The Curve of Binding Energy
The foregoing conservation arguments do not indicate which nuclear
reactions are likely to be exothermic or endothermic. We must
examine mass defects and binding energies to understand which
nuclear reactions produce rather than absorb energy. If we add the
masses of the Z protons and N neutrons that make up a nucleus, say
of element X, we find that the weights of these constituent masses
exceed the weight MX of the nucleus as a whole. The difference is
defined as the mass defect:
which is positive for all nuclei. Thus the nucleus weighs less than the neutrons and protons from which it is composed. Multiplying the mass defect by the square of the speed of light then yields units of energy:
.
This is the binding energy of the nucleus. We may interpret it as follows. If the nucleus could be pulled apart and separated into its constituent protons and neutrons, there would be an increase in mass by an amount equal to the mass defect. Thus an equivalent amount of energy—the binding energy—would need to be expended to carry out this disassembly. All stable nuclei have positive binding energies holding them together. If we normalize the binding energy to the number of nucleons, we have
This quantity—the binding energy per nucleon—provides a measure of nuclear stability; the larger it is the more stable the nucleus will be.
Figure 1.1 is the curve of binding energy per nucleon. At low atomic mass the curve rises rapidly. For larger atomic weights, above 40 or so, the curve becomes quite smooth reaching a maximum of slightly less than 9MeV and then gradually decreases. Exothermic reactions are those in which result in reaction products with increased binding energy, going from less to more stable nuclei. Two classes of such reaction are candidates for energy
production: fusion reactions in which two light weight nuclei combine to form
a heaver nuclei, higher on the binding energy curve, and fission
reactions in which a heavy nucleus splits to form two lighter nuclei,
each with a higher binding energy per nucleon.
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reactions are likely to be exothermic or endothermic. We must
examine mass defects and binding energies to understand which
nuclear reactions produce rather than absorb energy. If we add the
masses of the Z protons and N neutrons that make up a nucleus, say
of element X, we find that the weights of these constituent masses
exceed the weight MX of the nucleus as a whole. The difference is
defined as the mass defect:
which is positive for all nuclei. Thus the nucleus weighs less than the neutrons and protons from which it is composed. Multiplying the mass defect by the square of the speed of light then yields units of energy:
.This is the binding energy of the nucleus. We may interpret it as follows. If the nucleus could be pulled apart and separated into its constituent protons and neutrons, there would be an increase in mass by an amount equal to the mass defect. Thus an equivalent amount of energy—the binding energy—would need to be expended to carry out this disassembly. All stable nuclei have positive binding energies holding them together. If we normalize the binding energy to the number of nucleons, we have
This quantity—the binding energy per nucleon—provides a measure of nuclear stability; the larger it is the more stable the nucleus will be.
Figure 1.1 is the curve of binding energy per nucleon. At low atomic mass the curve rises rapidly. For larger atomic weights, above 40 or so, the curve becomes quite smooth reaching a maximum of slightly less than 9MeV and then gradually decreases. Exothermic reactions are those in which result in reaction products with increased binding energy, going from less to more stable nuclei. Two classes of such reaction are candidates for energy
production: fusion reactions in which two light weight nuclei combine to form
a heaver nuclei, higher on the binding energy curve, and fission
reactions in which a heavy nucleus splits to form two lighter nuclei,
each with a higher binding energy per nucleon.
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