(i) When amorphous solid (glass) are heated and cooled slowly, they acquire crystallinity at same temperature. Glass objects of ancient  monuments, over a period of years, are exposed to sunlight and cooled during night times, which has resulted in the crystallization of the glass object which imparts milky colour to the ancient monuments.
(ii) Density = \(\frac { Z\times M }{ a^{ 3 }\times N_{ A } } \)
\(4=\frac { Z\times 72 }{ (5\times 10^{ -8 })^{ 3 }\times 6.023\times 10^{ 23 } } \)
So Z = 4.18
As Z = 4 so 4 units of FeO are present and hence 4Fe²⁺ and 4O^2- are present in each unit cell.

The substances whose conductance lies between that of conductors (metals) and insulators are called semiconductors. They have conductivity values ranging from 10-6 to 104 n-1m-1. Two main types of semiconductors are n-type and p-type.
(i) n-type semiconductors: These are the semiconductors in which the current is carried by the electrons in the normal way. For example, silicon and germanium belong to group 14 of the periodic table and have four valence electrons each. In their crystals, each atom forms four covalent bonds with its neighbors,' When it is doped with an element of group 15 such as P or As, which contains five valence electrons, they occupy some of the lattice sites in silicon or germanium crystal. Four of the five valence electrons are used in the formation of four covalent bonds with the four neighboring Si atoms .and the fifth electron is extra and becomes delocalised. This delocalised electron will be able to conduct and such type of conduction is called n-type conduction. Hence silicon or germanium doped with an extra electron of impurity are called n-type semiconductors'.
(ii) p-type semiconductors: These are the semiconductors in which current is carried by the movement of positive holes. For example, when Ge or Si are doped with electron deficient atoms such as Ga or In (of Group 13) containing three valence electrons, the atoms of Ga or In will replace Ge atoms. Each In or Ga atom will use its three electrons for forming three covalent bonds with neighboring Ge atoms and the place for the fourth bond will remain missing and is called electron vacancy or hole. Such holes can move through the crystals like a positive charge giving rise to conductivity. This type of conduction is called p-type conduction. Hence, Si or Ge doped with electron deficient atoms as an impurity are called p-type semiconductors.

219.17pm

1.125

0.676g cm^-3

\(2\sqrt{2}r\)

\(4r=\sqrt{2}a\)
\(\Rightarrow\ r={\sqrt{2}a\over 4}={a\over 2\sqrt{2}}\)
for fcc element, where' a' is the edge length of unit cell and 'r' is the radius of atom.Z = 4 for fcc element.
Now, \(d={Z\times M\over N_4\times d}\)
\(\Rightarrow\ a^3={Z\times M\over N_A\times d}\)
\(={4\times63.55\over 6.02\times\times10^{23}\times8.93}\)
a³ = 4.728 x 10^-23 crrr'
= 47.28 x 10^-24 crrr',
a = 3.615 x 10^-8 cm
= 361.5 pm
\(4r=\sqrt{2}a\)
\(r={a\over 2\sqrt{2}}={361.5\over 2\times1.414}=127.82 \ pm\)

(iii) The packing efficiency of simple cubic lattice is 52.4%, body-centred is 68% and that of hexagonal close-packed lattice is 74%.
Therefore, hexagonal dose-packed lattice has the highest packing efficiency.

Z=2
\(d=\frac { Z\times M }{ a^{ 3 }\times N_{ A } } \)
\(N_{ A }=\frac { Z\times M }{ d\times a^{ 3 } } \)
\(N_{ A }=\frac { 2\times 300 }{ [7.5\times (5\times 10^{ -8 }cm)^{ 3 }] } \)
\(=6.4\times 10^{ 23 }atoms\)

a = 250 pm = 250 x 10^-12 m = 250 x 10^-10 cm
2 x 10²⁴ atom weighs = 300 g
6.022 x10²³ atoms weigh =\(\frac { 300\times 6.022\times 10^{ 23 } }{ 2\times 10^{ 24 } } \)
= 90.3 g
\(d=\frac { M\times Z }{ a^{ 3 }\times N_{ A } } \)
=\(\frac { 4\times 90.3 }{ (250\times 10^{ -10 })\times 6.022\times 10^{ 23 } } \)
= 38.4 g cm^-3

(i) Schottky defect
(ii) Density of the crystal decreases.
(iii) Crystal having
(a) high coordination number and
(b) ions (cations and anions)of almost similar sizes.
For example: KCI, KBr. 

