Physical models of crystal structures of sodium and graphite are built as well as a molecular model of carbon nanotube in zigzag type. Their energy levels are calculated for both their free ions, atoms crystals and molecule. The effective atomic numbers are used in potential calculation, as well as muffin-tin potentials are used in crystals and molecule. For crystals, Wigner-Seitz Method is applied. The calculated energy levels of carbon atom and ions have high error and are improved by using first order perturbation theory to include electron-electron interactions which give the better result. The similar technique is applied to graphite and zigzag carbon nanotube. The result, energy level of nanotube is -44.86 eV, comparable to the top of the potential well. This energy suggests that zigzag carbon nanotube is a semiconductor.