Question

Relation between a and r in fcc derivation

Answer 1

For fcc, atom are present at the corners and at the centres of each faces of the cube.
let the cell edge =a
distance between the nearest neighbours =d
radius of the of the atom =r
From figure,
PR=√PQ^2+QR^2
PR=√a^2+a^2
PR=a√2........................1)
d=PR/2
d=a√2/2
d=a/√2........................2)
r=d/2=a/2√2...............3)
Equation 3 give the relation between 'a'and 'r'.