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A radionuclide is an atom that has excess nuclear energy, making it unstable. This excess energy can be used in one of three ways: emitted from the nucleus as gamma radiation; transferred to one of its electrons to release it as a conversion electron; or used to create and emit a new particle from the nucleus. Wikipedia
The existence of isotopes contradicts part of Dalton's original atomic theory because he said all atoms of a given element are identical have the same mass size and chemical properties.
Radioactive isotopes are isotopes that undergo spontaneous decay to produce daughter nuclei.
According to John Dalton, atoms can neither be created nor destroyed. The implication of this is that we can not make any new element or nucleus.
However, with the discovery of radioactivity, we can now see that it is possible to create as many atoms of new elements as possible by means of radioactive decay of unstable nuclei.
Hence, from the phenomenon of radioactivity, we can see that atoms can be created against the ideas of John Dalton.
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