NCERT Solutions Class 12 Chemistry Chapter 1: The Solid State – Complete Guide

Chapter 1 of Class 12 Chemistry deals with The Solid State, a fundamental topic that explores the structure and properties of solids. This chapter is crucial for both board exams and competitive examinations like JEE and NEET. Let’s explore the key concepts, important formulas, and problem-solving approaches.

Introduction to Solid State

Solids are characterized by definite shape, definite volume, high density, incompressibility, and rigidity. The constituent particles (atoms, molecules, or ions) are held together by strong interparticle forces and have fixed positions, though they can oscillate about their mean positions.

Classification of Solids

Based on Arrangement of Particles

Crystalline Solids:

Regular and orderly arrangement of constituent particles
Sharp melting point
Anisotropic (different properties in different directions)
True solids
Examples: NaCl, Diamond, Quartz

Amorphous Solids:

Irregular arrangement of particles
Melt over a range of temperatures
Isotropic (same properties in all directions)
Pseudo solids or supercooled liquids
Examples: Glass, Rubber, Plastics

Types of Crystalline Solids

Type	Constituent Particles	Bonding	Properties	Examples
Ionic	Cations & Anions	Electrostatic	High MP, Brittle, Conduct when molten	NaCl, MgO
Covalent	Atoms	Covalent bonds	Very high MP, Hard, Poor conductors	Diamond, SiC
Molecular	Molecules	Dispersion/Dipole/H-bond	Low MP, Soft, Non-conductors	Ice, I₂
Metallic	Metal atoms	Metallic bond	Variable MP, Malleable, Good conductors	Fe, Cu, Au

Crystal Lattice and Unit Cell

Crystal Lattice

A three-dimensional arrangement of points representing the positions of constituent particles in a crystal is called a crystal lattice or space lattice. Each point is called a lattice point.

Unit Cell

The smallest repeating unit in a crystal lattice that represents the complete crystal structure is called a unit cell. There are seven crystal systems based on unit cell dimensions.

Types of Unit Cells

Primitive (Simple): Particles only at corners
Body-Centered: Particles at corners + one at body center
Face-Centered: Particles at corners + one at each face center
End-Centered: Particles at corners + one at two opposite face centers

Number of Atoms in Different Unit Cells

Contribution of Atoms at Different Positions

Corner atom: 1/8 (shared by 8 unit cells)
Face-centered atom: 1/2 (shared by 2 unit cells)
Body-centered atom: 1 (belongs to one unit cell)
Edge-centered atom: 1/4 (shared by 4 unit cells)

Atoms per Unit Cell

Simple Cubic (SC): 8 × 1/8 = 1 atom
Body-Centered Cubic (BCC): (8 × 1/8) + 1 = 2 atoms
Face-Centered Cubic (FCC): (8 × 1/8) + (6 × 1/2) = 4 atoms

Close Packing Structures

Close Packing in Two Dimensions

Square Close Packing: Coordination number = 4
Hexagonal Close Packing: Coordination number = 6

Close Packing in Three Dimensions

Hexagonal Close Packing (HCP): ABAB… pattern, coordination number = 12
Cubic Close Packing (CCP/FCC): ABCABC… pattern, coordination number = 12

Packing Efficiency

Packing efficiency = (Volume occupied by atoms / Total volume of unit cell) × 100

Packing Efficiency Values

Simple Cubic: 52.4%
Body-Centered Cubic: 68%
Face-Centered Cubic: 74%
HCP: 74%

Voids in Close Packing

Tetrahedral Voids

Formed when a sphere of second layer is above the void of first layer. Number of tetrahedral voids = 2 × number of spheres

Octahedral Voids

Formed when triangular voids of first and second layers do not overlap. Number of octahedral voids = number of spheres

Density Calculations

The density of a crystalline solid can be calculated using:

ρ = (Z × M) / (a³ × Nₐ)

Where:

ρ = Density
Z = Number of atoms per unit cell
M = Molar mass
a = Edge length of unit cell
Nₐ = Avogadro’s number

Defects in Crystals

Point Defects

Stoichiometric Defects (Intrinsic):

Vacancy Defect: Missing atoms from lattice sites. Decreases density.
Interstitial Defect: Extra atoms in interstitial sites. Increases density.
Schottky Defect: Equal vacancies of cations and anions. Common in ionic compounds with similar cation and anion sizes (NaCl, KCl).
Frenkel Defect: Smaller ion displaced to interstitial site. Common when there’s large size difference (AgCl, ZnS).

Non-Stoichiometric Defects:

Metal Excess Defect: Due to anionic vacancies or extra cations in interstitial sites
Metal Deficiency Defect: Due to cationic vacancies

Impurity Defects

Foreign atoms occupy lattice positions. Example: Doping of Si with As (n-type) or B (p-type) semiconductors.

Important Formulas Summary

Relation between r and a for SC: a = 2r
Relation between r and a for BCC: a = 4r/√3
Relation between r and a for FCC: a = 2√2r
Density: ρ = ZM/a³Nₐ

Conclusion

The Solid State chapter forms the foundation for understanding material properties and their applications. Focus on understanding the concepts of unit cells, packing efficiency, and defects. Practice numerical problems on density calculations and relationship between atomic radius and edge length. This chapter carries significant weightage in both board exams and competitive examinations.