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 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

Answer: (A)

No. of oxygen atoms per unit cell in ccp $=4\left(O^{2 -}\right)$
No. of octahedral voids per unit cell $=4\left(\text{A} \left(\text{l}\right)^{3 +}\right)$
No. of Tetrahedral voids per unit cell $=8\left( Mg ^{2+}\right)$
Total negative charge due to oxygen atoms $=8$
Net charge must be zero.
$\text{m4}\left(3\right)+\text{2n}\left(8\right)+4\left(- 2\right)=0$
$3m+4n=2$
(A) $\frac{3}{2}+\frac{4}{8}=2$ is correct.
(B) $3\times 1+4\times \frac{1}{4}=4\neq 2$ is incorrect.
(C) $3\times \frac{1}{2}+4\times \frac{1}{2}=4\neq 2$ is incorrect
(D) $3\times \frac{1}{4}+4\times \frac{1}{8}=\frac{3}{4}+\frac{2}{4}=\frac{5}{4}\neq 2$ is incorrect.