Select right expression for determinig packing fraction (P.F.) of NaCl unit cell (assume ideal ) , if ions along an edge diagonal are absent :

Options

A. `((13)/(2)pir^(3)+(13)/(3)pir^(3))/(8(r_(+)-r_(-))^(3))`
B. `((13)/(3)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

1

Explanation

On face diagonal of NaCl, `3Cl^(-)` (2 corners+1 f.c) present. If ions along f.c. are removed `therefore` volume occupied
`=[(8-2)xx(1)/(8)+(6-1)xx(1)/(2)](4)/(3)pir^(3)`
`(6xx(1)/(5)+5xx(1)/(2))xx(4)/(3)pir^(3)=((3)/(4)+(5)/(2))xx(4)/(3)pir^(3)`
`=((3+10)/(4))(4)/(3)pir^(3)=(13)/(4)xx(4)/(3)pir^(3)`