Question

If the unit cell of a mineral has cubic packed (c.c.p.) 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 $\frac{1}{2},\frac{1}{8}$

A ccp structure has $4$ atoms/ions per unit cell, $4$ octahedral voids and $8$ tetrahedral voids.

Thus, in the unit cell of the mineral, there are $4$ oxide ions, $4m$ $A{l}^{3+}$ ions and $8n$ $M{g}^{2+}$ ions respectively.

For charge balance, $4(-2)+4m(3+)+8n(2+)=0$

The above equation will be balanced when $m=\frac{1}{2}$ and $n=\frac{1}{8}$

Hence, $m$ and $n$, respectively, are $\frac{1}{2},\frac{1}{8}$.