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.

Explanation

( C) An atom at the corner of a cube is shared among 8 unit cells. As there are 8 corners in a cube, number of corner atom (A) per unit cell
`=8xx(1)/(8)=1`
A face-centered atom in a cube is shared by two unit cells. As there are 6 faces in a cube, number of face-centered 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, the formula of the solid is `AB_(3)C`.