Chapter 12.3, Problem 12.3.2SR

Interpretation Introduction

Interpretation:

A metal that crystallizes in body-centered cubic lattice has to be identified using given data. The molar mass of the metal has to be calculated.

Concept Introduction:

In crystalline solids, the components are packed in regular pattern and neatly stacked.

The components are imagined as spheres and closely packed. This phenomenon is called “close packing” in crystals. The two major types of close packing of the spheres in the crystal are – hexagonal close packing and cubic close packing. Cubic close packing structure has face-centered cubic (FCC) unit cell.

In body-centered cubic unit cell, each of the six corners is occupied by every single atom.  Center of the cube is occupied by one atom.  Each atom in the corner is shared by eight unit cells and a single atom in the center of the cube remains unshared.  Thus the number of atoms per unit cell in BCC unit cell is,

$\text{8}\text{×}\frac{\text{1}}{\text{8}}\text{atoms}\text{in}\text{corners}\text{+}\text{1}\text{atom}\text{at}\text{the}\text{center}\text{=}\text{1}\text{+}\text{1}\text{=}\text{2}\text{atoms}$