Energy bands are considered continuous due to the large number of closely spaced energy levels. The range of energy levels in a crystal of copper is approximately 1 x 10^–19 J. Assuming equal spacing between levels, the spacing between energy levels may be approximated by dividing the range of energies by the number of atoms in the crystal.

(a) How many copper atoms are in a piece of copper metal in the shape of a cube with edge length 0.5 mm? The density of copper is 8.96 g/cm³. 

(b) Determine the average spacing in J between energy levels in the copper metal in part (a). 

(c) Is this spacing larger, substantially smaller, or about the same as the 1 x 10^–18 J separation between energy levels in a hydrogen atom?