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Which of the following expression is correct for packing fraction of NaCl if a - ions from one face and one diagonal are removed?

Options

  1. A13 3 π r - 3 + 16 3 π r + 3 8 ( r + + r - ) 3
  2. B13 3 π r - 3 + 4 3 π r + 3 8 ( r + + r - ) 3
  3. C16 3 π r - 3 + 13 3 π r + 3 8 ( r + + r - ) 3
  4. D4 3 π r - 3 + 13 3 π r + 3 8 ( r + + r - ) 3

Correct answer

A. 13 3 π r - 3 + 16 3 π r + 3 8 ( r + + r - ) 3

Step-by-step solution

Effective number of remaining C l - = 4 - 2 × 1 8 + 1 2 = 13 4 Effective number of N a + = 4 Packing fraction = Occupied volume Total volume = 13 4 × 4 3 π r - 3 + 4 × 4 3 π r + 3 8 ( r + + r - ) 3 13 3 π r - 3 + 16 3 π r + 3 8 ( r + + r - ) 3

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