Question

The density of aluminium is $2.7\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$; that of silicon is $2.3\mathrm{g}/\mathrm{c}{\mathrm{m}}^3$. Explain why Si has the lower density even though it has heavier atoms.

Short answer

Because of the less coordinated number of atoms in silicon; it is less dense than aluminium.

Step-by-step solution

Define the density of the solid

The density of any substance depends on its mass and volume in general. In the crystal lattice, as the number of atoms per unit cell increases, the density of the crystal lattice increases.

Determine the density of aluminium

The coordination number of atoms in a crystal lattice represents the number of atoms surrounding a certain atom. As the coordination number increases, the crystal lattice will have a better packed structure. In the crystal structure of silicon, the coordination number of atoms is 4, so atoms are less tightly packed that decreasing the density of silicon compared to aluminium. In aluminium the coordination number is 12. Hence aluminium is denser than silicon because of the high coordination number