How are we able to find fresh radioactive materials

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How can we be mining for radio active material if the earth was formed so long ago, would these materials not have run the course of depletion already? or is man kind creating them ? like Uranium or Plutonium

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The elements are constantly decaying and emitting radioactive decay. The time taken for elements to decay to a point where we can no longer detect them is governed by their half lives. The half life is the time it takes for a half of any given quantity of a radioactive element to decay. So if we start with a kilo of an element, after one half life you would have half a kilo of the original element (and half a kilo of whatever it decays to). After two half lives you have half of half a kilo (250g) of the original element; after three half-lives half of half of half a kilo (125g) and so on…

So if an element has a long half life, enough of it will remain for us to mine it. For instance, the half life of the most common form of uranium (uranium 238) is about 4.5 billion years – which is coincidentally about the age of the Earth. We can say that half of the U238 that originally existed on the Earth has decayed. Another form of uranium (U235) has a shorter half life of only 700 million years, so we know it has been through more than six half lives and only about 1/64th of the original U235 is still found on Earth – but there’s enough left that we can still extract it and use it in power stations.

For elements like plutonium, the half lives are very short indeed (about 25,000 years); so even if there had been any on Earth in the beginning, it would have been through so many half lives that any concentrations in nature would be below our detection thresholds. So plutonium is considered a ‘synthetic element’ – it had to be made by humans from uranium.

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