Chapter 10, Problem 10.87SP

Interpretation Introduction

Interpretation:

The length in picometers of unit-cell diagonal that passes through the center atom has to be given.

Concept Introduction:

Body-centered unit cell:

A body – centered cubic cell is a type of unit cell with atoms arranged in all the vertices of the unit cell and one atom at the center of the cube.

Figure 1

A body – centered cubic unit cell has its all the eight vertices arranged with atoms in it.  Eight atoms are arranged in a simple cubic unit cell in eight vertices.  Each atom in a vertex is shared by eight neighboring unit cells such that each cubic unit cell has $\frac{\text{1}}{\text{8}}\text{th}$ of an atom at each vertex.  Further, each body – centered cubic unit cell has one atom at the center.  So 8 vertices have $\text{8}\text{×}\frac{\text{1}}{\text{8}}=1\text{atom}\text{+}\text{1}$ atom at the body of the cube gives 2 atoms per body – centered cubic unit cell.