Solid State Short Notes for Class 12, IIT-JEE & NEET

Packing efficiency is the percentage of a unit cell's volume occupied by atoms. FCC (face-centred cubic) and HCP (hexagonal close-packed) arrangements both achieve 74% packing efficiency — the highest possible for equal spheres. BCC achieves 68% and simple cubic only 52.4%. Most metals prefer FCC or HCP for this reason.

Count each corner atom as 1/8, each face-centred atom as 1/2, each edge-centred atom as 1/4, and each body-centred atom as 1. Simple Cubic gives Z = 1, BCC gives Z = 2, and FCC gives Z = 4. This value of Z is then used directly in the density formula: ρ = ZM / (Nₐ × a³).

Schottky defect involves equal numbers of missing cations and anions (vacancies), which decreases density. Frenkel defect involves a cation leaving its lattice site to occupy an interstitial position — density stays the same. Schottky appears in solids with similar-sized ions (NaCl), while Frenkel appears where the cation is much smaller than the anion (AgCl, ZnS).

In FCC (face-centred cubic), each atom touches 12 nearest neighbours — coordination number is 12. In BCC (body-centred cubic), the body-centre atom touches all 8 corner atoms — coordination number is 8. In simple cubic, each atom touches 6 neighbours — coordination number is 6. Higher coordination number means more efficient packing.

Solid State is important for both. NEET typically tests 1–2 questions per paper, most often on crystal structure, types of solids, or defects. JEE Main also asks 1–2 questions, often on packing efficiency or density calculations. For CBSE boards, the chapter carries 3–5 marks and defects + crystal systems are the most common topics in the long-answer section.

F-centres (Farbe centres, German for "colour") are anionic vacancies where electrons are trapped to maintain electrical neutrality. These electrons absorb specific visible-light wavelengths and re-emit others, giving the crystal a characteristic colour. NaCl with F-centres appears yellow; KCl with F-centres appears violet. This is a direct consequence of metal excess defect.