Question

If unit cell of a mineral has cubic closed packed array of oxygen atoms with m fraction of octahedral holes occupied by aluminium ion 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

$\frac{1}{2},\frac{1}{8}$

The number of oxygen atoms per unit cell in CCP = $4\left(O^{2-}\right)$

The number of octahedral voids per unit cell = $4\left(A{l}^{3+}\right)$
The number of tetrahedral voids per unit cell = $8\left(M{g}^{2+}\right)$
Overall magnitude of negative charge due to oxygen atoms = 8
Overall, the unit cell is neutral, hence:
$4m\times \left(3\right)+8n\times \left(2\right)+4\times (-2)=0$
$3m+4n=2$

In the above equation, substitute the values of the given options.

$\left(A\right)\frac{3}{2}+\frac{4}{8}=2isright$. The others don't work out.