\(M=\frac { d\times { a }^{ 3 }\times NA }{ g } \)
d = Density of the material
a = Length of the edge of the cell.
N_A = Avogadro number
Z = No. of atoms
\(M=\frac { 10.5{ gcm }^{ -3 }{ (4.07\times { 10 }^{ -6 }cm) }^{ 3 }\times \left( 6.023\times { 10 }^{ 23 }{ mol }^{ -1 } \right) }{ 4 } \)
Atomic mass of silver M = 107.08 g mol^-1.

(i) The intermolecular forces of attraction that are present in solids are very strong.
(ii) The constituent particles of solids cannot: move from their positions. They have fixed positions.
(iii) However, they can oscillate about their mean positions.
(iv) This is the reason solids are rigid.

Formula is Ni_o.96 O_1.00
So the ration of Ni = O = 96.00
So if there are 100 atom of oxygen, as atoms of Ni
Let the number of atoms of Ni⁺² = x
The number of atoms of Ni⁺² = 96 - x
Charge on Ni = charge on O
So that oxygen has charge = 2
3 (96 - x) + 2x = 2(100)
288 - 3x + 2x = 200
-x = -88
x = 88
Percentage of Ni + 2 = (atom of Ni⁺² / total number of atoms of Ni 100.)
= 100.(94/98) x 100 = 96%
Percentage of Ni⁺³ = 100 - Ni⁺²
= 100 - 96 = 4%

There are seven types of unit cell, Cubic, tetragonal, orthorhombic, hexagonal, monoclinic, triclinic and rhombohedral. They differ in the arrangement of their crystallographic axes and angles.
i) Cubic: a = b = c; α = β = ૪ = 90^o.

ii) Tetragonal: a = b ≠ c; α = β = ૪ = 90°.

iii) Orthorhombic:  a  ≠ b  ≠ c; α = β = ૪ = 90°.

iv) Hexagonal: a = b ≠ c; α = β = 90^o, ૪ = 120^o. 

v) Monoclinic: a ≠ b ≠ c; α = ૪ = 90^o, β ≠ 90^o, 

vi) Triclinic: a ≠ b ≠ c; α  ≠ β ≠ ૪ ≠ 90^o.

vii) Rhombohedral:  a = b = c; α = β = ૪ ≠ 90^o. 

(i) The defects in ionic solids is by adding impurity ions.
(ii) If the impurity ions are in different valance state from that of host, vacancies are created in the crystal lattice of the host.
(iii) For example, addition of CdCl₂ to silver chloride yields solid solutions where the divalent cation Cd²⁺ occupies the position of Ag⁺.
(iv) This will disturb the electrical neutrality of the crystal.
(v) In order to maintain the same, proportional number of Ag⁺ ions leaves the lattice.
(vi) This produces a cation vacancy in the lattice, such kind of crystal defects are called impurity defects.

Schottky defect:
(i) Schottky defect arises due to the missing of equal number of cations and anions from the crystal lattice.
(ii) This effect does not change the stoichiometry of the crystal.
(iii) Ionic solids in which the cation and anion are of almost of similar size show schottky defect. Ex: NaCl.
(iv) Presence of large number of schottky defects in a crystal, lowers its density.

Frenkel defect:
(i) Frenkel defect arises due to the dislocation of ions from its crystal lattice.
(ii) The ion which is missing from the lattice point occupies an interstitial position.
(iii) This defect is shown by ionic solids in which cation and anion differ in size.
(iv) Unlike Schottky defect, this defect does not affect the density of the crystal.
(v) For example AgBr, in this case, small Ag⁺ ion leaves its normal site and occupies an interstitial position.

(i) The colour develops because of the presence of electrons in the 8 anionic sites.
(ii) These electron absorb energy from the visible region of radiation and get excited. 
(iii) For example when crystals of NaCl are heated in an atmosphere of sodium vapours, the sodium atoms get deposited on the surface of the crystal and the deposited Na atoms.
(iv) During this process, the Na atoms on the surface lose electrons to form Na⁺ ions 
(v) These electrons get excited by absorbing energy from the visible light and impart yellow colour to the crystals.

In bcc unit cell, ΔABC
AC² = AB² + BC²
\(AC=\sqrt { { AB }^{ 2 }+{ BC }^{ 2 } } \)
\(\\ AC=\sqrt { { a }^{ 2 }+{ a }^{ 2 } } =\sqrt { { 2a }^{ 2 } } =\sqrt { 2 } a\)

In ΔACG
AG² = AC² + CG²
\(AG=\sqrt { { AC }^{ 2 }+{ CG }^{ 2 } } \)
\(AG=\sqrt { { \left( \sqrt { 2a } \right) }^{ 2 }+{ a }^{ 2 } } \)
\(AG=\sqrt { { 2a }^{ 2 }+{ a }^{ 2 } } =\sqrt { { 3a }^{ 2 } } \)
\(AG=\sqrt { 3a } \)
\(\sqrt { 3 } a=4r\)
\(r=\frac { \sqrt { 3 } }{ 4 } a\)
∴ Volume of the sphere with radius 'r' \(=\frac { 4 }{ 3 } { \pi r }^{ 3 }\)
\(=\frac{4}{3}\pi { \left( \frac { \sqrt { 3 } }{ 4 } a \right) }^{ 3 }\)\(=\frac { \sqrt { 3 } }{ 16 } \pi { a }^{ 3 }\)
Number of spheres belong to a unit cell in BCC arrangement is equal to two and hence the total volume of all spheres.
(i) Packing fraction = \(=\frac{Total \quad volume \quad occupied \quad by \quad spheres \quad in \quad a \quad unit \quad cell}{volume \quad of \quad the \quad unit \quad cell}\times100\)
\(\therefore\)Volume of all spheres \(=2\times \left( \frac { \sqrt { 3 } \pi { a }^{ 3 } }{ 16 } \right) =\frac { \sqrt { 3 } \pi { a }^{ 3 } }{ 8 } \)
Packing fraction \(=\frac { \left( \frac { \sqrt { 3 } \pi { a }^{ 3 } }{ 8 } \right) }{ ({ a }^{ 3 }) } \times 100\)
\(=\frac { \sqrt { 3 } \pi }{ 8 } \times 100\)
\(\\ =\sqrt { 3 } \pi \times 12.5\)
= 1.732 x 3.14 x 12.5
= 68%

The defects which are caused by missing or misplaced atoms or ions in the crystal.

(i) In ionic compounds, electricity is conducted by ions.
(ii) In solid state, ions are held together by A strong electrostatic forces and are not free to move about within the solid.
(iii) Hence, ionic solids do not conduct electricity in solid state
(iv) However, in molten state or in solution form, the ions are free to move and can conduct electricity.

(i) The intermolecular forces of attraction that are present in solids are very strong.
(ii) The constituent particles of solids have fixed position.
(iii) Hence, solids have a definite volume.

Number of X type atoms in the unit cell \(=8 \times \frac{1}{8}=1\)
Number of Y type atoms in the unit cell \(=1 \times \frac{1}{1}=1\)
Hence the formula is XY (or) X₁Y₁

Linear arrangement of spheres in one direction is repeated in two dimension (i.e.) more number of rows can be generated identical to the one dimensional arrangement such that all spheres of different rows align vertically as well as horizontal.
If we denote the first row as A type arrangement, then the above mentioned packing is called AAA type, because all rows are identical as the first one. In this arrangement each sphere is in contact with four of its neighbours.

Packing efficiency = 68%
\(\therefore\)empty space percentage = 100 - 68 = 32%