Chapter 12, Problem 12.41SP

Interpretation Introduction

Interpretation:

The radius of sodium atom and edge length of the cell is to be calculated.

Concept introduction:

A unit cell is smallest repeating unit of a crystal lattice. Unit cells are classified as primitive and non-primitive. Unit cells that have atoms at only corners are primitive and unit cells that have atoms at positions other than corners are non-primitive.

Unit cells that are non- primitive are of various types:

Face centered unit cell (fcc), body centered unit cell (bcc), edge centered unit cell, end centered unit cell.

Contribution of an atom at a position is as follows:

$\begin{array}{cc}\text{position in unit}\text{cell}& \text{contributions}\\ \text{center of body}& \text{1}\\ \text{center of face}& \text{1/2}\\ \text{center of edge}& \text{1/4}\\ \text{corners}& \text{1/8}\end{array}$

The number of particles per unit cell, also denoted by Z is as follows:

$\begin{array}{cc}\text{Unit}\text{cell}& Z\\ \text{scc}& \text{1}\\ \text{fcc}& \text{4}\\ \text{bcc}& \text{2}\\ \text{edge-centered}\text{cubic}& \text{4}\\ \text{end-centered}\text{cubic}& \text{2}\end{array}$

The elements or substances exist more in solid than liquid and gases. These solids can be of two types amorphous and crystalline. The crystalline solids are solids that contain their constituent particle in arranged manner. While amorphous solids are solid in which constituent particles get arranged randomly such as rubber.