Which of the follwing expression is correct for packing fraction of NaCl if the ions along the face are diagonally removed 

Options

A. `((13)/(2)pir_(-)^(3)+(16)/(3)pir_(+)^(3))/(8(r_(+)+r_(-))^(3))`
B. `((13)/(2)pir_(-)^(3)+(4)/(3)pir_(+)^(3))/(8(r_(+)+r_(-))^(3))`
C. `((16)/(3)pir_(-)^(3)+(13)/(3)pir_(+)^(3))/(8(r_(+)+r_(-))^(3))`
D. `((4)/(3)pir_(-)^(3)+(13)/(3)pir_(+)^(3))/(8(r_(+)+r_(-))^(3))`

Answer

A

Explanation

If the ions along one face diagonal are removed. The ions at the two comers and face centre are removed. Then no. of `Cl^(-)` removed are:

`1 xx 1/2 = 1/2, 2 xx 1/8 = 1/4`
Total `=3/4`, Remaining `1/4`
`Na^(+)` ions remains are such no. of `Na^(+)` ions 4. In NaCl `2r^(+) + 2r^(-)` =a
P.F `=(4/3 xx 13/4 pir_(-)^(3) + 4 xx 4/3 pi r_(+)^(3) )/(2r^(+) + 2r^(-))^(3) = (13/8 pir_(-)^(3) + 16/3 pir_(-)^(3))/(8(r^(+) + r^(-))^(3))`