A compound made up of elements `A` and `B` crystallizes in the cubic structures. Atoms `A` are present on the corners as well as face centres whereas atoms `B` are present on the edge centres centres as well as body centre. What is the formula of the compound? Draw the structure of its unit cell.

Options

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

Answer

C

Explanation

Atoms Aper unit cell `=underset(("corners"))(8xx(1)/(8))+underset(("face centres"))(6xx(1)/(2))`
`1+3=4`
AtomsB per unit cell
`underset (("edge centres"))(=12xx(1)/(4))+underset(("body centre"))(1=3+1=4)`
`:.` Ratio A : B = 4 : 4 = 1 : 1 . Hence, formula is AB.