ChemistryCHEM 16
Solid State & Mole Concept
Crystal systems, unit cells, packing efficiency, defects, stoichiometry calculations
NCERT XII Ch.1 / NCERT XI Ch.1
NCERT Ref
Concept Core
Essential theory — everything NCERT tests on Solid State & Mole Concept
UNIT CELLS
SC (simple cubic): 1 atom/unit cell. BCC: 2 atoms. FCC/CCP: 4 atoms. HCP: 6 atoms per unit cell (eff).
Radius ratio: SC: r/R=1. BCC: r/R=√3/2. FCC: r/R=1/√2.
Packing efficiency: SC: 52.4%. BCC: 68%. FCC/CCP: 74%. HCP: 74%.
CRYSTAL SYSTEMS & TYPES
7 crystal systems: cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, triclinic.
Solid types: Ionic (NaCl, high mp, brittle), Covalent network (diamond, SiO₂, very hard), Molecular (ice, soft, low mp), Metallic (Fe, Cu, conductor).
DEFECTS IN CRYSTALS
Schottky: equal cations + anions missing. Decreases density. Seen in NaCl, KCl, CsCl.
Frenkel: ion displaced to interstitial site. Density unchanged. AgBr (photographic film), AgCl, ZnS.
F-centres: electron trapped in anion vacancy → colour (NaCl is yellow if heated in Na vapour).
MOLE CONCEPT
1 mole = 6.022 × 10²³ particles (Avogadro's number, N_A). Molar mass = mass of 1 mole (g/mol).
Limiting reagent: consumed first, limits product amount. % yield = (actual/theoretical) × 100. Empirical formula: simplest ratio. Molecular formula: actual ratio.
Molarity (M) = moles/L. Molality (m) = moles/kg solvent.
SEMICONDUCTOR DOPING
n-type: Group 15 dopant (P, As) in Si/Ge → extra electrons. p-type: Group 13 dopant (B, Al) → holes.
Electrical conductivity: metals > semiconductors > insulators. Band theory: valence band, conduction band, band gap. Semiconductor: small band gap (<3 eV).
Fact & Formula Vault
High-yield facts, numbers, and formulas
Atoms per Unit Cell
SC: 1 atom
BCC: 2 atoms
FCC/CCP: 4 atoms
HCP: 6 atoms
Packing Efficiency
SC: 52.4%
BCC: 68%
FCC/HCP: 74% (most efficient)
Coordination number: FCC=12, BCC=8, SC=6
Crystal Defects
Schottky: density decreases (vacancies)
Frenkel: density same (interstitial)
NaCl, KCl: Schottky
AgBr, ZnS: Frenkel
F-centre: colour (anion vacancy)
Worked Examples
NEET-style questions solved step-by-step
EASYIn FCC unit cell, how many atoms per unit cell?▾
In FCC unit cell, how many atoms per unit cell?
FCC: 8 corner atoms × 1/8 + 6 face atoms × 1/2 = 1 + 3 = 4 atoms per unit cell. This is also CCP (cubic close packing) structure.
MEDIUMAgBr shows Frenkel defect. What happens to density?▾
AgBr shows Frenkel defect. What happens to density?
In Frenkel defect, the Ag⁺ ion moves to an interstitial position within the same crystal — no atoms leave. Therefore density remains unchanged. (Unlike Schottky, where ions are missing, decreasing density.)
HARDAn element forms BCC structure with edge length 'a'. Radius of atom?▾
An element forms BCC structure with edge length 'a'. Radius of atom?
In BCC: atoms touch along body diagonal. 4r = a√3. Therefore r = a√3/4. BCC packing efficiency = 68%.
Mistake DNA
Common NEET traps for this chapter
⚠ FCC vs CCP
FCC and CCP are the SAME arrangement. FCC = face-centred cubic (crystallographic). CCP = cubic close packing (stacking description). Both have 4 atoms/unit cell and 74% packing.
✓ Fix: FCC = CCP. Same thing, different names.
⚠ Schottky vs Frenkel
Schottky: ions missing → density decreases. Frenkel: ions displaced to interstitial → density unchanged. AgBr = Frenkel. NaCl = Schottky.
✓ Fix: Schottky = density↓. Frenkel = density same.
⚠ Mole and molecules
1 mole of H₂O = 6.022×10²³ molecules = 18 g. 1 mole of H₂ = 6.022×10²³ molecules = 2 g. Avogadro number applies to any particle (atom, molecule, ion).
✓ Fix: NA = 6.022×10²³ for 1 mole of any particle.
Chapter Intelligence
Exam data and last-minute strategy
NEET Frequency
2–3 Q/year. Atoms per unit cell (FCC, BCC, SC), packing efficiency, Schottky vs Frenkel defects, limiting reagent, molar mass calculations.
High-Yield
FCC = 4 atoms, 74% packing. BCC = 2 atoms, 68%. SC = 1 atom, 52%. Schottky: density↓. Frenkel: density same. F-centre: colour.
Strategy
Atoms per unit cell: practice the corner (1/8) + face (1/2) + body (1) counting. Defects table: Schottky vs Frenkel. Mole concept: dimensional analysis.
🧪 Practice with Full Mock Tests
7 full-length NEET mocks · 180 Qs · +4/−1 · Mock 1 FREE
Open Mock Tests →
