In a face centred cubic arrangement of \(\mathrm{P}\) and \(\mathrm{Q}\) atoms, atoms of \(\mathrm{P}\) are at the corner of the unit cell and atoms of \(\mathrm{Q}\) are at the face centres. One of the \(\mathrm{P}\) atom is missing from one corner in unit cell. The simplest formula of compound is: (a) \(\mathrm{PQ}_{3}\) (b) \(\mathrm{P}_{7} \mathrm{Q}_{3}\) (c) \(\mathrm{P}_{7} \mathrm{Q}_{24}\) (d) \(\mathrm{P}_{7 / 8} \mathrm{Q}_{3}\)

Understanding the intricate structure of crystals is foundational in solid-state chemistry. A crystal lattice is an orderly arrangement of atoms in a crystalline solid where each point, called a lattice point, represents the position of an atom, ion, or molecule. Among the 14 types of lattice structures, the face-centered cubic (fcc) unit cell is one of the closest packed structures, providing high packing efficiency.

This means the atoms are arranged in such a way that they occupy the maximum available space. In an fcc lattice, atoms are located at each of the corners and the center of each face of the cube-shaped cell. This distribution results in a highly symmetrical arrangement, which is a key characteristic of metals like gold, silver, and copper.

In the case of an impure or defective fcc lattice, an atom might be missing from its expected position, as noted in the original exercise with a missing P atom. Such defects can significantly alter the properties of the material, influencing its strength, electrical conductivity, and other physical characteristics.

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. However, it also applies to determining the proportions of elements within compounds. This field uses principles of conservation of mass and balanced equations to calculate the ratios of elements and molecules.

In solid-state chemistry, stoichiometry plays a pivotal role in defining the chemical composition of a crystalline solid. The stoichiometry of a compound dictates the simplest formula, which reflects the integer ratio of the different types of atoms present within a crystal lattice. By deducing the number of atoms of each element in a unit cell and considering their arrangement within the lattice, we can determine the empirical formula of the compound.

The exercise provided demonstrates this concept by calculating the numbers of P and Q atoms in a face-centered cubic unit cell and then finding the simplest formula that represents their ratio. This kind of problem-solving is integral to understanding how materials are composed at an atomic level.

Solid-state chemistry explores the synthesis, structure, and properties of solid materials. It sits at the intersection of chemistry, physics, and engineering, with a focus on understanding the behavior of solids from a molecular and atomic perspective. This branch of chemistry is vital for numerous applications, including the development of new materials, electronics, and pharmaceuticals.

In this discipline, chemists analyze the arrangement of atoms in a material's crystal lattice to predict its physical and chemical properties. For instance, the electrical and thermal conductivity, as well as the malleability of a solid, can often be inferred from its crystal lattice structure. When there is a deviation from the ideal arrangement, such as a missing atom in an otherwise perfect lattice, it can lead to unique properties or defects that may be exploited in material engineering.

Essential concepts such as point defects, dislocations, and non-stoichiometry in compounds are all investigated within the realm of solid-state chemistry. These factors can influence the color, hardness, and melting point of materials, which are crucial considerations for industrial applications.