Chapter 8, Problem 8.15PAE

Interpretation Introduction

Interpretation: The atomic radius of polonium has to be determined when its density is given.

Concept introduction:

• The density of a crystal is given by the formula $d=\frac{\text{M}\times \text{z}}{{\text{a}}^{\text{3}}\times {\text{N}}_{\text{A}}}$ where d is the density of the crystal, M is the molar mass in $\text{g/mol}$, z is the number of atoms per unit cell, a is the edge length in cm, ${\text{N}}_{\text{A}}$ is the Avogadro’s number.
• Value of z for simple cubic lattice = 1, for bcc lattice = 2, for ccp or fcc lattice = 4

Given:

The density of polonium atom $=9.32{\text{ g /cm}}^{\text{3}}$

The crystal is in simple cubic crystal lattice form.