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

The correct option is A $\frac{1}{2},\frac{1}{8}$

Oxide ions are at ccp positions, hence $4O^{2–}$ ions. Also, there are four octahedral voids and eight tetrahedral voids. Since ‘m’ fraction of octahedral voids contain $A{l}^{3+}$ and ‘n’ fraction of tetrahedral voids contain $M{g}^{2+}$ ions, to maintain etectroneutrality 2(2Al ^{3+}= + 6~charge)\) and $(M{g}^{2+}=+2charge)$, will make unit cell neutral
Hence, $m=\frac{2}{4}=\frac{1}{2},n=\frac{1}{8}$