Rare earths are a set of 17 chemical elements in the periodic table, specifically 57 through 71. Scandium and Yttrium are also considered rare earth elements because they tend to occur in the same ore deposits and exhibit similar chemical properties.
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Rare earths are not particularly rare. These elements are found in the earth's crust. However, because they are widely dispersed and not found in concentrated forms, they received the term "rare earth." A complicated process is necessary to mine and extract them, and the mildly radioactive slurry tailings, as well as the toxic acids required during the refining process can have serious environmental consequences.
We've put together a gallery of the different elements labeled "Rare Earth," their atomic numbers and symbols, and what they are used for.