In an ionic compound, oxide ions have ccp arrangement Cations `A` are present in one eighth of the tetrahedral voids whilst cations `B` occupy half of the octahedral voids.the empirical formula of the compound is

Options

A. `ABO_(4)`
B. `ABO_(2)`
C. `AB_(2)O_(4)`
D. `A_(2)BO_(4)`

Answer

3

Explanation

Unit cell of ccp arragement is fcc thus
Number of oxide ions per unit cell `=4`
No. of tetrahedral voids per unit `=8`
No. of octahedral voids per unit cell `=(1)/(8)xx8=1`
No of cations `B` per unit celll `=(1)/(2)xx4=2`
Hence ration `A:B:O^(2-)=1:2:4`.Consequently empirical formula in `AB_(2)O_(4)`.