Which of the following has highest value of energy gap?

(i) Solid is the form of matter which possesses a definite shape and a definite volume.

(ii) If intermolecular forces > thermal energy, substance exists as solid

(iii) Classification of Solid: Crystalline (Regular arrangement of particles, anisotropic), Amorphous (No regular arrangement of particles, isotropic).

(iv) Classification of crystalline solids: Ionic, Molecular, Covalent/Network, Metallic

2. Crystal systems (types and characteristics):

(i) Types: 

(a) Cubic $(\mathrm{a}=\mathrm{b}=\mathrm{c}, \mathrm{\alpha }=\mathrm{\beta }=\mathrm{\gamma }=90°)$

(b) Tetragonal $(\mathrm{a}=\mathrm{b}\ne \mathrm{c}, \mathrm{\alpha }=\mathrm{\beta }=\mathrm{\gamma }= 90°)$

(c) Orthorhombic/Rhombic $(\mathrm{a}\ne \mathrm{b}\ne \mathrm{c}, \mathrm{\alpha }=\mathrm{\beta }=\mathrm{\gamma }=90°)$

(d) Monoclinic $(\mathrm{a}\ne \mathrm{b}\ne \mathrm{c}, \mathrm{\alpha }=\mathrm{\gamma }=90°\ne \mathrm{\beta })$

(e) Triclinic $(\mathrm{a}\ne \mathrm{b}\ne \mathrm{c}, \mathrm{\alpha }\ne \mathrm{\beta }\ne \mathrm{\gamma }\ne 90°)$

(f) Rhombohedral/Trigonal $(\mathrm{a}=\mathrm{b}=\mathrm{c}, \mathrm{\alpha }=\mathrm{\beta }=\mathrm{\gamma }\ne 90°)$

(g) Hexagonal $(\mathrm{a}=\mathrm{b}\ne \mathrm{c}, \mathrm{\alpha }=\mathrm{\beta }=90°, \mathrm{\gamma }=120°).$

(ii) Contribution by particles present at different positions

Corner $=\frac{1}{8}$, Face-centre $=\frac{1}{2}$, Body-centre $=1$, Edge-centre $=\frac{1}{4}$

(iii) Number of particles per unit cell of a cubic crystal

Simple $=8\times \frac{1}{8}=1$, Body-centred $=8\times \frac{1}{8}+1=2$, Face-centre $=8\times \frac{1}{8}+6\times \frac{1}{2}=4$

(iv) If the number of close packed spheres be $\mathrm{N}$, then:

The number of octahedral voids generated $=\mathrm{N}$ and the number of tetrahedral voids generated $=2\mathrm{N}$

(v) Relationship between radius (r) of an atom and edge length (a)

Simple cubic r=a2, Face centred cubic r=a22, Body centred cubic r=34a

Density of unit cell, d=Z×Ma3×NAg cm-3

Where Z=No. of atoms in unit cell; $\mathrm{M}=$Atomic mass; $a=$Edge length (in cm)

${\mathrm{N}}_{\mathrm{A}}=$Avogadro number $(6.022\times {10}^{23})$

(vi) Packing efficiency:

ccp and hcp: Packing efficiency $=\frac{\text{Volume occupied by} 4 \text{sphere sin the unit cell}}{\text{Total volume of the unit cell}}\times 100\mathrm{\%}=74\%$

(vii) BCC:

Packing efficiency $=\frac{\text{Volume occupied by} 2 \text{sphere sin the unit cell}}{\text{Total volume of the unit cell}}\times 100\mathrm{\%}= 68\%$ 

(viii) Simple cubic:

Packing efficiency $=\frac{\text{Volume of one atom}}{\text{Volume of the cubic unit cell}}\times 100\mathrm{\%}=52.4\%$

3. Imperfections/defects in solids:

(i) Any departure from perfectly ordered arrangement of constituent particles is called defect or imperfection.

(ii) Stoichiometric defects: When ratio between cations and anions remains the same. Two types are Schottky defect and Frenkel defect.

(iii) Non-stoichiometric defects: When ratio of cations and anions changes as a result of the defect. Metal excess and Metal deficiency are the two types of this defect.

(iv) Impurity defects. Adding impurities to crystalline solids to change their properties is called doping.