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Band TheoryThe color of metals can be explained by band theory, which assumes that overlapping energy levels form bands.The mobility of electrons exposed to an electric field depends on the width of the energy bands, and their proximity to other electrons. In metallic substances, empty bands can overlap with bands containing electrons. The electrons of a particular atom are able to move to what would normally be a higher-level state, with little or no additional energy. The outer electrons are said to be "free," and ready to move in the presence of an electric field.Some substances do not experience band overlap, no matter how many atoms are in close proximity. For these substances, a large gap remains between the highest band containing electrons (the valence band) and the next band, which is empty (the conduction band). As a result, valence electrons are bound to a particular atom and cannot become mobile without a significant amount of energy being made available. These substances are electrical insulators. Semiconductors are similar, except that the gap is smaller, falling between these two extremes.The highest energy level occupied by electrons is called the Fermi energy, Fermi level, or Fermi surface.Above the Fermi level, energy levels are empty (empty at absolute zero), and can accept excited electrons. The surface of a metal can absorb all wavelengths of incident light, and excited electrons jump to a higher unoccupied energy level. This creates current, which rapidly discharges to emit a photon of light of the same wavelength. So, most of the incident light is immediately re-emitted at the surface, creating the metallic luster we see in gold, silver, copper, and other metals. This is why most metals are white or silver, and a smooth surface will be highly reflective, since it does not allow light to penetrate deeply.If the efficiency of absorption and re-emission is approximately equal at all optical energies, then all the different colors in white light will be reflected equally well. This leads to the silver color of polished iron and silver surfaces.The efficiency of this emission process depends on selection rules. However, even when the energy supplied is sufficient, and an energy level transition is permitted by the selection rules, this transition may not yield appreciable absorption. This can happen because the energy level accommodates a small number of electrons.For most metals, a single continuous band extends through to high energies. Inside this band, each energy level accommodates only so many electrons (we call this the density of states). The available electrons fill the band structure to the level of the Fermi surface and the density of states varies as energy increases (the shape is based on which energy levels broaden to form the various parts of the band).If the efficiency decreases with increasing energy, as is the case for gold and copper, the reduced reflectivity at the blue end of the spectrum produces yellow and reddish colors.
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