from this we can draw a projection diagram, which look like the following.
Polonium is on of very few metals that display simple cubic packing... this a somewhat rare packing as it means the atoms a not particularly close. One would expect the ions to be as close together as possible as a result of strong ionic attraction in metals. But here due to the geometry of the ions and the inter ion attractions are not sufficiently strong to pull the ions into a close packing structure. Since the ions are less well packed the volume occupied is less, hence the density observed is lower in these metals than closed packed metal.
Calculating the occupied volume.
If we look at the unit cell, which is cubic, and call the length of one side 'a' the volume of the cube is a3.The number of atoms in the unit cell is eight, but only 1/8 of each atom is inside the boundary of the cube-since each is corner shared by 8 cubes. the total number of spheres is 1/8*8=1
The volume of a sphere is given by
4/3πr3, where r = a /2
=4/3π(a/2)3
=4/3πa3/8
Since we only have 1 complete sphere the percentage of the cube occupied is simply
=(volume of sphere/volume of unit cell) *100
=(4/3π(a/2)3)/a3
= (4/3πa3/8)/a3
=1/6π
=0.5235 volume occupied.
In a simple cubic 52.3% of the space is occupied this percentage can be used to calculate the mass of a single atom from the density, or vice versa.
