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 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 \(\times\cfrac{1}{8}\) = 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 \(\times\cfrac{1}{2}\) = 3

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

Thus, number of atoms [C] at the body centre per unit cell = 1

Hence, the formula of the solid is AB₃C.