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Radioactive elements are used all the time. I'm sure you've heard off Nuclear bombs. There's something right there... Uranium is used in nuclear fuel to create those bombs. Radioactive elememts are...
Francium is radioactive, extremely rare, and was discovered in France (hence the name). It is pretty much useless because of its short half-life and rarity. Hope this helps.
All elements after lead (Pb) on the periodic table are radioactive. Isotopes of lighter elements (C-14 for example) can be radioactive as well. And, in fact, all elements have radioactive isotopes.
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