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 C atom at the body centre?

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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 $8 \times \frac{1}{8} = 1$
Face-centred atom in a cube is shared by two unit cells.
As there are 6 faces in a cube, number of face-centred
atom $(B)$ per unit cell $6 \times \frac{1}{2} = 3$
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 $A B_{3} C$ .

Chemistry - Solid State Question with Solution | TestHub

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