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An element crystallizes both in fcc and bcc lattice. If the density of the element in the two forms is the same, the ratio of unit cell length of fcc to that of bcc lattice is

Options

  1. A( 2 ) 1 / 3
  2. B1 2 1 / 3
  3. C( 4 ) 1 / 3
  4. D1 4 1 / 3

Correct answer

A. ( 2 ) 1 / 3

Step-by-step solution

Z = a 3 × d × N A M fcc (4) = a 1 3 × d × N A M …(i) bcc (2) = a 2 3 × d × N A M …(ii) Dividing equation (i) by (ii) 2 = a 1 a 2 3 a 1 a 2 = 2 1 / 3

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