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I understand that greater binding energy per nucleon implies a more stable atom and atoms undergo nuclear fusion and fission to attain higher binding energy per nucleon. The binding energy per nucleon curve (https://en.wikipedia.org/wiki/File:Binding_energy_curve_-_common_isotopes.svg) shows that radioactive isotopes of hydrogen (deuterium and tritium) are more stable than hydrogen itself. Is this not incorrect? Is my assumption of greater binding energy per nucleon $=>$ more stable atom incorrect?

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$^1_1H$ is a special case as the proton does not have any other nucleons to bind onto. I suppose that you could call the binding energy per nucleon zero which means that you require no energy to split up the nucleus of $^1_1H$ into its constituent parts?

Note also that the binding energy per nucleon is not necessarily the full measure of whether a nucleus is stable or not.

$^2_1H$ has a binding energy per nucleon of 1.11 MeV and is a stable isotope of hydrogen whereas $^3_1H$ has a binding energy per nucleon of 2.83 MeV and is an unstable isotope of hydrogen with a half life of 12.32 years.

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