Chapter 8, Problem 8.21PAE

Interpretation Introduction

Interpretation: The Avogadro’s number has to be determined when the side of the crystal and its density are 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:

Density of crystal= $\text{7}{\text{.874 g/cm}}^3$

Edge length = $286.65\text{pm}$

The crystal is in body-centred crystal lattice form.