Why is glass transparent?

Glass is an amorphous solid and therefore has no regular crystal structure. Glass is in a sense a supercooled liquid which has been rapidly cooled from the melt so that the atoms do not have time to adopt an ordered crystal structure. Glass, which consists essentially of silicon dioxide, occurs in nature as quartz, which, however, has an ordered crystal structure. Both glass and quartz are transparent, provided that the substances are chemically pure and contain no impurities. Therefore, the transparency of glass has nothing to do with its amorphous structure.

Glass is transparent because it is an electrical insulator. An insulator is characterized by the fact that its electrons are bound and can not move freely under the influence of an external electric field. The bound electrons from the outer atomic shells are called valence electrons and are responsible for the chemical bonding in the solid state. Silicon has four electrons and the oxygen has six electrons in the outer shell, so that in the silicon dioxide octet rule can be met and the atoms can assume a noble gas configuration. Thus, all valence states in the silica are occupied and there are no surplus electrons, so no electric charge carriers are available for charge transport.

For electrically conduction carriers to form in the material, valence electrons must be raised to a higher energy level. For this purpose, an excitation energy must be used which is greater than or equal to the energy gap $E_g$ between conduction band and valence band. If this energy gap is very large ( $E_g > 3 \,\text{eV}$ ), such excitation can not take place by thermal lattice vibration, so that the material is an insulator at room temperature. Silicon dioxide has a particularly large band gap (almost 9 eV), so that it represents a good insulator.

For light to be absorbed, the energy of a photon, $E = h \nu$ , must be transferred to an electron in the solid. Since all valence states are occupied, a valence electron can only be excited into the conduction band, so that at least the energy $E_g$ must be provided for the excitation. Since visible light only contains energies of 1.6 to 3 eV, the light absorption in isolators with $E_g > 3 \,\text{eV}$ can not take place. Since glass is an insulator with an large band gap, light rays can penetrate glass virtually without weakening. Exceptions are colored glasses containing metallic ions as impurities. These add additional energy levels in the bandgap to the solid, so that certain wavelengths of light can be absorbed and the glass therefore gets its coloration.

Note that the physics of electrons in a solid can only be understood using quantum mechanics. Unlike in classical mechanics, where particles can take on any kind of energy, in quantum mechanics for bound states there are only discrete energy levels. Certain energies are therefore forbidden, so that in particular the energy gaps results for the band structure of solids.