The fraction of total volume occupies by the atoms present in a simple cube is

Options

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

Answer

D

Explanation

Packing fraction of a simple cube
`= ( " Volume of one sphere ")/( "Volume of cubic unit cell")`
Edge length `a=2r` or `r = a//2 `
`:.` Packing fraction `= (((4)/(3) pi (a)/(2))^(3))/(a^(3)) = ( pi )/( 6)`