If the unit cell of a mineral has cubic close packed (ccp) array of...

No. of oxygen atoms per unit cell in ccp $= 4 \left(O^{2 -}\right)<br /><br />No.$ of octahedral voids per unit cell= 4 \left(\text{A}{\text{l}^{3+}\right)

No. of Tetrahedral voids per unit cell = 8 \left(\text{M}{\text{g}^{3 +}\right)

Total negative charge due to oxygen atoms $= 8$

Net charge must be zero.

$\text{m4}\left(3\right)+ \text{2n}$\left(8\right)$+ 4 \left(-2\right)$ =0$<br /><br />3m + 4n = 2$

(A) $\dfrac{3}{2} + \dfrac{4}{8} =$2$is correct.<br /><br />(B) 3 \times1 + 4 \times \dfrac{1}{4} =$4 \ne 2$is incorrect.<br /><br />(C) 3 \times \dfrac{1}{2} +4 \times \dfrac{1}{2} =4 \ne 2$ is incorrect

(D) $3 \times \dfrac{1}{4} +4 \times \dfrac{1}{8} = \dfrac{3}{4} + \dfrac{2}{4} = \dfrac{5}{4} \ne2$ is incorrect.