Solid State

Concept overview

Solid state chemistry describes how atoms, ions or molecules pack into crystalline arrangements. The smallest repeating unit is the unit cell, and all bulk properties — density, packing efficiency, coordination number — follow from its geometry.

The three cubic unit cells you need are: simple cubic (1 atom per cell, 52% packing), body-centred cubic or BCC (2 atoms per cell, 68% packing), and face-centred cubic or FCC / cubic close packing (4 atoms per cell, 74% packing). Hexagonal close packing (HCP) matches FCC at 74% and differs only in stacking sequence — ABAB versus ABCABC. These four constants and their relationships to edge length and atomic radius are the single most tested block of formulas in this chapter.

Density of a unit cell is d = (Z × M) / (a³ × N_A), where Z is atoms per cell, M is molar mass, a is edge length in the same length units as d, and N_A is Avogadro's number. Rearranging this to find atomic mass, edge length or packing type is the workhorse numerical of the chapter.

Ionic solids extend the framework to lattices of cations and anions. Radius ratios r₊/r₋ predict coordination geometry: 0.155–0.225 gives triangular, 0.225–0.414 tetrahedral, 0.414–0.732 octahedral, and above 0.732 cubic. NaCl adopts an FCC lattice of Cl⁻ with Na⁺ in all octahedral holes; CsCl adopts a simple cubic arrangement. ZnS, CaF₂ and their variants round out the classic ionic structures.

Point defects (Schottky, Frenkel, F-centres) and their consequences for density and conductivity complete the chapter, and along with n-type / p-type semiconductor concepts these appear as reliable JEE Main questions.

Key formulas & concepts

• Simple cubic: Z = 1, r = a/2, packing 52%
• BCC: Z = 2, r = a√3/4, packing 68%
• FCC (cubic close packing): Z = 4, r = a√2/4, packing 74%
• Density of unit cell: d = ZM / (a³ N_A)
• Radius ratio ranges: 0.225–0.414 tetrahedral; 0.414–0.732 octahedral
• Tetrahedral voids per FCC: 8 per unit cell (2 per atom)
• Octahedral voids per FCC: 4 per unit cell (1 per atom)

Common mistakes to avoid

• Using r = a/2 for FCC — the correct relation is r = a√2/4 because FCC atoms touch along the face diagonal.
• Forgetting to convert edge length from pm to cm when applying the density formula.
• Confusing Schottky (missing cation-anion pair, decreases density) with Frenkel (cation dislocation, doesn't change density) defects.
• Treating HCP and FCC packing efficiencies as different — both are 74%; only the stacking sequence differs.

JEE Main relevance

JEE Main drops 1–2 solid-state questions every paper: usually one density/packing calculation and one defect or ionic-lattice type-identification problem. These are formula-driven and repeat almost verbatim across years.

JEE Advanced relevance

Advanced solid-state problems combine the geometry of voids with stoichiometry — for instance, in a MX-type solid where X⁻ forms FCC and M⁺ occupies half the tetrahedral voids, what is the M:X ratio? These problems test whether you can convert 'fraction of voids occupied' into a formula unit ratio.

Previous-year questions (PYQ)

Solid-state PYQs favour density formula and ionic lattice-identification. Drill both in the JEETutorAI PYQ bank filtered to this chapter — the calculations are all similar with different numbers.