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JEE Advanced 2019 Paper 1 · Chemistry · Solutions, Solid State and Surface Chemistry · medium

(s) about ionic and close-packed crystal structures.

One or more options correct

Select the correct statement(s) about ionic and close-packed crystal structures.
  1. A. In zinc blende (ZnS), Zn2+\mathrm{Zn^{2+}} occupies half of the tetrahedral voids of a ccp S2−\mathrm{S^{2-}} lattice and both ions have coordination number 4.
  2. B. In fluorite (CaF2\mathrm{CaF_2}), the coordination numbers of Ca2+\mathrm{Ca^{2+}} and F−\mathrm{F^-} are 8 and 4 respectively.
  3. C. The packing efficiency of hcp is smaller than that of ccp because the hcp layers repeat as ABAB.
  4. D. In a rock-salt type lattice, if the anions in the fcc array just touch along the face diagonal and the cation just fits the octahedral void, then r+/r−=2−1r_+/r_-=\sqrt2-1.
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Answer: A, B, D

(A) In zinc blende the sulphide ions form ccp, and zinc ions fill alternate (half) of the 8 tetrahedral voids per 4 anions, i.e. 4 of 8; each ion is 4-coordinate, so (A) is true. (B) In CaF2\mathrm{CaF_2}, calcium forms the fcc array and fluoride fills all tetrahedral voids; each Ca2+\mathrm{Ca^{2+}} touches 8 F−\mathrm{F^-} and each F−\mathrm{F^-} touches 4 Ca2+\mathrm{Ca^{2+}}, so (B) is true. (C) Both hcp and ccp are closest packings with the same packing efficiency, π/(32)=74%\pi/(3\sqrt2)=74\%; the stacking sequence does not change it, so (C) is false. (D) With anions touching along the face diagonal, a=22 r−a=2\sqrt2\,r_-; along the edge a=2(r++r−)a=2(r_++r_-). Equating, r+=(2−1)r−=0.414 r−r_+=(\sqrt2-1)r_-=0.414\,r_-, so (D) is true.
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