The unit cell cube length for LiCl is …

In LiCl structure the chloride ion forms a face centred  unit cell( anion - anion contact ). Hence chloride ions contact each other across the diagonal of the face. If we draw  a diagonal on the face of a unit cell , we find that -

length of the  diameter  = radii  of  4 chloride ions (ie. one radius from each corner chloride ion and one  diameter  which equals to two radii of  chloride ion ,  at the center of the face )

Thus  , when the length of  diameter is represented by d  and  radius of each chloride ion by  r ,

d   =  4r

applying Pythagorean theorem we get , 

a²    +   a²     =   d²  

Substituting the given value for  a  =   5.14 A^o   ( or =   0.514 nm ) in the above  equation ,

( 0.514 nm )²     +   ( 0.514 nm )²     =    d²   =   (4r) ²  =  16 r²   

^{{tex}\therefore{/tex}}  solving for  r   we get  ,

r    =   Sqrt [ {  (  0.514 nm )²    +   ( 0.514 nm )²    }  ]   / {tex}\sqrt16{/tex} 

     =  0.182 nm 

or , =  1.82 A^o   for  chloride ion