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UPSC Civil Services (Mains)

Chemistry optional

  • 2 papers
  • 250 marks each
  • 3 h per paper
  • 5 of 8 questions, Q1 and Q5 compulsory

Paper I covers physical and inorganic chemistry.

UPSC Civil Services (Mains), Chemistry optional · 2018 · Paper I

Q2(d)(i). Derivation of Bragg's equation

  • 5 marks
  • Answered
Question

Derive Bragg's equation.

Answer in brief

nλ=2dθ: rays reflected from successive lattice planes reinforce only when their path difference 2dθ is a whole number of wavelengths.

Key points

  • A crystal is a stack of parallel lattice planes a distance d apart. X-rays of wavelength λ strike them at the glancing angle θ, and each plane reflects a small part of the beam (angle of reflection = angle of incidence).
  • The ray reflected at B in the second plane travels farther than the ray reflected at O in the first. Draw OA and OC perpendicular to the lower ray; the extra path is AB + BC.
  • In right-angled triangle OAB, OB =d and the angle at O is θ, so AB =dθ. In the same way BC =dθ: path difference =2dθ
  • The reflected rays are in phase (constructive interference) only when the path difference is a whole number of wavelengths: 4pt] nλ=2dθ n=1,2,3,… (order of reflection)

The full model answer

Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.

  1. A crystal is a stack of parallel lattice planes a distance d apart. X-rays of wavelength λ strike them at the glancing angle θ, and each plane reflects a small part of the beam (angle of reflection = angle of incidence).
  2. The ray reflected at B in the second plane travels farther than the ray reflected at O in the first. Draw OA and OC perpendicular to the lower ray; the extra path is AB + BC.
  3. In right-angled triangle OAB, OB =d and the angle at O is θ, so AB =dθ. In the same way BC =dθ: path difference =2dθ
  4. The reflected rays are in phase (constructive interference) only when the path difference is a whole number of wavelengths: 4pt] nλ=2dθ n=1,2,3,… (order of reflection)
  5. At other angles the rays from the many planes cancel, so reflections appear only at sharp angles. θ≤1 needs λ≤2d, which is why X-rays (about 100 pm) are used.

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Model answer to Q2(d)(i), 2018 Paper I: solution page 14
Solution page 14 of 55
Read the whole 2018 solution2018 question paper

All parts of Question 2