Question

Structure of a mixed oxide is cubic close-packed (CCP). The cubic unit cell of mixed oxide is composed of oxide ions. One fourth of the tetrahedral voids are occupied by divalent metal A and the octahedral voids are occupied by a mono-valent metal B. The formula of the oxide is ?

• A. $AB{O}_2$
• B. $A_{2}B{O}_2$
• C. $A_2{B}_3{O}_4$
• D. $A{B}_2{O}_2$

Answer 1

The correct option is D $A{B}_2{O}_2$

In cubic closed packing, the number of octahedral voids is equal to the number of atoms and the number of tetrahedral voids is equal to twice the number of atoms.

Number of atoms in a $CCP$ array $=1$

Number of atoms of $A=1\times 2\times \frac{1}{4}=\frac{1}{2}$

Number of atoms of $B=1$

Number of atoms of $O=1$

Therefore, the formula is $A_{1/2}BC$ or $A{B}_2{O}_2$.

So, the correct option is $D$