The unit cell in a body centred cubic lattice is given in the figure. Each sphere has a radius 'r' and the cube has side 'a'. What fraction of the total cube volume is empty?

Options

A. `1-8/3 (pir^3)/a^3`
B. `8/3 (pir^3)/a^3`
C. `r/a`
D. `2-4/3 (pir^3)/a^3`

Answer

A

Explanation

Fraction of occupied space
`="Occupied volume"/"Total volume" =8/3 (pir^3)/a^3`
Fraction of empty space = `1-8/3 (pir^3)/a^3`