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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 · 2026 · Paper I

Q7(c)(ii). Bragg condition for constructive interference

  • 5 marks
  • Answered
Question

For Bragg X-ray diffraction studies of crystalline solid, what is the Bragg condition for constructive interference? Explain.

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 treated as a stack of parallel lattice planes a distance d apart. X-rays of wavelength λ meet the planes at the glancing angle θ, and each plane reflects a small part of the beam.
  • The ray reflected at B in the second plane travels farther than the ray reflected at O in the first. With OA and OC perpendicular to the lower ray, the extra path is AB + BC. In triangle OAB, OB =d and AB =dθ; in the same way…
  • 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)
  • At any other angle the rays from the many planes cancel, so reflections appear only at a few sharp angles. Since θ≤1, λ≤2d is needed, which is why X-rays (about 100 pm, close to interplanar spacings) are used. The measured θ…

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 treated as a stack of parallel lattice planes a distance d apart. X-rays of wavelength λ meet the planes at the glancing angle θ, and each plane reflects a small part of the beam.
  2. The ray reflected at B in the second plane travels farther than the ray reflected at O in the first. With OA and OC perpendicular to the lower ray, the extra path is AB + BC. In triangle OAB, OB =d and AB =dθ; in the same way BC =dθ: path difference =2dθ
  3. 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)
  4. At any other angle the rays from the many planes cancel, so reflections appear only at a few sharp angles. Since θ≤1, λ≤2d is needed, which is why X-rays (about 100 pm, close to interplanar spacings) are used. The measured θ gives d, and from d the cell edge (for a cubic cell d₁₁₁=a/√3).

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Model answer to Q7(c)(ii), 2026 Paper I: solution page 47
Solution page 47 of 55
Read the whole 2026 solution2026 question paper

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