The Solid State explains how the particles in a solid are arranged, covering crystalline versus amorphous solids, the four crystal types, unit cells and the seven crystal systems, packing efficiency, density of a unit cell, voids and ionic structures, and point defects. It is a high-scoring, formula-driven chapter that opens Class 12 Chemistry. Mastering atoms per unit cell, packing, the density formula and defects reliably earns easy marks in NEET.
Table of Contents
- Key Concepts
- Weightage in Board & Entrance Exams
- Important Definitions
- Solved Examples
- Important Questions for Board Exams
- Quick Revision Points
Key Concepts
1. Crystalline vs Amorphous Solids
A solid has a fixed shape and volume because its particles are packed closely and can only vibrate about fixed positions. But not all solids are built the same way. Common salt and diamond are neatly ordered; glass and rubber are not. That difference splits every solid into two families: crystalline and amorphous.
In a crystalline solid the particles are arranged in a perfectly repeating, long-range order. In an amorphous solid (like glass, rubber or plastic) the order lasts only over a short range, so it behaves almost like a very slow-flowing liquid. This one idea decides how each solid melts, breaks and bends.
| Property | Crystalline solid | Amorphous solid |
|---|---|---|
| Arrangement | Long-range order (regular) | Short-range order (irregular) |
| Melting point | Sharp, definite | Melts over a range |
| Nature | True solid | Pseudo solid / supercooled liquid |
| Heat of fusion | Definite value | Not definite |
| Cutting | Clean cleavage, flat faces | Irregular surfaces |
| Anisotropy | Anisotropic | Isotropic |
| Examples | NaCl, diamond, quartz, metals | Glass, rubber, plastics |
Anisotropy means a property (like refractive index or electrical conductivity) has different values when measured along different directions. Crystalline solids are anisotropic because their ordered arrangement looks different along different directions; amorphous solids are isotropic (same in all directions).
2. The Four Types of Crystalline Solids
Crystalline solids are further classified by the particles at the lattice points and the force holding them. There are four types, and the exam loves asking you to match a substance to its type and predict its melting point and conductivity.
| Type | Particles | Binding force | Properties | Examples |
|---|---|---|---|---|
| Ionic | Cations & anions | Electrostatic (ionic) | Hard, brittle, high m.p.; conduct only when molten or dissolved | NaCl, MgO, ZnS, CaF₂ |
| Molecular | Molecules | Dispersion / dipole / H-bond | Soft, low m.p., poor conductors (insulators) | Ice, dry ice (CO₂), I₂, Ar |
| Covalent / network | Atoms | Covalent bonds | Very hard, very high m.p., insulators (except graphite) | Diamond, SiO₂, SiC |
| Metallic | Positive kernels in a sea of electrons | Metallic bond | Malleable, ductile, lustrous, good conductors | Fe, Cu, Ag, Au |
Molecular solids split further into non-polar (H₂, CO₂, held by weak dispersion forces), polar (HCl, SO₂, held by dipole-dipole forces) and hydrogen-bonded (ice, held by hydrogen bonds). Graphite is the famous exception: it is a covalent solid, yet it is soft and conducts electricity because of its layered sheets and delocalised electrons.
3. Crystal Lattice, Unit Cell and the 7 Crystal Systems
A crystal lattice (space lattice) is a three-dimensional array of points, each showing the position of a particle (atom, ion or molecule). The smallest repeating portion that, on stacking in all three directions, builds the whole lattice is the unit cell.
A unit cell is described by three edge lengths (a, b, c) and three angles (α, β, γ). Different combinations give exactly seven crystal systems and, once you allow centring, 14 Bravais lattices.
