What is the packing efficiency and number of atoms per unit cell present in a face centered cubic system?

Step-by-step solution

In a face-centered cubic (FCC) unit cell, atoms are present at the 8 corners and the centers of the 6 faces. Number of atoms from corners = 8 1 8 = 1 Number of atoms from faces = 6 1 2 = 3 Total number of atoms per unit cell ( Z ) = 1 + 3 = 4 Let a be the edge length of the unit cell and r be the radius of the atom. In an FCC lattice, atoms touch each other along the face diagonal. Face diagonal = 2 a = 4r a = 2 2 r Volume of the unit cell = a^3 = (2 2 r)^3 = 16 2 r^3 Volume occupied by 4 atoms = 4 4 3 r^3 = 16 3 r