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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?

Options

  1. AA 2 B C
  2. BA B 2 C
  3. CA B 3 C
  4. DA B C 2

Correct answer

C. A B 3 C

Step-by-step solution

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 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 × 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 .

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