The fraction of total volume occupied by atoms in a simple cube is

Options

A. `(pi)/(3sqrt(2))`
B. `(pi)/(4sqrt(2))`
C. `(pi)/(4)`
D. `(pi)/(6)`

Answer

d

Explanation

Volume of cube `= a^(3)`
Volume of unit cell `= 1 xx (4)/(3) pi r^(3) = (4)/(3) pi ((a)/(2))^(3) = (pi a^(3))/(6)`
`:.` Packing fraction `= (pi a^(3))/( 6//CI^(3)) = (pi)/(6)`