Final answer:
The binding energy per nucleon for 56Fe is 8.79 MeV/nucleon. This is calculated by deriving the mass defect from the atomic mass and nucleons' masses, converting it into MeV, and dividing by the total number of nucleons.
Step-by-step explanation:
The binding energy per nucleon for 56Fe can be calculated using its atomic mass and the mass defect formula. The mass defect (Δm) is the difference between the total mass of the separate nucleons and the mass of the nucleus. It's expressed as Δm = (ZmH + Nmn) - mnucl, where Z is the number of protons, mH is the mass of a hydrogen atom (approximated as the proton mass), N is the number of neutrons, mn is the neutron mass, and mnucl is the mass of the nuclide.
The nuclear binding energy (BE) can then be calculated by converting the mass defect from atomic mass units (amu) to megaelectronvolts (MeV) using the conversion factor 1 amu = 931 MeV. Once we have the total binding energy, we divide by the number of nucleons (protons + neutrons) to find the binding energy per nucleon.
In this case, the mass difference between the nucleons' total mass and the atomic mass of 55.9349 amu for 56Fe is 0.528462 amu. Converting this to MeV, we have 0.528462 amu × 931 MeV/amu = 492 MeV for the total nuclear binding energy. Dividing by the number of nucleons (56), we get 492 MeV/56 nucleons = 8.79 MeV/nucleon.