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Crystal Lattice and Unit Cell

There are thr...

Question

There are three ionic compounds, first compound has fcc lattice of anions and cations are present in all tetrahedral voids, second compound has fcc lattice of anions and cations are present in all octahedral voids and the third compound has simple cubical lattice in which cubical void is occupied by cation, then the order of packing efficiency of these will be :

I > I I > I I I

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I I > I > I I I

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I I I > I I > I

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I I I > I > I I

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Solution

The correct option is B $I > I I > I I I$
Since packing efficiency of various crystal systems are

Crystal System Packing Efficency
FCC $74$ %
Simple Cubic $52.4$ %
Now, number of tetrahedral voids $= 2 \times$ Number of octahedral voids.
Since the crystal system (III) is a simple cubic lattice, it will have the least packing efficiency.
Now, both crystal systems $I$ and $I I$ are FCC but the number of voids is filled in crystal system I than II because of a greater number of tetrahedral voids than octahedral voids. So, crystal system I have the most packing efficiency.

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In which of the following structures coordination number for cations and anions in the packed structure will be same ?

(a) $C l^{-}$ ions form fcc lattice and $N a^{+}$ ions occupy all octahedral voids of the unit cell

(b) $C a^{2 +}$ ions form fcc lattice and $F^{-}$ ions occupy all the eight tetrahedral voids of the unit cell

(d) $S^{2 -}$ ions form fcc lattice and $Z n^{2 +}$ ions go into alternate tetrahedral voids of the unit cell

0.2

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0.95

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4

C

A

75 %

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