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UPSC Combined Geo-Scientist

Chemist

  • 3 descriptive papers
  • 200 marks each
  • 3 h per paper

Mains Paper II covers physical chemistry.

UPSC Combined Geo-Scientist, Mains · 2021 · Mains Paper II

Q1(c). Formula from corner and face-centre positions

Question

A compound formed by elements X and Y crystallizes in the cubic structure. X atoms are situated at the corners and Y atoms are at the centre of faces. What is the formula of the compound?

Answer in brief

X per cell = 1, Y per cell = 3 ⇒ formula XY₃.

Key points

  • A corner atom is shared by 8 unit cells: X per cell = 8 × 1/8 = 1.
  • A face-centre atom is shared by 2 unit cells: Y per cell = 6 × 1/2 = 3.
  • Ratio X : Y = 1 : 3 ⇒ formula XY₃.
  • Example: ordered Cu₃Au (Au at the corners, Cu at the face centres; the L1₂ structure).
  • Check: 1 + 3 = 4 atoms per cell; corners and face centres hold different atoms, so the Bravais lattice is primitive cubic (4-atom basis).

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.

Model answer to Q1(c), 2021 Mains Paper II: solution pages 3 and 4
Solution pages 3 and 4 of 36
Read the whole 2021 solution2021 question paper

Topic notes: crystal systems, Bragg's law, X-ray diffraction and radius ratio, with every Civil Services, IFoS and Geo-Scientist PYQ →

Coversunit cellnumber of atoms per unit cellface-centred cubicformula of compoundCu3Au

All parts of Question 1