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

Options

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

Answer

A

Explanation

For simple cube,
`"Radius (r)"=(a)/(2)" [a = edge length]"`
`"Volume of the atom"=(4)/(3)pi((a)/(2))^(3)`
`therefore" Packing fraction"=((4)/(4)pi((a)/(2))^(3))/(a^(3))=(pi)/(6)`