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The partially full d-orbitals in transition metals have energy splittings that happen to lie in the visible range. Depending on the arrangement of substituents (known as ligands) that attach to them, the electron energies split according to crystal field theory. Similar splitting in the s or p orbitals produce gaps in the ultraviolet, and any visible light goes right through, so we don't see any color. In transition metals, however, visible light excites the electrons from a lower d orbital to a higher one and only letting some light through.
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