In a face centred cubic lattice, atom `A` occupies the corner positions and atom `B` occupies the face centred positions. If one atom of `B` is missin from one of the face centred points,, the formula of the compound is `:`

Options

A. `A_(2)B`
B. `AB_(2)`
C. `A_(2)B_(3)`
D. `A_(2)B_(5)`

Answer

D

Explanation

Contribution by atoms A on the corners
`=8xx(1)/(8)=1`
Contribution by atoms B on the face centres
`=5xx(1)/(2)=(5)/(2)`
(Total atoms on face centres = 6 . As one atom is missing atoms actually present = 5 )
`:.` Ratio of A : B `=1:(5)/(2)=2:5`
Hence, formula ` =A_(2)B_(5)`.