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Binding energy

The basic building blocks of atoms are protons neutrons and electrons. Protons and neutrons can be split into quarks but this takes place at energies higher than are found in stars.

atomic Binding Energy Graph
The binding energy of atomic nuclei plotted against the atomic number of the nuclei. Energy is released by the fusion of light elements into heavier elements (elements on the left) or the fission of heavy elements into lighter elements (elements on the right). Iron is the highest element on the graph, and the most stable. It cannot release energy through either fusion or fission.
Protons carry a positive charge and reside with neutrons in the nucleus of an atom. At room temperature the atom contains the same number of electrons as there are protons in the nucleus, which makes the atom electrically neutral. It is the electrons that define the physical and chemical properties of the elements as we experience them on Earth. An atom of hydrogen has one proton and one orbiting electron while an atom of iron-56 has 26 electrons surrounding a nucleus containing 26 protons and 30 neutrons. The normal notation is 56Fe. It is the number of protons that defines the identity of an element. For each element the number of neutrons can vary and atoms with the same number of protons but differing numbers of neutrons are referred to as isotopes. For example iron has stable isotopes with 28, 30 and 31 neutrons.

The neutrons and protons are held together in the nucleus by the 'strong force'. The strong force only acts over very small distances but is able to overcome the electrostatic repulsion between protons. The most tightly bound nuclei are those close to iron in the periodic table of elements. The tightness of this binding is measured by the binding energy per nucleon where 'nucleon' is a collective name for neutrons and protons. It is also sometimes called the mass defect per nucleon. This reflects the fact that the total mass of the nucleus is less than the sum of the mass of the individual neutrons and protons that formed the nucleus. The difference in mass is equivalent to the energy released in forming the nucleus. The graph plots binding energy as a function of atomic number or number of nucleons per atom. The general decrease in binding energy beyond iron is caused by the fact that, as the nucleus gets bigger, the ability of the strong force to counteract the electrostatic force between the protons becomes weaker. The peaks in binding energy at 4,8,16 and 24 nucleons is a consequence of the great stability of helium-4 a combination of two protons and two neutrons. The maximum binding energy at iron means that elements lighter than iron release energy when fused. This is the source of energy in stars and hydrogen bombs. From the graph it can be seen that the greatest release of energy occurs fusing hydrogen to form helium.

Elements heavier than iron only release energy when split, as was the case with the plutonium and uranium used in the first atomic bombs. Elements heavier than iron are made in stars by capturing neutrons onto atomic nuclei. This takes place in some red giants and in supernovae explosions. A new isotope is created when an atom captures a neutron. If this isotope is unstable then a neutron can convert into a proton, releasing an electron. This is called beta decay and is a form of radioactive decay also observed on Earth. By converting a neutron into a proton the atom has increased its atomic number by one and become the adjacent element in the periodic table. It may then capture another neutron, and so on, so that using iron as seed nuclei it is possible to build all the elements heavier than iron in the periodic table.

The difference between element synthesis in red giants and supernovae is that in supernovae the flux of neutrons is greater and it is possible for the atom to capture a second, or third neutron, before it has a chance to beta-decay. This leads to the production of a different set of elements to those produced in red giants, where the flux of neutrons is much less.

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