Radium exists in Uranium ores because Uranium over time decays and one of the intermediate steps in that chain is Radium. So Marie Curie just took a bunch of Uranium ore and separated out everything in it, (I don’t know the exact chemical reactions, but it’ll be like purifying any other sample, basically find some property that one element has that the other doesn’t, and use that to separate them out) then did a bunch of tests, and made sure that the thing they had purified had actually been a new element.
They could tell that there was probably something unknown in the sample, because the ore was more radioactive than pure Uranium would be.
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