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

Options

A. `(pi)/(2)`
B. `sqrt(3pi)/(8)`
C. `sqrt(2pi)/(6)`
D. `(pi)/(6)`

Answer

D

Explanation

In a simple cube arrangement , the number of atoms is `1`
Also `a = 2r`
Therefore packing fraction
`= ("volume occupied by one atom")/("volume of unit cell")`
`(4//3m^(3))/(a^(3)) = (4//3 pi r^(3))/((2r)^(2)) = (pi)/(6)`