Edge length of NaCl unit cell is 552 pm. Then which are correct statements

Options

A. distance between `Na^(+)` and `Cl^(-)` ions is 276 pm
B. radii of `Na^(+) and Cl^(-)` ion will be 95 pm and 181 pm
C. nearest distance between two `Na^(+)` ions is `276sqrt2` pm
D. nearest distance between `Cl^(-)` ions is `95sqrt2` pm

Answer

A, B, C

Explanation

For `NaCl a=2r_(C )+2r_(q), a=2r_(c )+2r_(a)=552 p m,r_(c )+r_(a)=276 p m`
In NaCl radius ratio `(r_(c ))/(r_(a))=0.52,(r_(c ))/(r_(a))=(95)/(181)`
Nearest distance between two `Na^(+)` ions is the distance from body centre to edge centre is Hypotenuse in a right angled triangle i.e.`sqrt((276)^(2)+(276)^(2))=276sqrt2 p m`.