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How does the instability of a radioactive atom relate to quantum mechanics?
In a popular sense, it is like emitting photons by an excited atom while its transition to lower energy levels.
answer : in the same way that the sky relates to my eyes when I see up. RA is a phenomemon, QM is a theory allowing some kind of understanding and predictibility of raw observations. Its efficiency with RA is well established. For a historical point of view, start searching "Coulomb_barrier", "Quantum Tunnelling" & "Gamov". Now, this newby question was the opportunity to oppose ( falsely ) the QM when it describes low or high measures ( ie atom level in labs vs RA of a mountain ). It would be also the beginning of a philosophical question about theory handling ... You know, there are a lot of beginners forums to ask such questions. If you get mad answers, just search for another one. Don't be sad if this page is filtered out in a few days ...
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