Question

If the distance between Na+ & Cl-ions in sodium chloride crystal is x pm, then length of the edge of the unit cell is:-

Answer 1

Answer : 220.65pm,91.35pm

The cubical closest packing has a face-centred cubic unit cell.I− ions occupy the corners and the face centres.These ions touch each other along the face diagonal of the cube.Hence

4rI−=2–√a

rI−=a22–√=624pm2(1.414)=220.65pm

Now along the edge,we will have I−Li+I− arrangement,where I− are at the corners and Li+ ion at the centre of the edge (octahedral void ).Since in closest packing,they touch each other,we will have

2r−I+2rLi+=a

rLi+=a2−rI−=624pm2−220.65pm=91.35pm