The Solid State

The Solid State

Question

CsCl crystallises in body centred cubic lattice. If 'a' its edge length, then which of the following expression is correct?

  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space 3 straight a
  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space fraction numerator 3 straight a over denominator 2 end fraction
  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space fraction numerator square root of 3 over denominator 2 end fraction straight a
  • straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space square root of 3 straight a end root

Answer

C.

straight r subscript Cs to the power of plus space plus straight r subscript Cl to the power of minus end subscript space equals space fraction numerator square root of 3 over denominator 2 end fraction straight a

In CsCl, Cl- lie at corners of simple cube and Cs+ at the body centre, Hence, along the body diagonal, Cs+ and Cl- touch each other so
FD space equals space straight b equals space square root of straight a squared plus straight a squared end root space equals space square root of 2 straight a
In space increment AFD comma
straight c squared space equals space straight a squared space plus straight b squared space equals straight a squared space plus space left parenthesis square root of 2 straight a right parenthesis squared space space equals straight a squared space plus 2 straight a squared
straight c squared space equals space 3 straight a squared
straight c equals square root of 3 straight a end root
As space increment AFD space is space an space equilibrium space triangles comma
therefore space square root of 3 straight a space equals space 4 straight r
rightwards double arrow straight r space equals space fraction numerator square root of 3 straight a over denominator 4 end fraction
Hence comma space straight r subscript cs to the power of plus end subscript space plus straight r subscript Cl space equals space 2 straight r space equals space 2 space straight x fraction numerator square root of 3 straight a over denominator 4 end fraction space equals space fraction numerator square root of 3 straight a over denominator 2 end fraction straight a space

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