Chapter 10.8, Problem 10.13P

Interpretation Introduction

Interpretation:

The density of Polonium in $\text{g}{\text{cm}}^{\text{-3}}$ has to be calculated.

Concept Introduction:

Simple cubic unit:

A simple cubic unit cell is the simplest form of a cubic unit cell.  A cube has eight vertices, twelve edges and six faces.  Similarly a cubic unit cell has eight vertices, twelve edges and six faces.  If in a cubic unit cell, the components occupy only the eight vertices, then the unit cell is known as simple cubic unit cell.

Figure 1

A simple cubic unit cell has its all the eight vertices arranged with atoms in it.  Thus 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.  Each layer of a lattice has four unit cells and the upper or lower to that layer has four unit cells.  So, each simple cubic unit cell has $\frac{\text{1}}{\text{8}}\text{th}$ of an atom at each vertex.  So 8 vertices have $\text{8}\text{×}\frac{\text{1}}{\text{8}}=1\text{atom}$ per unit cell.

Density:

Density can be defined as property that links mass of an object to its volume.  It is derived quantity and its unit is $\text{g}{\text{ml}}^{\text{-1}}$ for liquids and $\text{g}{\text{cm}}^{\text{-3}}$ for solid.  The density of material can be calculated with the help of formula,

$\text{Density = }\frac{\text{Mass}\left(\text{g}\right)}{\text{Volume}\left(\text{ml}\text{or}{\text{cm}}^{\text{3}}\right)}$