UPSC Civil Services (Mains), Chemistry optional · 2022 · Paper I

Q2(c). Simple cubic cell from the (100) reflection; room for an interstitial atom

20 marks
Topic: Solid state
Answered

Question

In a certain material of simple cubic structure, (100) diffraction is obtained at θ = 14.88° with radiation of λ = 1.541 Å. Can this material accommodate an atom of 1.08 Å radius interstitially in void space without lattice distortion? (sin 14.88° = 0.257)

Answer in brief

Yes. a = d₁₀₀ = 2.998 Å, so R = 1.499 Å, and the cubic void at the body centre has r = (√3 − 1)R = 1.097 Å, larger than 1.08 Å, so the atom fits without distortion.

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

CoversBragg equationsimple cubic latticeinterplanar spacingcubic voidradius ratio 0.732interstitial site

All parts of Question 2

2(a) Adiabatic expansion of tyre air against a constant external pressure10 marks
2(b) Particle in a box: probability in the first 1/a of the width20 marks
2(c) Simple cubic cell from the (100) reflection; room for an interstitial atom20 marks