Playbook
Solid State
130 q - 3.04/paper - 5% HARD. ρ = zM/(a³N_A) solved for a different unknown each time; packing efficiency holds the HARD.
- Questions in the bank
- 130
- q/paper (2024–25 papers)
- 3.04
- Tagged HARD
- 5%
- Subtopics
- 5
Strand: Calculate
When you’ll see it
A unit cell — simple cubic, bcc or fcc — with a density, an edge length, a radius, or a count of atoms, voids or defects.
How this chapter is tested
130 q at 3.04 a paper, 5% HARD. The density page is the largest (42 q, 7%): every question is ρ = zM/(a³N_A) solved for a different unknown — density, molar mass, edge length, or z, which then names the cell (1 sc, 2 bcc, 4 fcc).
The radius page (30 q, never HARD) links a and r: r = a/2 for simple cubic, a√3/4 for bcc, a√2/4 for fcc. Packing Efficiency and Voids (27 q, 15%) holds most of the HARD — 52%, 68% and 74%, and the counts of octahedral (n) and tetrahedral (2n) voids. Types of solids and defects (31 q) are recall.
The sub-skills
The distinct skills inside the chapter, in the order to learn them.
The density equation
ρ = zM/(a³N_A). Keep a in cm (1 pm = 10⁻¹⁰ cm) so a³ comes out in cm³.
Radius from edge
sc: r = a/2. bcc: r = √3a/4. fcc: r = √2a/4 = a/(2√2).
Packing and voids
sc 52.4%, bcc 68%, fcc/hcp 74%. For n atoms in close packing: n octahedral, 2n tetrahedral voids.
Defects and magnetism
Schottky lowers density, Frenkel does not; ferromagnetic, antiferromagnetic and ferrimagnetic by domain alignment.
Traps to expect
Distractor shapes this chapter reuses. The Traps page covers the patterns that cut across chapters.
Picometres left unconverted
An edge in pm must become cm before cubing: 400 pm = 4 × 10⁻⁸ cm. A slip of one power of ten in a moves the density a thousandfold, and the options are built around that slip.
Using z for the wrong cell
bcc has 2 atoms per cell and fcc 4. Swapping them halves or doubles the answer.
Learn it before you drill it
This chapter has full teaching notes — foundations, worked examples, self-checks and a per-subtopic mastery checkpoint. Read the notes once, then drill subtopic by subtopic below.
Solid State notesDrill every solid state question
130 questions from the bank, scoped to 5 bundled subtopics.
Drill one subtopic at a time
The 5 subtopics this playbook covers, in catalog order.
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