Question

Gold (atomic radius = 0.144 nm) crystallises in a face-centred unit cell. What is the length of a side of the cell?

Answer 1

atomic radius , r = 0.144 nm
type of unit cell = face centered
so, use the relation between atomic radius and length of side length ,
side length of unit cell = 2√2 × atomic radius
[ note :- if r is radius and a is side length of unit length then, √2a = (r + 2r + r) , √2a = 4r => a = 2√2r]

side length = 2√2 × 0.144 nm
= 2 × 1.414 × 0.144 nm
= 0.407 nm

hence, length of unit cell = 0.407 nm = 407pm