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

Options

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

Answer

B

Explanation

In a simple cube, no. of atoms/unit cell =`8xx1/8=1`
Volume of the atom =`4/3pir^3`
Volume of the cube=`a^3=(2r)^3=8r^3 (because a=2r)`
`therefore` Fraction occupied=`(4/3 pir^3)/(8r^3)=pi/6`