In an atom, where electrons race around the nucleus like buzzing bees, the velocity of an electron doesn't get anywhere near the speed of light until the atomic nucleus fills up with lots of positively charged protons - the negatively charged electrons have to move faster to keep from being pulled into the highly positive nucleus. This occurs in the transition metals of the periodic table of elements, metals ranging from tantalum and tungsten to platinum and gold. In a gold atom, with 79 protons in the nucleus, the 79 electrons whip around the nucleus at about half the speed of light.
The net effect is that gold's electrons are much heavier and are pulled in closer to the nucleus, lowering the energy levels and making the atom more compact. According to this hypothesis, gold's s shells, which are its lowest energy spherically symmetric electron shells, contract. This shields the electrons in outer, asymmetric p and d orbits from the nuclear charge, allowing them to expand slightly. In gold, the contraction of the outermost (6s) shell and the expansion of the next-inner (5p) shell reduces the energy difference between the two to the equivalent of a photon of blue light. This allows gold to absorb blue light and, thus, look yellow. Silver, because it exhibits a much less dramatic relativistic effect, is unable to absorb any visible light and is totally reflective.
This same shielding effect allows the more tightly bound s shell to easily accept electrons from other molecules, while the partly shielded d shell can easily donate electrons to a reaction.
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