| Crystal system | Edge lengths | Angles | Bravais lattices | Example |
|---|---|---|---|---|
| Cubic | a = b = c | α = β = γ = 90° | 3 (P, I, F) | NaCl, Cu |
| Tetragonal | a = b ≠ c | α = β = γ = 90° | 2 (P, I) | White tin, SnO₂ |
| Orthorhombic | a ≠ b ≠ c | α = β = γ = 90° | 4 (P, I, F, C) | Rhombic sulphur |
| Hexagonal | a = b ≠ c | α = β = 90°, γ = 120° | 1 (P) | Graphite, ZnO |
| Rhombohedral | a = b = c | α = β = γ ≠ 90° | 1 (P) | Calcite, HgS |
| Monoclinic | a ≠ b ≠ c | α = γ = 90°, β ≠ 90° | 2 (P, C) | Monoclinic sulphur |
| Triclinic | a ≠ b ≠ c | α ≠ β ≠ γ ≠ 90° | 1 (P) | CuSO₂·5H₂O |
The letters mean: P = primitive (points only at corners), I = body-centred (extra point at the centre), F = face-centred (extra points on all faces), C = end-centred (extra points on one pair of opposite faces). Adding these across the seven systems gives 3 + 2 + 4 + 1 + 1 + 2 + 1 = 14 Bravais lattices.
4. Number of Atoms per Unit Cell (Z)
An atom sitting at a shared position does not belong entirely to one cell. Sharing decides the contribution each atom makes, and adding those contributions gives Z, the number of atoms per unit cell.
- Corner atom: shared by 8 unit cells → contributes 1/8.
- 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 to 1 cell only → contributes 1.
Now count each cubic cell:
- Simple cubic (SCC): 8 corners × 1/8 = Z = 1.
- Body-centred cubic (BCC): 8 corners × 1/8 + 1 body centre = 1 + 1 = Z = 2.
- Face-centred cubic (FCC): 8 corners × 1/8 + 6 faces × 1/2 = 1 + 3 = Z = 4.
5. Close Packing, Packing Efficiency and Coordination Number
Atoms are treated as hard spheres that pack to fill space as tightly as possible. Packing efficiency is the percentage of the unit cell's volume actually occupied by spheres, and the coordination number is how many nearest neighbours touch a given sphere.
Two arrangements achieve the tightest packing (74%): hexagonal close packing (HCP), which follows an ABAB pattern, and cubic close packing (CCP / FCC), which follows an ABCABC pattern. Both leave only 26% empty space.
| Structure | Coordination number | Packing efficiency | Relation of a and r |
|---|---|---|---|
| Simple cubic | 6 | 52.4% | a = 2r |
| Body-centred cubic | 8 | 68% | √3 a = 4r |
| FCC / CCP | 12 | 74% | √2 a = 4r |
| HCP | 12 | 74% | – |
The edge-radius relations come from where the spheres touch: in SCC they touch along the edge, in BCC along the body diagonal (√3 a = 4r), and in FCC along the face diagonal (√2 a = 4r). These three relations are the key to almost every solid-state numerical.
6. Density of a Unit Cell
Because one unit cell contains Z atoms of known mass, we can find the density of the whole crystal from a single cell. This links the microscopic edge length to a measurable quantity, so it is a very common numerical.
The formula is:
d = (Z × M) / (a³ × N₀)
where Z = atoms per unit cell, M = molar mass (g mol⁻¹), a = edge length (cm), and N₀ = Avogadro's number (6.022 × 10²³). The term a³ is the volume of the cell, and Z × M / N₀ is the total mass of atoms inside it.
Worked idea: for an FCC metal (Z = 4) with M = 27 g mol⁻¹ and a = 4.05 × 10⁻⁸ cm, the density is d = (4 × 27) / ((4.05 × 10⁻⁸)³ × 6.022 × 10²³) ≈ 2.7 g cm⁻³ – which correctly identifies the metal as aluminium.
7. Tetrahedral and Octahedral Voids & the Radius Ratio
Even in the tightest packing, gaps remain between the spheres. These gaps, called voids (interstitial holes), are where smaller ions fit in ionic crystals. Their shape gives them their names.
A tetrahedral void is enclosed by 4 spheres; an octahedral void is enclosed by 6 spheres. In a close-packed lattice of N spheres there are exactly 2N tetrahedral voids and N octahedral voids. Tetrahedral voids are smaller than octahedral voids.
