Introduction: Why Solid State is Important for CBSE Class 12 Boards
Chapter 1 of CBSE Class 12 Chemistry — The Solid State — is one of the highest-scoring topics in board exams. Every year, 5-6 marks are guaranteed from this chapter in the form of short answer questions, numerical problems, and MCQs. Students who master the concepts of unit cells, packing efficiency, and point defects can score full marks consistently.
This post covers the complete CBSE Class 12 Chemistry Solid State notes aligned with the NCERT textbook, with board-pattern MCQs and exam tips for 2027.
Classification of Solids: Amorphous vs Crystalline
Solids are broadly classified into amorphous and crystalline based on the arrangement of constituent particles:
| Property | Amorphous Solids | Crystalline Solids |
|---|---|---|
| Arrangement | Random, short-range order | Regular, long-range order |
| Melting point | No sharp melting point (melts over range) | Sharp melting point |
| Isotropy | Isotropic (same properties in all directions) | Anisotropic (different properties in different directions) |
| Cleavage | Irregular cleavage | Clean cleavage along planes |
| Examples | Glass, rubber, plastic | NaCl, diamond, quartz, ice |
Board Tip: Remember — amorphous = isotropic, crystalline = anisotropic. This distinction appears almost every year as a 1-mark question.
Crystal Lattice and Unit Cell
A crystal lattice is a regular three-dimensional arrangement of points representing constituent particles. A unit cell is the smallest repeating unit of the crystal lattice.
Types of Unit Cells:
- Primitive (Simple Cubic — SC): Particles at corners only
- Body-Centred Cubic (BCC): Particles at corners + 1 at body centre
- Face-Centred Cubic (FCC): Particles at corners + 1 at each face centre
- End-Centred: Particles at corners + 2 face centres (opposite faces only)
Number of Atoms Per Unit Cell (Z): Derivation
This is a crucial derivation — memorise the logic, not just the answers.
- Corner atom: Shared by 8 unit cells → contributes 1/8 per unit cell
- Face-centre atom: Shared by 2 unit cells → contributes 1/2
- Edge-centre atom: Shared by 4 unit cells → contributes 1/4
- Body-centre atom: Belongs entirely to 1 unit cell → contributes 1
SC: Z = 8 corners × (1/8) = 1
BCC: Z = 8 × (1/8) + 1 × 1 = 1 + 1 = 2
FCC: Z = 8 × (1/8) + 6 × (1/2) = 1 + 3 = 4
Close Packing in Solids
Close packing maximises the use of available space in a crystal:
- 1D close packing: Spheres arranged in a row — each sphere touches 2 neighbours
- 2D close packing: Square close packing (coordination number 4) or Hexagonal close packing (coordination number 6)
- 3D close packing:
- Hexagonal Close Packing (hcp): Third layer placed directly above first layer (ABAB… pattern). Coordination number = 12. Examples: Mg, Zn.
- Cubic Close Packing (ccp) / Face-Centred Cubic: Third layer shifted so it occupies tetrahedral voids of second layer (ABCABC… pattern). Coordination number = 12. Examples: Cu, Ag.
Board Tip: Both hcp and ccp have coordination number 12 and packing efficiency 74%. This is a common source of confusion — get it right.
Packing Efficiency
Packing efficiency = (Volume occupied by atoms in unit cell / Total volume of unit cell) × 100
| Structure | Coordination Number | Z | Packing Efficiency | Examples |
|---|---|---|---|---|
| Simple Cubic (SC) | 6 | 1 | 52.4% | Polonium (Po) |
| Body-Centred Cubic (BCC) | 8 | 2 | 68% | Fe, W, Cr, Na, K |
| Face-Centred Cubic (FCC/ccp) | 12 | 4 | 74% | Cu, Ag, Au, Al, Ni |
| Hexagonal (hcp) | 12 | 6* | 74% | Mg, Zn, Ti |
*hcp has 6 atoms per hexagonal unit cell
Point Defects in Crystals
Point defects are deviations from ideal crystal structure at specific lattice points. NCERT covers:
Stoichiometric Defects (do not change stoichiometry):
- Schottky Defect: Equal number of cations and anions are missing. Occurs in ionic crystals with high coordination number and similar-sized ions (NaCl, KCl, KBr). Decreases density of crystal.
- Frenkel Defect (Dislocation Defect): Smaller ions (usually cations) are displaced from their lattice positions to interstitial sites. Occurs in ionic crystals with large size difference between ions (AgBr, ZnS). Does not change density.
