Lead crystallizes in a face-centered cubic structure with a density of 11.34 g/cm3. Polonium crystallizes in a simple cubic structure with a density of 9.3 g/cm3. Explain why lead has a greater density than polonium even though polonium atoms are heavier, and smaller than lead atoms.

In a face-centered cubic structure, each unit cell has 4 atoms. Each of the 8 corner atoms contribute 1/8 part to the unit cell and each of the 6 atoms at face-centres contribute 1/2 part to the unit cell. So, each unit cell has net 4 atoms.

In a simple cubic structure, there are 8 atoms, one at each corner. So, each one of them contribute 1/8 part to the unit cell. So, the unit cell has only 1 atom effectively.

Hence, each cell units of lead has 4 times as atoms as in the unit cells of polonium.

Due to this, density of lead is higher despite the fact that it's atomic mass is smaller and the size is bigger than that of a polonium atom.

The face-centered cubic structure is characterized in that there are four atoms in each unit cell. Each atom located in a corner corresponds one eighth of the unit cell and the atoms located in the center correspond a medium of the unit cell. This results in that in each unit cell it has four atoms.

On the other hand, in the simple cubic structure there are eight atoms, located at each corner. Each of these atoms contributes one eighth of the unit cell. Therefore, in each unit cell there is only one atom.

In each cell of the element lead contains four times more atoms than in the cell of polonium. This means that lead is much denser and larger than the element polonium.