What are the key concepts in Solid State?

Explore the ordered world of crystalline solids: unit cells, packing, defects, and how structure determines electrical and magnetic properties.

Is Solid State important for NEET & JEE?

Yes. Solid State is part of the Chemistry Class 12 NCERT syllabus and is directly tested in NEET and JEE examinations. StudyHub provides structured notes, diagrams, and practice questions covering all exam-level subtopics.

How can I practice Solid State questions on StudyHub?

Open StudyHub and select Chemistry → Solid State. Choose Easy, Medium, or Hard difficulty. Hard-tier questions are at NEET & JEE level with full step-by-step explanations.

Solid State — Free Chemistry Class 12 Notes & Quiz

1 Read the chapter ~6 min

🎯 Key Points

4 main solid types: ionic (NaCl), covalent/network (diamond), metallic (Cu), molecular (ice)
SC: 1 atom/cell, CN=6, 52.4% packing; BCC: 2 atoms/cell, CN=8, 68%; FCC/ccp: 4 atoms/cell, CN=12, 74%
Schottky defect: missing ion PAIRS, density decreases; Frenkel defect: ion DISPLACED (not missing), density unchanged
Conductors: overlapping bands; insulators: large band gap (>3eV); semiconductors: small band gap (~1eV)
n-type semiconductor: doped with higher-valence element (extra electrons); p-type: doped with lower-valence element (extra holes)
For BCC: 4r=a√3; for FCC: 4r=a√2; corner atom contributes 1/8, face=1/2, edge=1/4, body=1 to the unit cell count

The three cubic unit cells: Simple Cubic has atoms only at corners; Body-Centred adds one atom at the centre; Face-Centred adds one atom at the centre of each of the 6 faces, giving the highest packing efficiency.

Types of Solids

Solids are classified based on the nature of the particles and the forces holding them together.

Ionic solids: Ions held by electrostatic attraction; high melting points; conduct electricity only when molten or dissolved; e.g., NaCl, MgO
Covalent (network) solids: Atoms joined by covalent bonds throughout; very hard and high melting; e.g., diamond, SiO₂, SiC
Metallic solids: Metal cations in a sea of delocalised electrons; good conductors; e.g., Fe, Cu, Na
Molecular solids: Molecules held by van der Waals forces, dipole interactions, or H-bonds; low melting points; non-conductors; e.g., ice, dry ice, I₂

Crystal Systems and Unit Cells

A unit cell is the smallest repeating unit that, when translated in 3D, builds the entire crystal lattice.

7 crystal systems: cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, triclinic
Simple Cubic (SC): 1 atom per unit cell; coordination number 6; packing efficiency 52.4%
Body-Centred Cubic (BCC): 2 atoms per unit cell; coordination number 8; packing efficiency 68%; e.g., Na, K, Cr, W
Face-Centred Cubic (FCC) / cubic close packing (ccp): 4 atoms per unit cell; coordination number 12; packing efficiency 74%; e.g., Cu, Ag, Au, Al

Simple cubic unit cell: identical atoms at the eight corners of a cube

Body-centred cubic unit cell: atoms at the eight corners plus one atom at the centre of the cube

Face-centred cubic unit cell: atoms at the eight corners plus one atom at the centre of each of the six faces

The three cubic unit cells (left to right): simple cubic — atoms only at the 8 corners (net 1 atom per cell); body-centred cubic (BCC) — corners plus 1 atom at the body centre (net 2 atoms); face-centred cubic (FCC) — corners plus 1 atom at each of the 6 face centres (net 4 atoms). Images: Elnaz.gharehdaghi, CC0, via Wikimedia Commons.

Packing and Radius Ratio

Hexagonal close packing (hcp) and cubic close packing (ccp) both achieve 74% efficiency
Radius ratio r/R predicts coordination number in ionic solids: 0.155–0.225 → 3; 0.225–0.414 → 4 (tetrahedral); 0.414–0.732 → 6 (octahedral); 0.732–1.000 → 8 (cubic)

Point Defects

Schottky defect: Equal numbers of cations and anions missing; reduces density; common in NaCl, KCl
Frenkel defect: Ion displaced from its site to an interstitial position; no change in density; common in AgCl, ZnS
Metal excess defect: Extra cations in interstitial sites with electrons to maintain neutrality; makes solid n-type semiconductor; e.g., ZnO on heating
Metal deficiency defect: Fewer cations; some higher-valence cations balance charge; makes solid p-type; e.g., FeO, FeS