Non-Stoichiometric Defects:
- Metal excess defect: Anionic vacancies with trapped electrons (F-centres — give colour to crystals). Example: NaCl in Na vapour → yellow colour.
- Metal deficiency defect: Cationic vacancies with compensating higher-valence cations (Fe₀.₉₃O structure).
Electrical Properties: Band Theory (Simple)
In solids, atomic orbitals overlap to form bands:
- Valence band: Lower energy band, filled with electrons
- Conduction band: Higher energy band, empty in insulators
- Band gap: Energy difference between valence and conduction bands
- Conductors (metals): Zero band gap (valence and conduction bands overlap). Electrons move freely.
- Semiconductors: Small band gap (~1-3 eV). At room temperature or with doping, electrons can jump to conduction band. Examples: Si, Ge.
- Insulators: Very large band gap (above 6 eV). Electrons cannot cross. Example: Diamond, wood.
Important NCERT Numerical: Density Formula
The density formula for a unit cell is the most important numerical in this chapter:
ρ = (Z × M) / (Nₐ × a³)
Where:
- ρ = density (g/cm³)
- Z = number of atoms per unit cell (1 for SC, 2 for BCC, 4 for FCC)
- M = molar mass (g/mol)
- Nₐ = Avogadro’s number (6.022 × 10²³ mol⁻¹)
- a = edge length of unit cell (in cm)
Typical board question: “An element having BCC structure has a unit cell edge length of 287 pm. If the density is 7.92 g/cm³, calculate the molar mass.”
Strategy: Use Z = 2 for BCC. Convert pm to cm. Rearrange formula for M = ρ × Nₐ × a³ / Z.
Board Exam Tips for Solid State
- This chapter contributes 5-6 marks every year in CBSE Class 12 Chemistry boards
- Most common question types: 1-mark definition (Schottky vs Frenkel), 2-mark short answer (derive Z for BCC), 3-mark numerical (density calculation)
- Always specify units — edge length in pm vs cm is a common calculation error
- Remember: Schottky decreases density; Frenkel does not
- AgBr shows both Schottky AND Frenkel defects — frequently asked
- NaCl is FCC structure (Z = 4) — this is the standard example in NCERT numericals
10 Practice MCQs: CBSE Class 12 Chemistry Solid State
Quiz data error: Syntax error
Frequently Asked Questions (FAQs)
1. What is the difference between Schottky and Frenkel defect?
In a Schottky defect, equal numbers of cations and anions are missing from their lattice positions, creating vacancies. This decreases the density of the crystal and is found in ionic solids with similar-sized ions and high coordination numbers (e.g., NaCl, KBr). In a Frenkel defect, a smaller ion (usually cation) is displaced from its normal lattice position to an interstitial site. The overall density remains unchanged. It is found in crystals with large size differences between ions (e.g., AgBr, ZnS). AgBr uniquely shows both defects, which is why it is photosensitive and used in photography.
2. How do I derive the number of atoms per unit cell for FCC?
In an FCC unit cell: (i) 8 atoms at the corners — each shared by 8 unit cells, contributing 8 × (1/8) = 1 atom. (ii) 6 atoms at face centres — each shared by 2 unit cells, contributing 6 × (1/2) = 3 atoms. Total Z = 1 + 3 = 4 atoms per unit cell. This is the standard derivation — practice writing it clearly in the board exam as it carries 2 marks.
3. Why is packing efficiency important and which structure has the highest?
Packing efficiency tells us what percentage of a crystal’s volume is actually occupied by atoms. Higher packing efficiency means less empty space. FCC (ccp) and hcp both achieve the maximum possible packing efficiency of 74% — this is the mathematical limit for equal-sized hard spheres. BCC achieves 68% and SC only 52.4%. Almost all metals with the highest density pack in FCC structure because of this efficiency advantage.
4. What is an F-centre and why does it cause colour?
An F-centre (Farbe centre, from German “colour”) is a type of metal excess defect where an anion vacancy is occupied by an electron. These trapped electrons absorb visible light at specific wavelengths and re-emit light of the complementary colour. For example, when NaCl is heated in sodium vapour, excess sodium atoms deposit Na⁺ ions at the crystal surface while their electrons diffuse into anionic vacancies, forming F-centres. This gives NaCl a yellow colour. Similarly, LiCl appears pink and KCl appears violet due to F-centres.
