UPSC Civil Services (Mains), Chemistry optional · 2024 · Paper I
Q1(b)(ii). Unit cell and the cubic Bravais lattices
Question
Define 'unit cell'. Draw all the Bravais lattices for a cubic system.
Answer in brief
A unit cell is the smallest block of a crystal lattice which, repeated along its three edges, builds the whole lattice; the cubic system has three Bravais lattices: primitive, body-centred and face-centred.
Key points
- A unit cell is fixed by its three edges a, b, c and the three angles between them; for cubic a = b = c, α = β = γ = 90°.
- Primitive (P): points at the 8 corners, 8 × ⅛ = 1 point per cell, 6 nearest neighbours (Po).
- Body-centred (I): corners + cell centre, 2 points per cell, 8 nearest neighbours (Na, α-Fe, W).
- Face-centred (F): corners + 6 face centres, 1 + 6 × ½ = 4 points per cell, 12 nearest neighbours (Cu, Al, Ag).
- A cube centred on one pair of faces loses the threefold axes; it is a smaller primitive tetragonal cell, not a separate cubic lattice.
The full model answer
As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.
Coversunit cellBravais latticescubic systembody-centred cubicface-centred cubic
All parts of Question 1
- 1(a)(i) Most probable distance of the 1s electron5 marks
- 1(a)(ii) Lattice energies of NaBr and NaI above the calculated values5 marks
- 1(b)(i) Separation factor for ²³⁵UF₆ and ²³⁸UF₆ in one effusion stage5 marks
- 1(b)(ii) Unit cell and the cubic Bravais lattices5 marks
- 1(c) Normal boiling point of mercury10 marks
- 1(d)(i) Will CCl₂F₂ condense at 18 atm and 20 °C?5 marks
- 1(d)(ii) Overvoltage and its applications5 marks
- 1(e) Temperature at which the uncatalysed reaction matches catalase at 20 °C10 marks