Calculate the binding energy per nucleon of a) \({ }_{2}^{4} \mathrm{He}(4.002603 \mathrm{u})\). c) \({ }_{1}^{3} \mathrm{H}(3.016050 \mathrm{u})\) b) \({ }_{2}^{3} \mathrm{He}(3.016030 \mathrm{u}) .\) d) \({ }_{1}^{2} \mathrm{H}(2.014102 \mathrm{u})\).

To calculate the mass defect of each isotope, you need to subtract the total mass of the individual protons and neutrons from the actual mass of the isotope. The mass of a proton is 1.007276 u and the mass of a neutron is 1.008665 u. Step 2: Calculate the binding energy

To calculate the binding energy for each isotope, you will need to multiply the mass defect by the atomic mass unit conversion factor: 931.5 MeV/c\(^2\). Step 3: Calculate the binding energy per nucleon

To calculate the binding energy per nucleon, simply divide the binding energy by the total number of nucleons (A) in each isotope. a) For \({ }_{2}^{4} \mathrm{He}(4.002603 \mathrm{u})\): Mass defect = (2 x 1.007276 u + 2 x 1.008665 u) - 4.002603 u = 0.030682 u Binding energy = 0.030682 u × 931.5 MeV/c\(^2\) = 28.601 MeV Binding energy per nucleon = 28.601 MeV / 4 = 7.15025 MeV/nucleon b) For \({ }_{1}^{3} \mathrm{H}(3.016050 \mathrm{u})\): Mass defect = (1 x 1.007276 u + 2 x 1.008665 u) - 3.016050 u = 0.008556 u Binding energy = 0.008556 u × 931.5 MeV/c\(^2\) = 7.972 MeV Binding energy per nucleon = 7.972 MeV / 3 = 2.657333 MeV/nucleon c) For \({ }_{2}^{3} \mathrm{He}(3.016030 \mathrm{u})\): Mass defect = (2 x 1.007276 u + 1 x 1.008665 u) - 3.016030 u = 0.006463 u Binding energy = 0.006463 u × 931.5 MeV/c\(^2\) = 6.021 MeV Binding energy per nucleon = 6.021 MeV / 3 = 2.007 MeV/nucleon d) For \({ }_{1}^{2} \mathrm{H}(2.014102 \mathrm{u})\): Mass defect = (1 x 1.007276 u + 1 x 1.008665 u) - 2.014102 u = 0.001839 u Binding energy = 0.001839 u × 931.5 MeV/c\(^2\) = 1.713 MeV Binding energy per nucleon = 1.713 MeV / 2 = 0.8565 MeV/nucleon