$word_{count}$: 200

The density formula d = $\frac{ZM}{N_Aa^3}$ is the most-tested equation in solid state. Common problem types: (1) Given a, M, structure type (SC/BCC/FCC) — find d. (2) Given d, M, a — find Z and hence structure type. (3) Given d and structure — find a or r. Steps: (a) Identify Z from structure. (b) Convert a to cm (pm x 10^-10). (c) Substitute carefully. Unit traps: edge length often given in pm but formula needs cm. Mass in g/mol. Check: d should be 2-20 g/$cm^3$ for most solids. Quick checks: if Z comes out as 1, 2, or 4 — it's SC, BCC, or FCC. Non-integer Z means calculation error. For ionic compounds: Z = number of formula units, M = formula mass. For NaCl: Z = 4, M = 58.5. Edge length for NaCl: a = 2($r_{Na+}$ + $r_{Cl-}$). For CsCl: body diagonal = 2($r_{Cs+}$ + $r_{Cl-}$).