The fraction of volume occupied by atoms in a body centered cubic unit cell is:

Explanation

Simple Cubic Unit Cell. In this type of unit cell there is one atom at each corner. Contrubution by one atom at each corner = `1/(8)`
Contribution by eight atoms at all eight corners `=8xx1/(8)=1`
Hence, a simple cubic unit cell has one atom per unit cell.
Face Centred Unit Cell. In this type of unit cell there is one atom at each corner and one atom at each face centre. As there are eight corners and six faces of a cube the number of atms per unit cell can be calculated as follows :
Contribution by one atom at each corner = `1/(8)`
Contribution of eight at all the eight corners = `8xx1/(8)=1`
Contribution by one atom at centre of each face `=1/(2)`
Contibution by six atoms at centres of six faces `=6,,1/(2)=3`
Total number of atoms in a face centred unit cell = 3 + 1 = 4
Hence a face centred unit cell has four atoms per unit cell.
Body Centred Unit Cell. In this type of unit cell therer is one atom at corner and one atom at the body centre of the cube. As there are eight corners of a cube, the number of atoms per unit cell can be calculated as follows.
Contribution by one atom at each corner = `1/(8)`
Contribution by eight atoms at all eight corners = 8 = 1
Number of atoms in centre of the cube = 1
Total number of atoms in a body centred unit cell = 1 + 1 = 2
Hence, a body centred cubic unit cell has two atoms per unit cell.