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GATE 2022 CY – Question 34

Inorganic Chemistry · Solids: Crystal systems and lattices, Miller planes, crystal packing, crystal defects, Bragg’s law, ionic crystals, structure of AX, AX2, ABX3 type compounds, spinels, band theory, metals and semiconductors, Zeolites and their applications. · 1 mark · Numerical answer

The diffraction angle (degrees, one decimal place) for the (321) planes of a BCC metal with atomic radius 0.125 nm is ______. Reflection order is 1; X-ray wavelength is 0.0771 nm.

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Correct answer: 59.0 to 61.0

Explanation

For bcc, a=4r/√3=0.288675nm. Interplanar spacing d321=a/√(3²+2²+1²)=0.0771517nm. Bragg’s law gives sinθ=λ/(2d)≈0.499665, soθ≈29.98°. The measured diffraction/scattering angle is 2θ≈**60.0°**, matching the official 59–61 interval.