Question

If the unit cell of a mineral has cubic close packed $(ccp)$ array of oxygen atoms with $m$ fraction of octahedral holes occupied by aluminium ions and $n $ fraction 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

Answer: (A)

$T.V.\quad O.V.\quad c.c.p.$
$Mg^{2+}\quad Al^{3+}\quad O^{2-}$
$8n \quad4m \quad4$
$∴ 8n × \left(+2\right) + 4m × \left(+3\right) + 4 × \left(-2\right) = 0$
On verifying option, we get
$n = \frac{1}{8}, m = \frac{1}{2}$