In a solid ,oxide `(O^(2-))` ions are arranged in ccp, cations `(A^(3+))` occupy one -sixth of tetrahedral void and cations `(B^(3+))` occupy one -third of the octahedral voids . What is the formula of the compound?

Options

A. `ABO_(3)`
B. `AB_(2)O_(3)`
C. `A_(2)BO_(3)`
D. `ABO_(2)`

Answer

A

Explanation

Number of `O^(2-)` ions in packing `=n`
Number of octahedral voids `=n`
Number of tetrahedral voids `=2n`
Number of `A^(3+)=(1)/(6)xx2n=(n)/(3)`
Number of `B^(3+)=(1)/(3)xxn=(n)/(3)`
`A^(3+):B^(3+): O^(2-)=(n)/(3):(n)/(3):n=1:1:3`
Formula of the compound `=ABO_(3)`