Volume of a solid based on number of atoms

[emol1414]

This is a silly doubt i guess...

Homework Statement

When you know an atom's radius you can easily determine its volume by considering it's a sphere.

But when you're dealing with solids, that is, a set of atoms... and then you have bands insted of orbitals... this differente configuration, the rearrengement... would drastically alterate this estimative of the volume?

I read that the "minimum" number of atoms to form a so-named "solid" is about 10^20, so I was wondering what volume would this number correspond to.

 

[ehild]

When atoms form a molecule, or their ions form a solid, they usually get closer to each other than the sum of their atomic radii. http://en.wikipedia.org/wiki/Ionic_radius.
Still, solids consisting of atoms or single-atomic ions can be considered as regularly packed spheres. The volume occupied by one atom or ion in the crystalline solid depends of the structure of the crystal.
Supposing you have a simple cubic structure, the crystal consisting of regular arrangement of cubic cells with the atoms placed at the corners. The atoms are supposed to touch each other, so the length of one side of the cubic cell is the same as the diameter of the atom (D). One atom belongs to each cell. The volume of the cell is D³. The volume of one atom is (π/6) D³, so the "packing density" in this type of crystal is π/6~0.52.

If you have 10²⁰ atoms, the volume is 10 ²⁰D³.

The atomic radii of the elements are of 100-200 pm. For example, R=144 pm for gold atoms. So the volume of the crystal that contains so many gold atoms is about 2.39 * 10^-9 m³, that corresponds to a cube of length 1.3 mm.

ehild