The curve of binding energy


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For Reaction And Binding Energies and Activity Calculations in Nuclear Physics

The process of combining protons to form helium is an example of nuclear fusion. Our oceans have plenty of hydrogen, and helium does not harm the environment, so it would be great if physicists could harness nuclear fusion to provide the world with energy.

Experiments in that direction have so far come up short. Sufficiently hot hydrogen will also be ionized, and to confine it, very strong magnetic fields have been used, because charged particles like those trapped in the Earth's radiation belt are guided by magnetic field lines.


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Fusion experiments also rely on heavy hydrogen which fuses more easily, and gas densities have been kept moderate. In spite of all such tricks, though fusion energy has been released, so far more energy is consumed by the apparatus then is yielded by the process. In the main isotopes of light nuclei, such as carbon, nitrogen and oxygen, the number of neutrons and of protons is indeed equal.

However, as we move to heavier nuclei, the disruptive energy of protons increases, since they are confined to a tiny volume and repel each other.

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The energy of the strong force holding the nucleus together also increases, but at a slower rate, as if inside the nucleus, only nucleons close to each other are tightly bound, not ones more widely separated. The net binding energy of a nucleus is that of the nuclear attraction, minus the disruptive energy of the electric force.


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As nuclei get heavier than helium, their net binding energy per nucleon deduced from the difference in mass between the nucleus and the sum of masses of component nucleons grows more and more slowly, reaching its peak at iron. As nucleons are added, the total nuclear binding energy always increases--but the total disruptive energy of electric forces positive protons repelling other protons also increases, and past iron, the second increase outweighs the first.

One may say 56 Fe is the most efficiently bound nucleus. To reduce the disruptive energy, the weak interaction allows the number of neutrons to exceed that of protons--for instance, in the main isotope of iron, 26 protons but 30 neutrons.

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Of course, isotopes also exist where the number of neutrons differs, but if these are too far from stability, after some time nucleons convert to a more stable isotope by beta emission radioactivity --protons turn into neutrons by dragging in an electron or emitting a positron , the positive counterpart of the electron , or neutrons become protons by emitting electrons. Among the heaviest nuclei, containing or more nucleons, electric forces may be so destabilizing that entire chunks of the nucleus get ejected, usually in combinations of 2 protons and 2 neutrons " alpha particles ," actually fast helium nuclei which are an extremely stable combination.

The curve of binding energy drawing plots binding energy per nucleon against atomic mass. It has its main peak at iron and then slowly decreases again, and also a narrow isolated peak at helium, which as noted is very stable.

The Curve Of Binding Energy by McPhee, John

The heaviest nuclei in nature, uranium U , are unstable, but having a lifetime of 4. In each of these, radioactive decay produces "daughter isotopes" which are also unstable, starting a chain of decays which ends in some stable isotope of lead. Site Map. Central Home Page.

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Note: This is part 2 of an overview of nuclear energy, longer and more detailed than the one in section S It was prepared by David P. Stern as part of the Virginia Flexbook on Physics prepared under auspices of the CK foundation, under the "creative commons, cite by attribution, share alike" protocol.

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It was meant to serve as supplemental text for high school physics. It also includes problems and questions. Index S Solar Layers S Binding energy curve average binding energy per nucleon in MeV against number of nucleons in nucleus for a number of relatively common abundant isotopes not chosen systematically; almost anything with an occurence of over. A few important ones for the purposes of nuclear fusion and nuclear fission are marked, as well as iron, which sits at the highest point on this graph and cannot yield energy from fusion or fission.

Nuclear Binding Energy Per Nucleon & Mass Defect Problems - Nuclear Chemistry

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