Chapter 13, Problem 31E

Interpretation Introduction

Interpretation:

Solid are the chemical substance which are characterised by definite shape and volume rigidity, high density, low compressibility. The constituent particles (atoms molecules or ions are closely packed and held together by strong force.

Types of solid:

The solid are of two types crystalline solids and amorphous solids.

Unit cell:

The smallest geometrical portion of the crystal lattice which can be as repetitive unit to build up the whole crystal is called unit cell.

Types of unit cell:

(i) Simple or primitive unit: In which the particle are present at the corners only.

(ii) Face centred unit cell: In which the particle are present at the corners as well as at the centre of each of six faces.

(iii) Body centred unit cell: In which the particles are present at the corners as well at the centre of unit.

(iv) End centred unit cell: In which the particles are present at the corners and at the centre of two opposite faces.

Concept introduction:

No of particles and their contribution

Unit cell	Corner	Face	Centre	Total
Body centred Unit cell	$8\times \frac{1}{8}=1$	$0$	$1$	$2$

It is cross section view of body centered unit cell.

From above it becomes clear that body centred cubic unit cell atoms touch each other along the body diagonal

So length of body diagonal $=\sqrt{3}l$

$\begin{array}{l}4r=\sqrt{3}l\\ r=\frac{\sqrt{3}l}{4}\text{ where r: radius of atom}\\ l:\text{side of cube}\end{array}$

To determine: the radius of the atom in pm in a body centered cubic unit cell that has volume of $2.62\times {10}^{-23}{\text{cm}}^3$