opposite charge that lies adjacent to it. \r\br\brVisualize two ions, one cation, and one anion, touching side-by-side. The straight line distance from the very edge of one ion to the very edge of the other is the unit cell's edge length. It's a fundamental factor as it contributes significantly to the physical properties, such as the density and packing of the ions within the crystal as well as determining distances for ionic radius calculation.

Understanding the size of ions, which is denoted as the ionic radius, is crucial in the realm of chemistry. The ionic radius refers to the measure of an ion's size in a crystalline lattice, usually expressed in picometers (pm) or angstroms (\r\br\br\(\text{Å} = 10^{-10} \text{m}\)). The determination of an ionic radius is not only of academic interest but also critical for explaining various physical and chemical properties of compounds. \r\br\brWhen it comes to rubidium chloride and similar ionic crystals, the ions are nestled close to one another. As they touch, we deduce that the distance between the centers of the anion and cation, along the edge of the unit cell, equals the sum of their respective radii. Thus, knowing one radius and the edge length allows us to compute the other. \r\br\brIn the provided exercise, we're given the edge length of the \r\br\br\(RbCl\) unit cell and the radius of the chloride ion. By deducting the chloride ion’s radius from the unit cell's edge length, we can unravel the radius of the rubidium ion. It's an elegant and straightforward calculation, emphasizing how intricately related these parameters are—and how the precise determination of one can illuminate our understanding of the other.