Which void a cation occupies is fixed by the radius ratio (r₊ / r₋, cation to anion). A cation must be just large enough to touch all the surrounding anions without rattling.
| Radius ratio (r₊/r₋) | Coordination number | Void / geometry | Example |
|---|---|---|---|
| 0.155 – 0.225 | 3 | Trigonal planar | B₂O₃ |
| 0.225 – 0.414 | 4 | Tetrahedral | ZnS |
| 0.414 – 0.732 | 6 | Octahedral | NaCl |
| 0.732 – 1.000 | 8 | Body-centred cubic | CsCl |
8. Structure of Ionic Solids (NaCl, CsCl, ZnS)
Three ionic structures are asked again and again. Learn the arrangement, the coordination and the number of formula units (Z) for each.
- Rock salt (NaCl) type: Cl⁻ ions form an FCC lattice and Na⁺ ions fill all the octahedral voids. Coordination is 6:6 and Z = 4. Radius ratio ≈ 0.52.
- Caesium chloride (CsCl) type: Cl⁻ ions at the corners of a cube and Cs⁺ in the body centre (or vice versa). Coordination is 8:8 and Z = 1. Radius ratio ≈ 0.93. On heating, CsCl converts to the NaCl type.
- Zinc blende (ZnS) type: S²⁻ ions form an FCC lattice and Zn²⁺ ions occupy alternate (half of the) tetrahedral voids. Coordination is 4:4 and Z = 4.
A quick memory hook: larger radius ratio means more neighbours can fit, so 4:4 (ZnS) → 6:6 (NaCl) → 8:8 (CsCl) follows the rising radius-ratio order.
9. Imperfections and Point Defects
Real crystals are never perfect. Deviations from the ordered arrangement are called defects. Point defects sit at or around a single lattice point, and they are the reason for colour, conductivity and non-stoichiometry in solids.
- Schottky defect: an equal number of cations and anions go missing. It appears in ionic solids with a high coordination number and ions of similar size (NaCl, KCl, CsCl, AgBr). It lowers the density of the crystal.
- Frenkel (dislocation) defect: a smaller ion (usually the cation) leaves its lattice site and squeezes into an interstitial hole. It appears in solids with a low coordination number and a large size difference between ions (ZnS, AgCl, AgBr, AgI). The density stays the same.
Metal excess defect (F-centre): when an anion is missing, its place is taken by an electron to keep the crystal neutral. This trapped electron is called an F-centre (from the German Farbenzentre, colour centre). It absorbs visible light and gives the crystal colour – this is why NaCl heated in sodium vapour turns yellow and LiCl turns pink. AgBr can show both Schottky and Frenkel defects.
10. Electrical Properties: Conductors, Insulators and Semiconductors
Solids span an enormous range of conductivity. The band theory explains it: in conductors the valence and conduction bands overlap, in insulators a large gap separates them, and in semiconductors the gap is small enough that some electrons cross it on heating.
A pure semiconductor like silicon or germanium is an intrinsic semiconductor. Its conductivity is boosted by doping – adding a tiny amount of another element – to give extrinsic semiconductors:
- n-type: silicon (group 14) doped with a group-15 element (P, As). The extra fifth electron carries the current, so the majority carriers are negative electrons.
- p-type: silicon doped with a group-13 element (B, Al, Ga). A missing electron creates a positive hole, and these holes carry the current.
Joining an n-type and a p-type layer makes a p-n junction, the basis of diodes, transistors and solar cells.
11. Magnetic Properties
The magnetic behaviour of a solid comes from its unpaired electrons, each of which acts like a tiny magnet. How those tiny magnets line up defines four categories that CBSE and NEET both test.
| Type | Behaviour in a field | Alignment of magnetic moments | Example |
|---|---|---|---|
| Diamagnetic | Weakly repelled | All electrons paired | NaCl, H₂O, TiO₂ |
| Paramagnetic | Weakly attracted | Random; align only in the field | O₂, Cu²⁺, Fe³⁺ |
| Ferromagnetic | Strongly attracted; stays magnetised | All parallel, same direction | Fe, Co, Ni, CrO₂ |
| Antiferromagnetic | Net moment zero | Equal and opposite (cancel) | MnO |
| Ferrimagnetic | Weakly attracted | Opposite but unequal (partial cancel) | Fe₃O₄ (magnetite) |
A useful contrast: in a ferromagnet the little magnets all point the same way and reinforce; in an antiferromagnet they point in opposite directions and cancel completely; in a ferrimagnet they oppose but do not fully cancel, leaving a small net moment.
