# The Solid State

Question 17

## A compound is formed by two elements M and N. The element N forms ccp and atoms of M occupy 1/3 of tetrahedral voids. What is the formula of the compound?

Solution
The number of tetrahedral voids formed is equal to twice the number of atoms of element N and only 1/3rd of these are occupied by the atoms of element M. Hence the ratio of number of atom of M and N is 2 x (1/3) : 1 or 2 : 3. So the formula of the compound is M2 N3.
Question 18

## Which of the following lattices has the highest packing efficiency:simple cubic body-centred cubichexagonal close packed lattice

Solution

C.

hexagonal close packed lattice

Hexagonal close packed lattice has the highest packing efficiency (74%).

Question 19

## An element with molar mass 2.7 x 10–2 kg mol–1 form a cubic unit cell with edge length 405 pm. If its density is 2.7 x 103 kg m–3. What is the nature of the cubic unit cell?

Solution
$\mathrm{Z}=\frac{\mathrm{d}×{\mathrm{a}}^{3}×{\mathrm{N}}_{\mathrm{A}}}{\mathrm{M}}$

Hence, the nature of the cubic unit cell is ccp.
Question 20

## What type of defect can arise when a solid is heated? Which physical property is affected by it and in what way?

Solution

Non-stoichiometric defects can arise when a solid is heated.
The crystals with this defect becomes coloured. Alkali halides like NaCl and KCl show this type of defect. When crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal. The CI ions diffuse to the surface of the crystal and combine with Na atoms to give NaCl. This happens by loss of electron by sodium atoms to form Na+ ions. The released electrons diffuse into the crystal and occupy an ionic sites. As a result the crystal now has an excess of sodium. They impart yellow colour to the crystals of NaCl.