Final answer:
The minimum energy needed to separate the nucleons of 11B is the product of the binding energy per nucleon (7 MeV) and the number of nucleons (11), resulting in a total of 77 MeV.
Step-by-step explanation:
The binding energy per nucleon of an atomic nucleus is a measure of the energy required to separate the nucleus into its individual protons and neutrons. For the isotope 11B, with a binding energy of approximately 7 MeV per nucleon, we must first calculate the total binding energy by multiplying per nucleon value by the total number of nucleons (protons plus neutrons) in the nucleus.
In the case of 11B, there are 11 nucleons in total. Therefore, the total binding energy would be:
Total Binding Energy = Binding Energy per Nucleon x Number of Nucleons
Total Binding Energy = 7 MeV/nucleon x 11 nucleons
Total Binding Energy = 77 MeV
This represents the minimum energy needed to separate all the nucleons in the 11B nucleus.