GATE 2020 CY – Question 30

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

A cubic crystal has a powder X-ray (111) peak at 2θ = 33.60° using Cu Kα radiation of wavelength 1.54 Å. Find lattice parameter a in Å to 2 decimals.

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Correct answer: 4.60 to 4.64

Explanation

First use θ = 16.80°. Bragg’s law gives $d_{111}=1.54/[2\sin16.8^\circ]$. For a cubic lattice, $a=d_{111}\sqrt{1^2+1^2+1^2}=\sqrt3d_{111}=4.61$ Å. Confusing θ with the supplied 2θ would halve the angle incorrectly.

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