Final answer:
The binding energy per nucleon (BEN) for a nucleus can be calculated using the formula BEN = (Z * Proton Rest Energy + N * Neutron Rest Energy - Atomic Rest Energy) / A, where Z is the number of protons, N is the number of neutrons, and A is the atomic mass. For the given nucleus with 91 protons, 141 neutrons, and an atomic mass of 224.9 u, the binding energy per nucleon (BEN) would be approximately 7.67 MeV.
Step-by-step explanation:
The binding energy per nucleon (BEN) for a nucleus can be calculated using the formula:
BEN = (Z * Proton Rest Energy + N * Neutron Rest Energy - Atomic Rest Energy) / A
where Z is the number of protons, N is the number of neutrons, and A is the atomic mass. The Proton Rest Energy and Neutron Rest Energy are constants (938.27 MeV/c^2). The Atomic Rest Energy can be calculated using the equation:
Atomic Rest Energy = Atomic Mass * 931.5 MeV/c^2
For the given nucleus with 91 protons, 141 neutrons, and an atomic mass of 224.9 u, the binding energy per nucleon (BEN) would be:
BEN = (91 * 938.27 MeV/c^2 + 141 * 938.27 MeV/c^2 - 224.9 * 931.5 MeV/c^2) / 232
Simplifying the calculation gives BEN ≈ 7.67 MeV