Q50 / 77 · NTA Abhyas (JEE Main) 2020 · Chemistry · Solid State

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?

  • A
    2 9 π 3 6 4
  • Correct answer
    B
    7 π 3 6 4
  • C
    1 9 π 3 6 4
  • D
    2 π 3 6 4

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 = a3

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

Hence, the correct answer is option: 'B'.

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