# The fraction of volume occupied in a primitive cubic cell is:

$\begin{array}{1 1} 0.52 \\ 0.48 \\ 0.62 \\ 0.34 \end{array}$

The atoms in a simple cubic crystal are located at the corners of the units cell, a cube with side $a$.
Adjacent atoms touch each other so that the radius of each atom equals $\large\frac{a}{2}$
There are eight atoms occupying the corners of the cube, but only one eighth of each is within the unit cell so that the number of atoms equals one per unit cell.
Packing Density $= \large\frac{\text{Volume of atoms}}{\text{Volume of unit cell}}$
Volume of atoms $= \large\frac{4}{3}$$\pi /r^3 and Volume of unit cell = a^3 Substituting r = \large\frac{1}{2}$$a$, we get:
Packing Density $= \Large \frac{ \frac{4\pi}{3} (\frac{a}{2})^3}{a^3}$$= \large\frac{\pi}{6}$$ = 0.52$
edited Jan 9