Question

What is the simplest formula of a solid whose unit cell has the atom A at each corner, the atom B at each face centre and a atom C at the body centre.
A. `A_(2)BC`
B. `AB_(2)C`
C. `AB_(3)C`
D. `ABC_(2)`

Answer 1

An atom at the corner of a cube is shared among it unit cells. As there are 8 corners in a cube, number of corner atom (A) per unit cell `=8((1)/(8))=1`
A face-centred atom in a cube is shared by two unit cells. As there are 6 faces in a cube, number of face-centred atoms (B) per unit cell `=6xx(1)/(2)=3`.
An atom in the body of the cube is not shared by other cells.
`therefore` Number of atoms (C) at the body centre per unit cell=1.
Hence (C), the formula of the solid is `AB_(2)C`.