Chapter 11, Problem 84E

(a)

Interpretation Introduction

Interpretation:

A body-centered cubic structure is given. The length of the line $c$ that runs from one corner of the cube diagonally through the center of the cube to the other corner in terms of atomic radius $r$ is to be calculated.

Concept introduction: A crystal lattice is the three dimensional arrangement of atoms in space. The smallest unit of a crystal lattice is called a unit cell. There are mainly two types of unit cell.

• Primitive unit cell
• Centered unit cell.

The centered unit cell is of three types.

• Body centered unit cell
• Face centered cell
• End centered unit cell.

(b)

Interpretation Introduction

Interpretation:

A body-centered cubic structure is given. Using Pythagorean Theorem, the expression for the length of the line $b$ that runs diagonally across one of the faces of the cube in terms of edge length $l$ is to be derived. Also, the expression for edge length $l$ in terms of $r$ is to be derived.

Concept introduction: A crystal lattice is the three dimensional arrangement of atoms in space. The smallest unit of a crystal lattice is called a unit cell. There are mainly two types of unit cell.

• Primitive unit cell
• Centered unit cell.

The centered unit cell is of three types.

• Body centered unit cell
• Face centered cell
• End centered unit cell.

(c)

Interpretation Introduction

Interpretation:

A body-centered cubic structure is given. The expression for edge length $l$ in terms of $r$ is to be derived.

Concept introduction: A crystal lattice is the three dimensional arrangement of atoms in space. The smallest unit of a crystal lattice is called a unit cell. There are mainly two types of unit cell.

• Primitive unit cell
• Centered unit cell.

The centered unit cell is of three types.

• Body centered unit cell
• Face centered cell
• End centered unit cell.