Question

If the unit cell of a mineral has cubic closed packed (ccp) array of oxygen atoms with ${}^{\prime }{m}^{\prime }$ fraction of octahedral holes occupied by aluminium ions and ${}^{\prime }{n}^{\prime }$ 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 array:
Number of oxygen atom $=4$

Number of octahedral holes $=4$

Number of tetrahedral holes $=8$

Number of $A{l}^{3+}$ ions $=4\times m$

Number of $M{g}^{2+}ions=8\times m$

Molecule of mineral will be neutral, hence

$4(-2)+4m(+3)+8n(+2)=0$

$12m+16n=8$

$3m+4n=2$

$\therefore m=\frac{1}{2}$ and $n=\frac{1}{8}$