Weightage in Board & Entrance Exams
| Exam | Typical Weightage | Most-Tested Areas |
|---|---|---|
| CBSE Board (Class 12) | 4–5 marks | Density numerical, Z of unit cells, packing efficiency, defects |
| NEET | 1–2 questions | Number of atoms per cell, voids, NaCl/CsCl/ZnS structures, semiconductors |
| JEE Main | 1–2 questions | Edge-radius relations, density, radius ratio, packing efficiency |
The single highest-yield skill in this chapter is the density numerical d = ZM/(a³N₀); it can be turned around to find Z, M or a. After that come counting Z, comparing packing efficiency, and identifying Schottky vs Frenkel defects.
Important Definitions
- Crystalline solid: a solid with long-range, regularly repeating order and a sharp melting point.
- Amorphous solid: a solid with only short-range order that softens over a temperature range (a pseudo solid).
- Unit cell: the smallest repeating unit of a crystal lattice that reproduces the whole crystal on repetition.
- Bravais lattices: the 14 distinct three-dimensional lattice arrangements possible across the 7 crystal systems.
- Coordination number: the number of nearest neighbours touching a given atom or ion.
- Packing efficiency: the percentage of the total volume of a unit cell occupied by the constituent particles.
- Void (interstitial site): the empty space left between packed spheres; tetrahedral (4 spheres) or octahedral (6 spheres).
- Schottky defect: a point defect in which equal numbers of cations and anions are missing, lowering the density.
- Frenkel defect: a point defect in which an ion moves from its lattice site to an interstitial site; density is unchanged.
- F-centre: an anion vacancy occupied by an electron, giving the crystal colour.
Solved Examples
Example 1
Q. An element has a body-centred cubic structure with edge length 288 pm and density 7.2 g cm⁻³. How many atoms are present in 208 g of it?
A. For BCC, Z = 2. Mass of one cell = Z × M / N₀; but first use d = ZM/(a³N₀) to get M. a = 288 pm = 2.88 × 10⁻⁸ cm, a³ = 2.39 × 10⁻²³ cm³. M = d × a³ × N₀ / Z = (7.2 × 2.39 × 10⁻²³ × 6.022 × 10²³) / 2 ≈ 52 g mol⁻¹. So 208 g = 4 mol, containing 4 × 6.022 × 10²³ = 2.41 × 10²⁴ atoms.
Example 2
Q. In an FCC arrangement of atoms, how many atoms belong to one unit cell?
A. 8 corners × 1/8 + 6 faces × 1/2 = 1 + 3 = 4 atoms.
Example 3
Q. A metal crystallises in a face-centred cubic lattice with edge length a. If the atomic radius is r, relate a and r, and give the packing efficiency.
A. In FCC the spheres touch along the face diagonal, so √2 a = 4r, giving r = a/(2√2). The packing efficiency is 74%.
Example 4
Q. In NaCl, chloride ions form an FCC lattice. Which voids do sodium ions occupy, and what is the coordination number?
A. Na⁺ ions fill all the octahedral voids, giving a 6:6 coordination.
Example 5
Q. Silicon is doped with phosphorus. What type of semiconductor is formed and why?
A. Phosphorus (group 15) has one extra valence electron beyond the four bonds it makes with silicon. This free electron carries current, so an n-type semiconductor is formed.
Example 6
Q. Why does a Schottky defect lower the density of a crystal while a Frenkel defect does not?
A. In a Schottky defect ions are actually removed from the crystal, so the same volume now has less mass and the density falls. In a Frenkel defect the ion is only relocated to an interstitial site within the same crystal, so total mass and volume are unchanged and the density stays the same.
