In a solid, oxide ions are arranged in ccp. Cations 'A' occupy one-sixth of the tetrahedral voids and cations 'B' occupy one-third of the octahedral voids. Which of the following is the correct formula of the oxide?

Question

In a solid, oxide ions are arranged in ccp. Cations 'A' occupy one-sixth of the tetrahedral voids and cations 'B' occupy one-third of the octahedral voids. Which of the following is the correct formula of the oxide? (A) ABO3 (B) A2BO3 (C) AB2O3 (D) None of these

Tardigrade Admin · Accepted Answer

Cation A=(1/6)× 8=(8/6)=(4/3) Cation B=(1/3)× 4=(4/3) O2 -=8× (1/8)+6× (1/2)=4 A: B: O2 -=(4/3):(4/3):4=1:1:3

Q. In a solid, oxide ions are arranged in ccp. Cations ' $A$ ' occupy one-sixth of the tetrahedral voids and cations ' $B$ ' occupy one-third of the octahedral voids. Which of the following is the correct formula of the oxide?

$A B O_{3}$

$A_{2} B O_{3}$

$A B_{2} O_{3}$

None of these

Cation $A = \frac{1}{6} \times 8 = \frac{8}{6} = \frac{4}{3}$
Cation $B = \frac{1}{3} \times 4 = \frac{4}{3}$
$O^{2 -} = 8 \times \frac{1}{8} + 6 \times \frac{1}{2} = 4$
$A : B : O^{2 -} = \frac{4}{3} : \frac{4}{3} : 4 = 1 : 1 : 3$

Q. In a solid, oxide ions are arranged in ccp. Cations 'A' occupy one-sixth of the tetrahedral voids and cations 'B' occupy one-third of the octahedral voids. Which of the following is the correct formula of the oxide?

ABO3​

A2​BO3​

AB2​O3​