Nuclear Binding Energy

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  • Find the composition of the copper-63 nucleus and determine the combined mass of its components.

    • Copper has 29 protons and copper-63 also has (63 - 29) 34 neutrons. The mass of a proton is 1.00728 amu and a neutron is 1.00867 amu.The combined mass is calculated:

    29 protons(1.00728 amu/proton) + 34 neutrons(1.00867 amu/neutron) or 63.50590 amu

  • Calculate the mass defect.

    • Dm = 63.50590 amu - 62.91367 amu = 0.59223 amu

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    Conversion of Mass Defect into Energy

    To convert the mass defect into energy:

    • Convert the mass defect into kilograms (1 amu = 1.6606 x 10-27 kg)
    • Convert the mass defect into its energy equivalent using Einstein's equation.
    Example: Determine the binding energy of the copper-63 atom.
    • Convert the mass defect (calculated in the previous example) into kg.
    (0.59223 amu/nucleus)(1.6606 x 10-27 kg/amu) = 9.8346 x 10-28 kg/nucleus
    • Convert this mass into energy using DE = Dmc2, where c = 2.9979 x 108 m/s.
    E = (9.8346 x 10-28 kg/nucleus)(2.9979 x 108 m/s)2 = 8.8387 x 10-11 J/nucleus

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    Expressing Nuclear Binding Energy as Energy per Mole of Atoms, or as Energy per Nucleon

    The energy calculated in the previous example is the nuclear binding energy. However, nuclear binding energy is often expressed as kJ/mol of nuclei or as MeV/nucleon.

    • To convert the energy to kJ/mol of nuclei we will simply employ the conversion factors for converting joules into kilojoules (1 kJ = 1000 J) and for converting individual particles into moles of particles (Avogadro's Number).
    (8.8387 x 10-11 J/nucleus)(1 kJ/1000 J)(6.022 x 1023 nuclei/mol) = 5.3227 x 1010 kJ/mol of nuclei
    • To convert the binding energy to MeV (megaelectron volts) per nucleon we will employ the conversion factor for converting joules into MeV (1 MeV = 1.602 x 10-13 J) and the number of nucleons (protons and neutrons) which make up the nucleus.
    (8.8387 x 10-11 J/nucleus)[1 MeV/(1.602 x 10-13 J)](1 nucleus/63 nucleons) = 8.758 MeV/nucleon

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