Important Questions for Board Exams
1-Mark Questions (VSA)
- Why are amorphous solids called pseudo solids or supercooled liquids?
- What is the coordination number of an atom in a body-centred cubic structure?
- How many octahedral voids are present in a close-packed lattice of N spheres?
- What is an F-centre?
2–3-Mark Questions (SA)
- Distinguish between Schottky and Frenkel defects with one example each.
- Calculate the number of atoms per unit cell in simple cubic, BCC and FCC structures.
- Explain how doping produces n-type and p-type semiconductors.
- Differentiate between crystalline and amorphous solids on any three properties.
5-Mark Questions (LA)
- Derive the packing efficiency of a face-centred cubic unit cell (show it is 74%).
- An element (M = 56, FCC, a = 3.86 × 10⁻⁸ cm) – calculate its density using d = ZM/(a³N₀).
- Describe the NaCl, CsCl and ZnS structures with their coordination numbers and radius-ratio ranges.
Quick Revision Points
- Crystalline = long-range order, sharp m.p., anisotropic; amorphous = short-range order, isotropic, pseudo solid.
- Four crystalline types: ionic, molecular, covalent/network, metallic. Graphite is the soft, conducting covalent exception.
- 7 crystal systems give 14 Bravais lattices; cubic has 3 (P, I, F).
- Atoms per cell: SCC = 1, BCC = 2, FCC = 4. Contributions: corner 1/8, face 1/2, edge 1/4, body 1.
- Packing efficiency: SCC 52.4%, BCC 68%, FCC & HCP 74%. Coordination: 6, 8, 12, 12.
- Edge-radius: SCC a = 2r; BCC √3 a = 4r; FCC √2 a = 4r.
- Density d = ZM/(a³N₀) – the top scoring numerical.
- N spheres → 2N tetrahedral + N octahedral voids. Radius ratio decides the void: 0.225 (tetra), 0.414 (octa), 0.732 (cubic).
- NaCl 6:6 (Z=4), CsCl 8:8 (Z=1), ZnS 4:4 (Z=4).
- Schottky lowers density (NaCl); Frenkel keeps density (ZnS, AgCl); F-centre gives colour.
- n-type = group-15 doping (extra electron); p-type = group-13 doping (hole).
- Magnetism: dia (paired), para (random unpaired), ferro (parallel), antiferro (cancel), ferri (unequal opposite, e.g. Fe₃O₄).
Class 12 Chemistry · Chapter 1 – swipe through all 10 cards to understand the whole chapter.
Crystalline vs Amorphous
Solids differ by how neatly their particles are ordered.
Amorphous (glass, rubber) = short-range order, isotropic, called pseudo-solids / supercooled liquids.
- Crystalline: definite shape, sharp melting point, true solids
- Amorphous: melt over a range, no overall pattern, isotropic
- Anisotropy + sharp m.p. are the signatures of a crystal
The Four Crystalline Solids
Sort crystals by the force that binds their particles.
Exception: graphite is covalent but soft and a good conductor (layered, delocalised electrons).
- Molecular: van der Waals / H-bonds → soft, low m.p., insulators
- Ionic: electrostatic → hard, brittle, conduct only molten/aqueous
- Metallic: electron sea → malleable conductors; Covalent: very hard, very high m.p.
Lattice, Unit Cell & Crystal Systems
The smallest repeating box that rebuilds the whole crystal is the unit cell.
Cell defined by edges a, b, c and angles α, β, γ. Cubic = most symmetric, triclinic = least.
- Cubic: a = b = c, α = β = γ = 90° (P, BCC, FCC → 3 lattices)
- Hexagonal: a = b ≠ c, α = β = 90°, γ = 120°
- Centring types: Primitive (P), Body (I), Face (F), End (C)
Atoms per Unit Cell (Z)
Count only each atom’s fair share of the cell.
Z: simple cubic = 1, BCC = 2, FCC = 4, HCP = 6.
- Simple cubic: 8 × ⅛ = 1
- BCC: 8 × ⅛ + 1 = 2
- FCC: 8 × ⅛ + 6 × ½ = 4
Packing Efficiency & Coordination
Closer packing means higher coordination number and more filled volume.
