When bonds are formed between nucleons, the energy released is called the binding energy. This means that the mass of the nucleus is less than the mass of the separate nucleons. The relationship between this mass difference or mass defect is that energy released:E = Δmc2 The mass defect Δm of a nucleus is the difference between the mass of the separate nucleons and the mass of the nucleus.The binding energy of the nucleus is the work done to separate the nucleus into its constituent nucleons.Binding energy per nucleon is a measure of stability of the nucleus and increases in both nuclear fission and fusion.
Worked ExampleCalculate the binding energy of a bismuth-212 nucleus in MeV.mass of a proton =1.00728umass of a neutron =1.00867umass of a bismuth-212 nucleus =211.80012uatomic number of bismuth is 831u=931.5MeV Solutionmass defect Δm = 83(1.00728)+(212-83)(1.00867)-211.80012=1.92255uConverting this to MeV by multiplying by 931.5binding energy = 1.92255 ×931.5 = 1790MeV
Worked ExampleCalculate the binding energy of a bismuth-212 nucleus in MeV.mass of a proton =1.00728umass of a neutron =1.00867umass of a bismuth-212 nucleus =211.80012uatomic number of bismuth is 831u=931.5MeV Solutionmass defect Δm = 83(1.00728)+(212-83)(1.00867)-211.80012=1.92255uConverting this to MeV by multiplying by 931.5binding energy = 1.92255 ×931.5 = 1790MeV