packing fraction of a unit cell is drfined as the fraction of the total volume of the unit cell occupied by the atom(s).
`P.E=("Volume of the atoms(s) present in a unit cell")/("Volume of unit cell")=(Zxx(4)/(3)pir^(3))/(a^(3))`
and `%` of empty space = `100- P.F.xx100 `
where Z= effective number of stoms in s cube .
r= radius of a an atoms
a = edge lenght of the cube
Packing fraction in face centered cubic unit cell is :

Explanation

Packing efficiency in face centred cubic lattice
If a is the edge length of the cube,
Face diagonal of the cube `=sqrt(2)a`
In f.c.c. (or c.c.p.) lattice atoms touch each other along the face diagonal of the cube.
`thereforesqrt(2)a=4rora=2sqrt(2)r`
In f.c.c. structure, number of atoms per unit cell = 4
`therefore"Packing efficiency"=(4xx"Volume of one atom")/("Volume of unit cell")xx100`
`=(4xx4/(3)pir^(3))/(a^(3))xx100=(16/(3)pir^(3))/((2sqrt(2)r)^(3))xx100`
`=(16/(3)pir^(3))/(8xx2sqrt(2)r^(3))xx100=pi/(3sqrt(2))xx100=(50sqrt(2)pi)/(3)=74%` (approx.)