FCC and HCP are the densest possible sphere packings.
- Edge–radius: SC a = 2r, BCC √3·a = 4r, FCC √2·a = 4r
- CN = number of nearest neighbours touching an atom
- √2 → FCC (face diagonal), √3 → BCC (body diagonal)
Density of a Unit Cell
One tiny cell predicts the density of the whole crystal.
a must be in cm (1 pm = 10⁻10 cm, 1 Å = 10⁻8 cm); ρ comes out in g cm⁻3.
- Z = atoms per cell, M = molar mass (g mol⁻1), N_A = 6.022 × 1023
- Rearrange: Z = (ρ · a3 · N_A) / M to find the cell type
- Cube the whole edge length, including its power of ten
Voids & Radius Ratio
Small ions fill the gaps left in the close-packed array of bigger ions.
Radius ratio r₊/r₋ decides the void: 0.225–0.414 tetrahedral (CN 4), 0.414–0.732 octahedral (CN 6), 0.732–1.0 cubic (CN 8).
- For N close-packed atoms: N octahedral, 2N tetrahedral voids
- Tetrahedral void → CN 4; octahedral void → CN 6
- Always compute the ratio as cation over anion (r₊/r₋)
Key Ionic Structures
Each classic structure is the framework plus which voids the cations fill.
Antifluorite (Na2O) is the reverse of fluorite → CN 4:8.
- Rock salt NaCl: Cl⁻ FCC, Na⁺ in ALL octahedral voids, Z = 4
- Zinc blende ZnS: S2⁻ FCC, Zn2⁺ in HALF the tetrahedral voids
- Fluorite CaF2: Ca2⁺ FCC, F⁻ in ALL tetrahedral voids
Point Defects
Real crystals carry missing or misplaced ions.
Schottky: NaCl, KCl, CsCl (similar sizes). Frenkel: ZnS, AgCl, AgBr (large size difference). F-centre → colour.
- Schottky: a cation + anion pair both missing → density falls
- Frenkel: a small cation shifts to an interstitial site → density same
- Metal-excess F-centre: anion vacancy holds an electron → NaCl turns yellow
Semiconductors & Magnetism
Doping and electron spins set a solid’s electrical and magnetic behaviour.
Conductivity of a semiconductor rises with temperature (unlike metals).
- n-type: P/As add extra electrons; p-type: B/Al create holes
- Paramagnetic = unpaired e⁻ (O2, Cu2⁺); Diamagnetic = all paired
- Ferro (Fe, Co, Ni) · Ferrimagnetic Fe3O4 · Antiferromagnetic MnO
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Frequently Asked Questions
Crystalline solids have long-range order, a sharp melting point and are anisotropic (properties differ with direction). Amorphous solids like glass and rubber have only short-range order, melt over a range, are isotropic, and are called pseudo-solids or supercooled liquids.
Use density = (Z times M) divided by (a cubed times N_A), where Z is the number of atoms per cell (1 for simple cubic, 2 for BCC, 4 for FCC), M is molar mass, a is the edge length in cm, and N_A is the Avogadro number 6.022 times 10 to the 23. The edge length must be converted to cm, since 1 pm is 10 to the minus 10 cm.
A corner atom counts as one-eighth, a face atom as one-half and a body-centre atom as one. So simple cubic has 1 atom, body-centred cubic (BCC) has 2, and face-centred cubic (FCC) has 4 atoms per unit cell.
In a Schottky defect a cation and an anion are both missing, so the density of the solid decreases (seen in NaCl, KCl, CsCl with similar ion sizes). In a Frenkel defect a smaller cation moves to an interstitial site, so the density stays unchanged (seen in ZnS, AgCl, AgBr with a large size difference).
Yes, it is part of the NEET Chemistry syllabus and usually contributes one to two questions, often direct and scoring. Focus on packing efficiency and coordination number, the unit-cell density formula, voids and radius ratio, ionic structures like NaCl and ZnS, and the Schottky versus Frenkel defects.