Question

What is the simplest formula of a solid whose cubic unit cell has the atom A at each corner, the atom B at each face centre and a C atom at the body centre-

(A) AB₂C 

(B) A₂BC

(C) AB₃C 

(D) ABC₃

Answer 1

Correct Answer is: (C) AB₃C 

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 = 8 × 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 = 6 x 1/2 = 3.

An atom in the body of the cube is not shared by other cells.

∴ Number of atoms (C) at the body centre per unit cell = 1.

Hence, the formula of the solid is AB₃C.