Problem 131 - A Complete Resource Book in Chemistry for JEE Main

Question

In \(\mathrm{CsCl}\) structure, the number of \(\mathrm{Cs}^{+}\)ions that occupy second nearest neighbor locations of a \(\mathrm{Cs}^{+}\)ion is

Step-by-Step Solution

Answer

Each \( \mathrm{Cs}^{+} \) ion in the CsCl structure has 6 second nearest neighbor \( \mathrm{Cs}^{+} \) ions.

Step 1: Understanding the CsCl Structure

In the CsCl crystal structure, each \( \mathrm{Cs}^{+} \) ion is located at the corners of a cube, while \( \mathrm{Cl}^{-} \) ions occupy the center of the cube. This creates a body-centered cubic (BCC) arrangement.

Step 2: Identifying Nearest Neighbors

The first nearest neighbors for a \( \mathrm{Cs}^{+} \) ion are the ions of opposite charge at the central position of adjacent cubic cells. Hence, each \( \mathrm{Cs}^{+} \) ion has one \( \mathrm{Cl}^{-} \) ion as its nearest neighbor located at the cube's center.

Step 3: Identifying Second Nearest Neighbors

Second nearest neighbors are ions of the same charge which are located at two unit cell edges away. In the BCC structure of CsCl, every \( \mathrm{Cs}^{+} \) ion is at the corner of the cube, and its second nearest \( \mathrm{Cs}^{+} \) neighbors are placed at the adjacent corners.

Step 4: Counting Second Nearest Neighbors

Given the cubic arrangement, each \( \mathrm{Cs}^{+} \) ion is surrounded by 6 other \( \mathrm{Cs}^{+} \) ions at its second nearest neighbor positions — they are located at the corners of surrounding cubes sharing only edges, not faces, of the central unit cell.

Key Concepts

Crystal Structure

A crystal structure is a unique arrangement of atoms or ions in a crystalline solid. In such structures, the constituents are organized in a repeating pattern that extends in all three spatial dimensions.
These patterns are essential because they influence the physical and chemical properties of the material. Each type of crystal can have different geometric configurations, which lead to differences in these properties. Understanding crystal structures is key to fields like chemistry, physics, and material science. They help in predicting stability, reactivity, and even the mechanical strength of materials. The CsCl crystal structure is a common example, showcasing a body-centered cubic arrangement that significantly affects its characteristics.

Body-Centered Cubic

The body-centered cubic (BCC) arrangement is one of the simplest and most common types of crystal structures. In BCC, each unit cell of the crystal lattice is cubic, with an atom or ion placed at each corner and a single atom or ion in the very center of the cube.
This pattern is particularly important in metals and some ionic compounds, including the CsCl structure. A BCC crystal consists of:

• Atoms at the eight corners of the cube.
• A central atom located at the center of the cube.

This configuration allows each atom in the center to be surrounded by eight other atoms. The BCC structure helps to maximize space and optimize the attractive forces between ions, contributing to the stability of the compound.

Nearest Neighbor

The concept of nearest neighbors in a crystal lattice refers to the surrounding atoms or ions that are closest to a given atom. Understanding these neighbors is crucial, as they have a significant impact on the atom's properties and interactions. The nearest neighbor is typically defined by the shortest distance between atoms in a solid. For ext{CsCl}, each ext{Cs}^+ ion has one nearest ext{Cl}^- ion, positioned at the center of the cube.
This positioning ensures that interactions are strongest between oppositely charged ions, which stabilizes the structure. Next come the second nearest neighbors, which are the same type of ions. In this scenario with ext{CsCl}, each ext{Cs}^+ ion is surrounded by other ext{Cs}^+ ions positioned at the corners of nearby cubes. As outlined, each ext{Cs}^+ ion has six second nearest ext{Cs}^+ neighbors. These relationships help define the overall structure and determine how the material behaves on a macroscopic level.