Binding energy per nucleon curve

Explaining the Binding Energy Curve (BEPN)

The curve of binding energy per nucleon can be divided into three main parts:

1] The steep slope at the start

2] The flat part close to the iron nucleus

3] A steady climb to the limit of natural elements


1] Here, as we go from hydrogen towards iron nuclei, BEPN increases as more nucleons are added and each contributes to the strong nuclear force, so binding the particles more strongly. Hydrogen with just one proton has a binding energy of zero; this is like a free mass far away from any other gravitational attracting body. Adding a neutron to make deuterium increases the binding energy as the strong nuclear force now comes into action. BEPN increases rapidly as particles are added, and this means that energy is being released. Adding nucleons to a nucleus is not easy, but happens in the extreme conditions found in the very hot ultra-dense cores of stars. This nuclear fusion is of course of a star’s energy output which keeps it hot and maintains the reaction. We can imagine nucleons and nuclei `falling downhill’ and converting potential energy (binding energy) to kinetic energy (`heat’) and radiation as they do.


2] Adding even more nucleons increases the binding forces but also increases the electrical repulsion effect as protons are added. This means that there comes a stage when adding more nucleons starts to decrease the BEPN. The turning point is iron, which has the greatest BEPN of all nuclides. No nucleons or nuclei can `fall’ further than iron, Just as it needs an input of energy to break up iron nucleus into smaller nuclei (going up the steep initial slope), it also needs an input of energy to create nuclei larger than iron (going up the shallower slope to the right).


3] The shallow riding slope is the effect of electrical repulsion (proton) beginning to have an increasing effect on the net force holding the nucleus together. So it is sometimes called the Coulomb slope. There is a tendency here for nuclei to fall down the slope towards iron by emitting a very stable unit – the helium nucleus, which has a high BEPN. It is emitted as the familiar alpha particle. Very large nuclei with a weak net binding force (low BEPN) can reach stability by simply falling apart. This is rare but can happen in large nuclei with an excess of neutrons (e.g. U-235) It can be stimulated by adding neutrons to the nucleus – which what happens in nuclear fission – in bombs and nuclear reactors.


All the nuclides to the right of iron on the graph have been made when stars have collapsed and subsequently exploded: the huge amounts of energy released have caused nuclei to fuse into heavy nuclei. All nucleons to the left of iron have been made as a consequence of the energy-producing nuclear fusion that keeps stars hot during their lifetime.


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