A compound formed by elements `A` and `B` crystallises in a cubic structure where `A` atoms are present at the corners of a cube and the `B` atoms are present at the face centres.The formula of the compound is

Options

A. `A_(2)B`
B. `AB_(3)`
C. `AB`
D. `A_(3)B`

Answer

2

Explanation

Each atom of a corner is shared between eight adjacent unit cells,Four unit cells in the same layer and four unit cells of the upper (or lower) layer.Therfore only `1//8`th of an atom (or molecule or ion) actually belongs to a particular unit cell).
since the cubic unit cell `8` atoms on its corners ,the total number of `A` atoms inone unit cell is
`=8xx(1)/(8)=1 "atom"`
Each atom located at the face-centre is shared between two adjacent unit cell and hence only `1//2` of each atom belongs to a unit cell. Since each cubic unit cell has `6` atoms on its face-centres the total number of `B` atoms in one unit cell is
`=6xx(1)/(2)=3 "atoms"`
Thus the empericle formula of the compound is `AB_(3)`.