Briefly explain what determines the characteristic color of (a) a metal and (b) a transparent nonmetal.

The color of an object is determined by the way it interacts with light. When light strikes an object, it may be absorbed, reflected, or transmitted. The wavelengths of light that are absorbed or transmitted determine the color we perceive. For example, if an object absorbs all wavelengths and reflects none, it appears black. If it reflects all wavelengths and absorbs none, it appears white.

Metals have a unique electronic structure, where their valence electrons (the outermost electrons) are delocalized, meaning they do not belong to individual atoms but are free to move throughout the metal lattice. As a result, metals can easily conduct electricity and heat. This delocalized electron structure is called a "sea of electrons" or "electron gas."

When light strikes a metal, the delocalized electrons are free to absorb and re-emit the photons of light. Metals tend to absorb photons with specific wavelengths that correspond to the energy gaps between their energy levels. As a result, they reflect the remaining wavelengths, which combine to form the metal's characteristic color. The specific wavelengths absorbed depend on the metal's electron configuration and the arrangement of its atoms.

Transparent nonmetals have a different electronic structure compared to metals. In these materials, the valence electrons are tightly bound to individual atoms and are not free to move throughout the material. This leads to a more localized distribution of electrons and a less mobile electronic structure.

In transparent nonmetals, the tightly bound electrons can only absorb specific wavelengths of light that precisely match the energy gaps between their allowed energy levels. If none of the wavelengths in the visible spectrum match these energy gaps, the transparent nonmetal will transmit visible light without absorbing it, creating a transparent appearance. When visible light is absorbed and re-emitted by electron transitions, the color we perceive is the color of the re-emitted light. In summary, the characteristic color of a metal is determined by the wavelengths of light it reflects after interacting with its delocalized electrons, while the characteristic color of a transparent nonmetal is determined by which wavelengths of light are absorbed and re-emitted by its localized electrons.