In NaCl type structure, if all ions along an edge diagonal are absent, the expression for packing fraction in limiting case is:

Options

A. `pi/(3sqrt2)(1+r_(c)^(3)/r_(a)^(3))`
B. `pi/(4sqrt2)(1+r_(c)^(3)/r_(a)^(3))`
C. `(sqrt2)pi/(24)((5/2)r_(c)^(3)+4r_(a)^(3))/r_(a)^(3))`
D. `pi/(2sqrt2)(1+r_(c)^(3)/r_(a)^(3))`

Answer

B

Explanation

When all the ions along the axis joining face centres is removed. i.e., two anions at face centres and cation at body centre are removed.
P.E. = `(3xx4/3pi(r_(c)^(3)+r_(a)^(3)))/((2sqrt2r_(a))^(3))=(4pi(r_(c)^(3)+r_(a)^(3)))/(16sqrt2r_(a)^(3))=pi/(4sqrt2)(1+(r_(c)^(3))/(r_(a)^(3)))`