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A body centred cubic lattice is made up of hollow sphere of B. Sphere of solid A are present in hollow sphere of B. Radius of A is half of the radius of B. What is the ratio of total volume of sphere B unoccupied by A in unit cell and volume of unit cell?

Options

  1. A2 9 π 3 6 4
  2. B7 π 3 6 4
  3. C1 9 π 3 6 4
  4. D2 π 3 6 4

Correct answer

B. 7 π 3 6 4

Step-by-step solution

Effective number of atoms of B present in a unit cell = 2 Total volume of B unoccupied by A in a unit cell = 2 × 4 3 R 3 - r 3 × π = 7 3 π R 3 r = R 2 Volume of unit cell = a 3 4 R 3 3 = 6 4 3 3 R 3 3 a = 4 R Ratio of total volume of sphere B unoccupied by A in unit cell and volume of unit cell = 7 / 3 π R 3 6 4 3 3 R 3 = 7 π 3 6 4

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