In the unit cell of NaCl, which of the following statements are correct?  

Options

A. `Na^(+)` ions have six `Cl^(-)` ions in its nearest neighbourhood
B. `Cl^(-)` ions have six `Na^(+)` ions in its nearest neighbourhood
C. Second ncarest neighour of `Na^(+)` ion are twelve `Na^(+)` ions
D. NaCl has `68%` of occupied space

Answer

A, B, C

Explanation

Co-ordination no of NaCl = 6:6, `Na^(+)` surrounded by 6C1, CI surrounded by `6Cl^(-), Cl^(-)` Second nearest neighbours of `Na^(+)` Nation are `12Na^+` i.e.. The ion at the body centre is surrounded by 4Nat at edge centre (X-direction) `4Na^+` (X-direction), `4Na^(+)` (Z-direction). In NaCl crystal these are `4Na^+` and
`4Cl^(-), 4r^(-) = sqrt(2a), 16 (r^(-))^(2) = 2a^(2)` (or) `a^(3) = 16sqrt(2)r^(3) , r_( c)/r_(a) = 0.414, P.F =(4 xx 4/3 pi(r^(+) + r^(-))^(3))/(16sqrt(2)r^(3))`
`=pi/(3sqrt(2))[1+ (r^(+)/r^(-))^(3)] = 0.79, %` occupied = 79%