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Element X crystallizes in 12 co-ordination fcc lattice. On applying high temperature it changes to 8 co-ordination bcc lattice. Find the ratio of the density of the crystal lattice before and and after applying high temperature

Options

  1. A1:1
  2. B3:2
  3. C2 : 3
  4. D2 2 3 : 3 3

Correct answer

D. 2 2 3 : 3 3

Step-by-step solution

Co. number is 12 means it is fcc lattice Co. number is 8 means it is bcc lattice fcc bcc ρ 1 = 4 × a t . m a s s N a × a 1 3 ρ 2 = 2 × a t . m a s s N a × a 2 3 ρ 1 ρ 2 = 4 2 × a 2 3 a 1 3 = 2 × 4 r 3 3 ( 2 2 r ) 3 = 2 × 4 × 4 × 4 2 × 2 × 2 × 2 × 2 ( 3 3 ) = 4 2 3 3 = 2 ( 2 ) 3 ( 3 ) 3

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