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For a given isotope, one can obtain the binding energy using the semi-empirical mass formula.

For example, From Codecogs has a binding energy of 1782.8 MeV. From this information, how can the likelihood of the isotopes stability be found?

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From the binding energy given experimentally, using precise QM calculations or using a given formula, one should first check for "stability in particles", if the binding is negative, you will of course not have stability.

Then the next thing, if you have a formula, is to check for each type of stability. For example, to check for stability against a given fission, calculate the binding energy of the fragments, obtain the new energy and compare.

To check for, let's say a beta minus, replace the nucleus (A,Z) in the formula by (A,Z+1), obtain the binding energy, the new total energy (you can safely neglect the mass of the neutrino and even the one of the electron in most cases) and compare.

For your specific example, this is a bit tricky because a large variety of decay channels are potentially allowed.

Edit

Another way to proceed is to look at a binding energy per nucleon or mass excess against A diagram:

binding energy

We can see that 237Np is far on the right as a binding energy per nucleon smaller that the most stable elements like 56Fe.

One can then conclude that 237Np can potentially decay to a more stable element to increase it's binding energy (although these decay, that can be alpha decay can have excessively small probability and a time constant excessively long).

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Good answer Cedric, but I wasn't referring to the possible decay channels of 237Np, I was referring to 237Np itself. The answer I was looking for should be a lot less complex and has to do with the binding energy per nucleon. –  Geodesic Nov 3 '10 at 0:41
    
@Geodesic: If it is not my edit then I don't understand the question. –  Cedric H. Nov 3 '10 at 0:48
    
Spot on! Thanks. –  Geodesic Nov 3 '10 at 0:57

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