In NaCl type structure, if all ions along an axis joining centres of the opposite face centers are missing, 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. `(pi)/(sqrt2)(1+(r_(c)^(3))/(r_(a)^(3)))`
D. `(pi)/(2sqrt(2))(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.F.=(3xx(4)/(3)pi(r_(c)^(3)+r_(a)^(3)))/((2sqrt(2)r_(a))^(3))=(4pi(r_(c)^(3)+r_(a)^(3)))/(16sqrt(2)r_(a)^(3))=(pi)/(4sqrt(2))(1+(r_(c)^(3))/(r_(a)^(3)))`.