Solid State (Class 12): Unit Cells, Packing and Density Numericals
A chapter where a handful of formulas cover almost every question — provided the student can picture the cell.
| Detail | Information |
|---|---|
| Class | 12 |
| Branch | Physical Chemistry |
| Core ideas | Unit cell types, atoms per unit cell, packing efficiency, density, defects |
| Assumes | Mole concept, Avogadro constant |
| Why it scores well | Few formulas, predictable question types |
| Enquiries | 9212142427 |
Counting atoms in a unit cell
Everything in this chapter starts here, and it is a sharing problem rather than a chemistry one. An atom at a corner is shared by eight cells, so it contributes one-eighth. An atom on a face is shared by two, contributing one-half. An atom on an edge is shared by four. An atom at the body centre belongs entirely to that cell.
- Simple cubic: 8 corners × 1/8 = 1 atom per cell.
- Body-centred cubic: 8 × 1/8 + 1 = 2 atoms.
- Face-centred cubic: 8 × 1/8 + 6 × 1/2 = 4 atoms.
Those three numbers — 1, 2 and 4 — are worth knowing without derivation, but the student should be able to derive them, because that is what a question asking about a modified cell is testing.
The relationship between edge length and radius
Which atoms touch determines the geometry, and that is the whole trick. In simple cubic, atoms touch along the edge, so a = 2r. In body-centred cubic they touch along the body diagonal, giving √3a = 4r. In face-centred cubic they touch along the face diagonal, giving √2a = 4r. Students who memorise these three without knowing which diagonal is involved cannot recover them if they blank, and cannot handle a question phrased differently.
Packing efficiency
Packing efficiency is the fraction of the cell volume actually occupied by spheres: simple cubic 52.4%, body-centred cubic 68%, and face-centred cubic and hexagonal close packing both 74%. Questions usually ask for one of these to be calculated rather than quoted, and the calculation is always the same — volume of the atoms in the cell divided by the volume of the cell, using the edge-length relationship above to express one in terms of the other.
Defects, briefly but properly
Schottky defects remove a cation and an anion together, so density falls. Frenkel defects move an ion into an interstitial site, so density is unchanged. That single contrast — what happens to density — is the most reliably examined point in this section, and it is a comparison rather than two separate facts to remember.
How to practise
Draw the cell before attempting any numerical, every time, even when it feels unnecessary. Almost all errors in this chapter are counting errors that a sketch would have prevented. Then work in a fixed order: identify the cell type, get Z, write the edge-length relationship, convert units, substitute.
FAQs
Is Solid State a scoring chapter?
Yes, among the most scoring in Class 12 Chemistry. The question types are limited and the formulas few, so a student who practises the standard numericals can rely on it.
My child gets the method right but the answer wrong. Why?
Almost always unit conversion — picometres to centimetres before cubing. Doing the conversion as a separate written step, before substituting, fixes it.
Do the edge-length relationships need to be memorised?
They should be memorised and also understood, because a question about a non-standard arrangement requires deriving rather than recalling.
How much weight does this chapter carry?
It is a compact chapter that reliably appears. Check the current year’s weighting on cbse.gov.in rather than assuming last year’s pattern.
Do you teach Class 12 Chemistry one-to-one?
Yes — home tuition, Gurugram classroom coaching, or live online. Call 9212142427.
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