In the fcc arrangement of `A` and `B` atoms whose `A` atoms are at corners of the unit cell and `B` are at the face centres one of the `A` atom is missing from one corner in each unit cell. What is the simplest formula of the compound?

Options

A. `A_(7)B_(3)`
B. `A_(8)B_(21)`
C. `A_(7)B_(24)`
D. `AB_(3)`

Answer

C

Explanation

Atoms of 'A' are present at 7 corners and atoms of 'B' are present at six face-centres.
`therefore` Number of atoms of 'A' `=7xx(1)/(8)=(7)/(8)`
Number of atoms of 'B'`=6xx(1)/(2)=3`
`A:B=(7)/(8):3=7:24`
Simplest formula of solid `=A_(7)B_(24)`