Question

If the unit cell of a mineral has cubic closed packing (CCP) array of oxygen atoms with $m$ fraction of octahedral holes occupied by aluminium ions and $n$ fraction of tetrahedral holes occupied by magnesium ions, $m$ and $n$, respectively, are

• A. $\frac{1}{2},\frac{1}{8}$
• B. $1,\frac{1}{4}$
• C. $\frac{1}{2},\frac{1}{2}$
• D. $\frac{1}{4},\frac{1}{8}$

Answer 1

The correct option is A $\frac{1}{2},\frac{1}{8}$

In ccp, $O^{2–}$ ions are 4.
Hence total negative charge $=–8$
Let $A{l}^{3+}$ ions be $x$, and $M{g}^{2+}$ ions be $y$.
Total positive charge $=3x+2y$
$\Rightarrow 3x+2y=8$
This relation is satisfied only by $x=2$ and $y=1$
Hence number of $A{l}^{3+}=2$.
and number of $M{g}^{2+}=1$.
$\Rightarrow n=$ fraction of octahedral holes occupied by $A{l}^{3+}$
$\frac{2}{4}=\frac{1}{2}$
and $m=$ fraction of tetrahedral holes occupied by $M{g}^{2+}$
$=\frac{1}{8}$