The binding energy per nucleon of B atomic number 5 and atomic mass 10 is 8.0 MeV and that of B atomic number 5 and atomic mass 11 is 7.5 MeV. The energy required to remove a neutron from B atomic number 5 and atomic mass 11 is:
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Nuclear binding energy is the energy holding the nucleus of an atom together. Binding energy per nucleon is the amount of energy needed to remove a neutron or proton from a nucleus. The binding energy per nucleon for a particular atom varies with the number of nucleons. The values given in this problem are averages per nucleon for two different isotopes of boron. The boron with a mass of 5 has 10 nucleons, consisting of five protons and five neutrons. The isotope with a mass of 11 has a total of 11 nucleons because it has an additional neutron.
The total binding energy for each atom is the average per nucleon times the number of nucleons:
(8.0 MeV/nucleon)(10 nucleons) = 80 MeV
(7.5 MeV/nucleon)(11 nucleons) = 82.5 MeV
In gaining a nucleon, the binding energy went up 2.5 MeV, so the binding energy of the eleventh nucleon is 2.5 MeV. That's how much energy would be required to remove a neutron from the Boron-11 atom.
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