Solid state physics - FFC structure of NaCl

[Anabelle37]

Homework Statement

NaCl is a face-centred cubic with a basis at Na(0,0,0) and Cl at (a/2,a/2,a/2) and lattice parameter a = 5.63 angstrom. calculate the separation between nearesr neighbours (Na and Cl).

The Attempt at a Solution

Just by looking at the NaCl structure the separation between nearesr neighbours looks like a/2, but I don't know how to explain the answer?

 

[read]

in fcc structure you have an atom at (x,y,z) and also at (1/2,1/2,0)+, (0,1/2,1/2)+, (1/2,0,1/2)+, that gives a/sqrt(2)