Electrical Properties and Band Theory

Conductors: overlapping valence and conduction bands
Insulators: large energy gap between valence and conduction bands (>3 eV)
Semiconductors: small energy gap (~1 eV); conductivity increases with temperature
n-type semiconductor: doped with higher-valence element (e.g., P in Si); extra electrons carry current
p-type semiconductor: doped with lower-valence element (e.g., B in Si); holes carry current

Magnetic Properties

Diamagnetic: All electrons paired; repelled by magnetic field; e.g., NaCl, TiO₂
Paramagnetic: Unpaired electrons; weakly attracted; e.g., O₂, Cu²⁺ salts
Ferromagnetic: Unpaired electrons align parallel in domains; strongly attracted; permanent magnets; e.g., Fe, Co, Ni
Antiferromagnetic: Adjacent spins align antiparallel; net magnetic moment zero; e.g., MnO
Ferrimagnetic: Unequal antiparallel spins; net magnetic moment present; e.g., Fe₃O₄

Quick Tips

Number of atoms in a unit cell: corner atom = 1/8; face atom = 1/2; body atom = 1; edge atom = 1/4
For BCC: 4r = a√3; for FCC: 4r = a√2
Packing efficiency = (volume of atoms in unit cell / volume of unit cell) × 100

🚀 JEE Advanced Edge

Density from unit cell data: ρ = (Z × M)/(NA × a³), where Z = number of atoms/formula units per unit cell, M = molar mass, NA = Avogadro's number, a = edge length. This is the standard formula linking crystallography to a measurable bulk property, and a very common JEE numerical.

Distinguishing Schottky vs Frenkel by density: Schottky defects (missing ion pairs) measurably DECREASE the crystal's density since mass is lost without volume changing; Frenkel defects (ion just moved to an interstitial site) cause NO change in density since no mass leaves the crystal — this is the key experimental distinguishing test.

Worked problem: A metal crystallises in FCC structure with edge length 400 pm and density 8.95 g/cm³. Find its molar mass. Approach: Z=4 for FCC. ρ = ZM/(NA·a³) → M = ρ·NA·a³/Z = (8.95 × 6.022×10²³ × (4×10⁻⁸)³)/4 = (8.95 × 6.022×10²³ × 6.4×10⁻²³)/4 ≈ 86.4 g/mol (close to Rb, illustrating the calculation method even if the exact element varies by rounding).

2 Revise ~2 min before the exam

📐 Formula Sheet

Packing efficiency: simple cubic 52%, BCC 68%, FCC/CCP and HCP 74%
Atoms per unit cell: simple cubic 1, BCC 2, FCC 4
Coordination number: simple cubic 6, BCC 8, FCC 12
Edge–radius relations: simple cubic a = 2r; BCC √3a = 4r; FCC √2a = 4r
Density: ρ = (Z·M)/(a³·N_A), with a in cm
Voids: tetrahedral = 2 × (atoms); octahedral = 1 × (atoms) in close packing
Defects: Schottky lowers density (missing pairs); Frenkel keeps density (ion displaced to an interstitial site)

3 Practice apply it

✍️ Worked Examples

Example 1 — Density of a unit cell
Q: An element (M = 56 g/mol) forms a BCC lattice with edge 2.9 × 10⁻⁸ cm. Find its density.
Step 1 — For BCC, Z = 2.
Step 2 — Apply ρ = ZM/(a³N_A): a³ = (2.9 × 10⁻⁸)³ ≈ 2.44 × 10⁻²³ cm³.
Step 3 — Compute: ρ = (2 × 56)/(2.44 × 10⁻²³ × 6.022 × 10²³) = 112/14.69 ≈ 7.6 g/cm³.
Answer: ≈ 7.6 g/cm³ (close to iron). Trap: the edge must be in cm so that density comes out in g/cm³.

Example 2 — Atoms in an FCC cell
Q: How many atoms belong to one FCC unit cell?
Step 1 — Corner atoms: 8 corners × ⅛ each = 1.
Step 2 — Face atoms: 6 faces × ½ each = 3.
Step 3 — Total: 1 + 3 = 4.
Answer: 4 atoms per FCC unit cell. Note: this is why FCC is also called cubic close packing, the densest cubic arrangement.

Example 3 — Radius from edge length
Q: A metal crystallises FCC with edge length 4.0 Å. Find its atomic radius.
Step 1 — For FCC, atoms touch along the face diagonal: √2·a = 4r.
Step 2 — Rearrange: r = √2·a/4 = (1.414 × 4.0)/4.
Step 3 — Compute: r ≈ 1.414 Å.
Answer: ≈ 1.41 Å. Note: in BCC the atoms touch along the body diagonal instead, giving √3·a = 4r.

Practice Solid State Quiz — 100% Free →