The Solid State

Question 81
CBSEENCH12005429

Name a salt that can be added to AgCl so as to produce cation vacancies.

Solution
CdCl2 can be mixed in AgCl to create cation vacancies, where Cd2+ will occupy some of the sites of Ag+ ions.
Question 82
CBSEENCH12005430

How many lattice points are there in one unit cell of each of the following lattice?
(a) face centred cubic
(b) face centred tetragonal
(c) body centred cubic

Solution

A face-centred cubic (fcc) unit cell contains atoms at all the corners and at the centre of all the faces of the cube.each atom located at the face-centre is shared between two adjacent unit cells and only 1/2 of each atom belongs to a unit cell

Thus, in a face-centred cubic
(fcc) unit cell:
(i) 8 corners atoms × 1/8 atom per unit cell = 8×1/8 = 1 atom
(ii) 6 face-centred atoms ×1/2 atom per unit cell = 6 ×1/2 = 3 atoms
∴ Total number of atoms per unit cell = 4 atoms

(a) z = 4,
(b) z = 4,

body centre wholly belongs to the unit cell in which it is present. Thus
in a body-centered cubic (bcc) unit cell:
(i) 8 corners × 1/8 per corner atom= 8×1/8 = 1 atom
(ii) 1 body centre atom = 1 × 1 = 1 atom
∴ Total number of atoms per unit cell =1+1 = 2

(c) z = 2.

Question 83
CBSEENCH12005431

Find out the number of atoms per unit cell in a face-centred cubic structure having only single atoms at its lattice points.

Solution

A face-centred cubic (fcc) unit cell contains atoms at all the corners and at the centre of all the faces of the cube.

It can be seen that each atom located at the face-centre is shared between two adjacent
unit cells and only1/2 of each atom belongs to a unit cell.
The number of atoms present at corners per unit cell= 8 corner atoms x 1/8 atoms per unit cell = 1

The number of atoms present at faces per unit cell
= 6 atoms at the faces x 1/2 atoms per unit cell
= 6 x 1/2 = 3 atoms

Therefore, total number of atoms per unit cell = 4 atoms.

Question 84
CBSEENCH12005432

What makes alkali metal halides sometimes coloured, which are otherwise colourless?

Solution
Metal excess defect is resposible for colour in alkylhalides.

When crystals of NaCl are heated in an atmosphere of sodium vapour, the sodium atoms are deposited on the surface of the crystal.
The Cl– 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 anionic sites and impart colour.

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