Chapter 11.6, Problem 1PPC

Interpretation Introduction

Interpretation:

The density of a billiard ball and a collection of billiards ball packed in simple unit cell and aface-centered unit cell are to be determined, and the reason that they are different is to be explained.

Concept Introduction:

A crystal lattice is made of small repeating unit cells.

A unit cell is of a primitive or a centered type. The spheres in a unit cell represent an atom, molecule, or ion.

Each sphere is shared by adjacent cells. The spheres at the corners are shared by eight unit cells. A sphere in the centre of each face is shared by two unit cells.

Volume of a sphere is

$\frac{\text{4}}{\text{3}}\text{π}{r}^{\text{3}}.$

Here, $r$ is the radius of sphere.

Volume of a unit cell $\left(V\right)$ is given by the relation as follows:

$V=a^{\text{3}}.$

Here, $a$ is the length of the edge.

Density of unit cell is mass divided by volume.

$D=\frac{m}{V}.$

Here, $D$ is the density, $m$ is the mass, and $V$ is the volume.