# How does the binding energy per nucleon of a nucleus affect its stability?

## Main Question or Discussion Point

How does the binding energy per nucleon of a nucleus affect its stability?

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As far as I was aware the higher the binding energy of a nucleus the more stable it was. Consequently I would guess that the higher the binding energy per nucleon the more stable it is. However nuclear physics isn't my strongest subject, so I could be off the mark.

I think so too, Barny.

But does any one know the reason for this?

I am assuming that binding energy means the amount of energy gained from putting nucleons together in a nucleus. I am not completely sure of the correct terminology.

If a nucleus has a higher binding energy per nucleon, that also means you need more energy per nucleon to get the nucleons away from eachother again. Basically, the higher the binding energy per nucleon, the more energy per nucleon you need to tear the nucleus apart, so the nucleus is more stable.

pam
How does the binding energy per nucleon of a nucleus affect its stability?
It is not necessarily the BE per nucleon that determines stability, but rather the difference in masses between an nucleus and possible decay products.

How does the binding energy per nucleon of a nucleus affect its stability?
The number of nucleons (summed over all particles) is conserved in a reaction. Reaction can only run against products with lower energies, this means against products with higher average binding energies.

It is not necessarily the BE per nucleon that determines stability, but rather the difference in masses between an nucleus and possible decay products.
Yes that's correct, but according to the semi-emperical mass formula (see e.g. http://en.wikipedia.org/wiki/Liquid_drop_model" [Broken])
A higher binding-energy gives a lower mass (energy) and hence a more stable nucleus.

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pam
and hence a more stable nucleus.
But the "hence" depends on the masses of possible decay nuclei.
Beta decay can be from a nucleus with greater BE per nucleon than the decay product.

Astronuc
Staff Emeritus
Here is a nice summary of binding energy
http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html

Binding energy per nucleon is the energy required to be put into the nucleus to disassociate the nucleus into it's nucleon consitutents. Taking the mass of Z protons and N neutrons, then subtracting the mass A of the nucleus containing Z protons and N neutrons, and applying Einstein's equation E = mc2, i.e. converting mass into its energy equivalence gives the binding eneryg. Dividing the total binding energy by the number of nucleons gives BE/nucleon, which is an average value.

There are also concepts such as binding energy of the last nucleon.

When a neutron is absorbed by a nucleus, in most cases, a gamma ray is emitted, and that gamma represents the binding energy. It's somewhat analogous to the heat of combustion, e.g. when a hydrocarbon CxHy + zO2-> a CO2 + H2O + heat (kinetic energy) + EM.

In fusion for instance, 2 nuclei combine (usually the lightest elements), reconfigure, and 2 new nuclei (with high binding energy per nucleon), and the energy released, i.e. the kinetic energy of the two nuclei is related to the difference (binding energy) of the sum of the masses of the parent nuclei (reactants) minus the sum of the masses of daughter nuclei (products).