Question

In a metal oxide, the oxide ions are arranged in hexagonal close packing and metal ion occupy two-third of the octahedral voids. The formula of the oxide is:

• A. $MO$
• B. $M_2{O}_3$
• C. $M{O}_2$
• D. $M_{2}O$

Answer 1

Answer: (B)

$M_2{O}_3$

Let the number of oxide ions in hexagonal close packing is $x$.
$\therefore$ The number of octahedral voids $=x$
Since, the metal ions occupy two third of octahedral voids.
$\therefore$ The number of metal ions $=\frac{2}{3}x$
$\Rightarrow \frac{\text{Number of oxide ion}}{\text{Number of metal ions}}=\frac{x}{\frac{2}{3}x}=\frac{3}{2}$
$\therefore$ The formula of the oxide is $M_2{O}_3$.