What is the packing efficiency of a metal crystal if it crystallizes in a face centered cubic lattice ?

Step-by-step solution

For a face-centered cubic (fcc) lattice, the atoms touch each other along the face diagonal of the unit cell. Let the edge length of the unit cell be a and the radius of each atom be r . The length of the face diagonal is 2 a . Since the atoms touch along the face diagonal, we have 2 a = 4r , which gives a = 2 2 r . The number of atoms per unit cell in an fcc lattice is Z = 4 . The volume occupied by the atoms is 4 4 3 r^3 = 16 3 r^3 . The total volume of the unit cell is a^3 = (2 2 r)^3 = 16 2 r^3 . Packing effici