The fraction of total volume occupied by the atom present in a simple cubic is

Options

A. `pi/4`
B. `pi/6`
C. `pi/(3sqrt2)`
D. `pi/(4sqrt2)`

Explanation

In a simple cube, no. of atoms/unit cell
` = 8 xx 1/8 =1 `
Volume of the atom = ` 4/3 pi r^(3)`
volume of the cube = ` a^(3) = ( 2r)^(3) = 8 r^(3)`
Fraction occupied = `( 4/3 pi r^(3))/( 8 r^(3) ) = pi/6`