$C a S$ exists in a cubic close packed arrangement of $S^{2 -}$ ions in which $C a^{2 +}$ ions occupy $1 / 2$ of the available tetrahedral holes. How many $C a^{2 +}$ and $S^{2 -}$ ions are contained in the unit cell?

1, 1

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2, 4

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4, 4

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4, 2

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Solution

The correct option is B $4, 4$
In CCP structure, $S^{2 -}$ ions are present at corner and face centre. Thus number of $S^{2 -}$ ions are= $8 \times \frac{1}{8}$ (corner) $+ 6 \times \frac{1}{2}$ (face centre)
$S^{2 -}$ ion= $1 + 3 = 4$ ions
as $2$ tetrahedral voids are present in $1$ body diagonal, there are $4$ body diagonal in a unit cell.
Thus total tetrahedral voids are $2 \times 4 = 8$ . As $C a^{2 +}$ are present in $\frac{1}{2}$ of tetrahedral voids. Thus number of $C a^{2 +}$ ions present= $\frac{8}{2} = 4$
$C a^{2 +} ⟶ 4$
$S^{2 -} ⟶ 4$

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CaS exists in a cubic close packed arrangement of S2− ions in which Ca2+ ions occupy 1/2 of the available tetrahedral holes. How many Ca2+ and S2− ions are contained in the unit cell?

$C a S$ exists in a cubic close packed arrangement of $S^{2 -}$ ions in which $C a^{2 +}$ ions occupy $1 / 2$ of the available tetrahedral holes. How many $C a^{2 +}$ and $S^{2 -}$ ions are contained in the unit cell?