Question

If the atomic radius of a metal that has the face-centered cubic crystal structure is 0.137nm, calculate the volume of its unit cell.

Answer 1

for FCC lattice,
length of face diagonal = a*sqrt(2) = 1.4142*a

This must equal 4*r

so,
1.4142*a = 4*r
1.4142*a = 4*0.137 nm
a = 0.3875 nm
= 3.875*10^-8 cm

volume = a^3
= (3.875*10^-8 cm)^3
= 5.82*10^-23 cm^3

Answer: 5.82*10^-23 cm^3