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.

Answer

AB

Explanation

Contribution made by the atoms (A)
Contribution on the corners `=8xx1//8=1`
Contribution on the faces `=6xx1//2=3`
`therefore` No. of atoms of A present = 1 + 3 = 4
Contribution made by the atoms (B)
Contribution on one edge = 1/4
Contribution on all the twelve edges `=12xx1//4=3`
Contribution on the body centre = 1
`therefore` No. of atoms of B present = 3 + 1 = 4
The formula of the compound : `A_(4)B_(4)` or AB.