When crystals of alkali metal halides such as NaCI are heated in the atmosphere of sodium vapour, the  excess of sodium atoms are deposited on the surface of the crystal. The CI^- ions diffuse to the surface and combine with sodium atoms to form NaCI. This happens by the loss electrons by Na atoms to form the visible light falls on the crystal and occupy anionic sites. As a result, the structure has an excess of sodium.
The crystals acquired yellow colour because when visible light falls on the crystals, they absorb energy from the visible region to excite the electrons. Hence, they are coloured. Similarly, excess of Li makes LiCI crystals pink and excess of K makes KCI crystals viloet.

(i) When there is spontaneous alignment of magnetic moments of domains in the same direction, we get ferromagnetism. These have strong magnetic effects and ordering of domains persists even when magnetic field is removed and ferromagnetic substance becomes permanent magnet.
(ii) When the magnetic moments of the domains are aligned in parallel or anti-parallel directions in unequal numbers resulting in net magnetic moment, we get ferromagnetism.

6.033\(\times\) 10²³

PQR₃

\(4{ Ca }^{ 2+ }and{ 8F }^{ - }ions \ means \ { 4CaF }_{ 2 }units\)
\(Z=4, \ d=\frac { Z\times M }{ { a }^{ 3 }\times { N }_{ A } } \)
\({ N }_{ A }=\frac { Z\times M }{ d\times { a }^{ 3 } }\)
\( =\frac { 4\times 78.08g{ mol }^{ -1 } }{ 3.18g{ cm }^{ -3 }\times { \left( 5.46 \right) }^{ 3 }\times { 10 }^{ -24 }{ cm }^{ 3 } } \)
\(=\frac { 312.32\times { 10 }^{ 24 } }{ 3.18\times { \left( 5.46 \right) }^{ 3 } } =\frac { 3123.2 }{ 517.61 } \times { 10 }^{ 23 }\)
\({ N }_{ A }=6.0338\times { 10 }^{ 23 }{ mol }^{ -1 }\)

If a is the edge length of fcc unit cell, then
face diagonal = 4r
\(4r=\sqrt { 2 } a\)
\( r=\frac { \sqrt { 2 } }{ 4 } a\)
\(=\frac { \sqrt { 2 } \times 400pm }{ 4 } \)
\(=1.414\times 100=141.4pm\) 
​

(i) It is because its conductance is intermediate between conductor and insulator.
(ii) In Schottky defect, both cations and anions are missing which lead to lowering in the density of a solid.
(iii) The glass is supercooled liquid, therefore, very old glass objects become slightly milky because of heating during the day and cooling at nights, i.e. annealing over a number of years, glass acquires some crystalline structure.

No.of atoms in the close packing = 0.5 mol = \(0.5\times 6.022\times { 10 }^{ 23 }=3.011\times { 10 }^{ 23 }\)
No.of octahedral voids = No.of atoms in the packing = \(3.011\times { 10 }^{ 23 }\)
No.of tetrahedral voids=  2\(\times \)No.of atoms in the packing = \(2\times 3.011\times { 10 }^{ 23 }=6.022\times { 10 }^{ 23 }\)
Total no.of voids\(=3.011\times10+6.022\times { 10 }^{ 23 }=9.033\times { { 10 }^{ 23 } }\)

(i) The energy gap between valence band and condition band in an insulator is very large where as in a conductor, the energy gap is very small or there is overlapping between valence band and conduction band.
(ii) In a conductor, there is verysmall energy gap or there is verlapping between valence band and conduction band but in a semiconductor, there is always a small energy gap between them.

1.123

The given structure is similar ti that of NaCl in which coordination number of each Na⁺ and Cl^- ions is 6

Frenkel defect is a dislocation defect as some cations are dislocation from lattice sites and occupy interstitial sites.

127pm

MX₂

(i) Ferrites are magnetic material. 
(ii) They are used in telephones and memory loops in computers.

(i) Piezoelectric crystals behaves as mechanical electrical transducer. 
(ii) Piezoelectric crystals are used as pickups in record players where they produce electric signals by application of pressure. 
(iii) We generally become tense and pessimistic under stress. But we should face every situation, accept every worst situation as challenge and maintain our mental balance. It will definitely result in our performance just like in piezoelectric crystals. We can learn from these non-living crystals to be optimistic as worst situations can be converted into an opportunity.