Quantum Physics

29.2 Binding Energy 943130120110100Figure 29.3 A plot of the neutronnumber N versus the proton numberZ for the stable nuclei (solid points).The dashed straight line correspondsto the condition N Z. They arecentered on the so-called line ofstability. The shaded area showsradioactive (unstable) nuclei.Neutron number N9080706050N =Z4030201000 10 20 30 40 50 60 70 80 90Proton number Z29.2 BINDING ENERGYThe total mass of a nucleus is always less than the sum of the masses of its nucleons.Also, because mass is another manifestation of energy, the total energy of thebound system (the nucleus) is less than the combined energy of the separatednucleons. This difference in energy is called the binding energy of the nucleus andcan be thought of as the energy that must be added to a nucleus to break it apartinto its separated neutrons and protons.EXAMPLE 29.2GoalThe Binding Energy of the DeuteronCalculate the binding energy of a nucleus.Problem The nucleus of the deuterium atom, called the deuteron, consists of a proton and a neutron. Calculatethe deuteron’s binding energy in MeV, given that its atomic mass—that is, the mass of a deuterium nucleus plus anelectron—is 2.014 102 u.Strategy Calculate the sum of the masses of the individual particles and subtract the mass of the combined particle.The masses of the neutral atoms can be used instead of the nuclei because the electron masses cancel. Use thevalues from Table 29.4 or Table B of the appendix. The mass of an atom given in Appendix B includes the mass of Zelectrons, where Z is the atom’s atomic number.SolutionTo find the binding energy, first sum the masses of thehydrogen atom and neutron and subtract the mass ofthe deuteron:Convert this mass difference to its equivalent in MeV:m (m p m n ) m d (1.007 825 u 1.008 665 u) 2.014 102 u 0.002 388 u931.5 MeVE b (0.002 388 u)1 u2.224 MeVRemarks This result tells us that to separate a deuteron into a proton and a neutron, it’s necessary to add 2.224 MeVof energy to the deuteron to overcome the attractive nuclear force between the proton and the neutron. One way ofsupplying the deuteron with this energy is by bombarding it with energetic particles.