Chapter 13, Problem 65E

Interpretation Introduction

Interpretation:

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

Type of solid:

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

Unit cell:

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

Concept introduction:

Side length $=l$, body diagonal $=\sqrt{l^2+l^2+l^2}=\sqrt{3}.l.$

Diagonal of face of cube $=\sqrt{2}l$

To determine:

A tetrahedral site in a closed packed lattice is formed by four spheres at the corners of a regular tetrahedron. This is equivalent to placing the spheres at alternate corners of a cube. In such a closed packed arrangement the spheres are in contact and if the spheres have a radius $r$, the diagonal hole is inside the middle of the cube. Find the length of the body diagonal of this cube and the radius of the tetrahedral hole.