Calculate the binding energy per nucleon for \({ }_{1}^{2} \mathrm{H}\) and \({ }_{1}^{3} \mathrm{H}\). The atomic masses are \({ }_{1}^{2} \mathrm{H}, 2.01410\), and \({ }_{1}^{3} \mathrm{H}, 3.01605\).

To find the mass defect for each isotope, we first need to determine the masses of individual protons and neutrons. The mass of a proton is approximately 1.00728 atomic mass units (amu), and the mass of a neutron is approximately 1.00867 amu. For deuterium (\({ }_{1}^{2} \mathrm{H}\)), there is 1 proton and 1 neutron in the nucleus. Therefore, the total mass of individual nucleons is: 1.00728 amu (proton) + 1.00867 amu (neutron) = 2.01595 amu The mass defect for deuterium is the difference between the mass of individual nucleons and the actual mass of the nucleus (given as 2.01410 amu): Mass Defect (Deuterium) = 2.01595 amu - 2.01410 amu = 0.00185 amu For tritium (\({ }_{1}^{3} \mathrm{H}\)), there is 1 proton and 2 neutrons in the nucleus. Therefore, the total mass of individual nucleons is: 1.00728 amu (proton) + 1.00867 amu (neutron) + 1.00867 amu (neutron) = 3.02462 amu The mass defect for tritium is the difference between the mass of individual nucleons and the actual mass of the nucleus (given as 3.01605 amu): Mass Defect (Tritium) = 3.02462 amu - 3.01605 amu = 0.00857 amu

To calculate the binding energy per nucleon, we need to divide the mass defect for each isotope by the total number of nucleons in the nucleus and then multiply by the speed of light squared (c^2). The conversion factor between amu and MeV is 931.5 MeV/c^2. For deuterium (\({ }_{1}^{2} \mathrm{H}\)), there are 2 nucleons in the nucleus. The binding energy per nucleon is: Binding Energy per Nucleon (Deuterium) = (0.00185 amu / 2) * 931.5 MeV/c^2 = 0.000925 amu * 931.5 MeV/c^2 = 0.8621 MeV For tritium (\({ }_{1}^{3} \mathrm{H}\)), there are 3 nucleons in the nucleus. The binding energy per nucleon is: Binding Energy per Nucleon (Tritium) = (0.00857 amu / 3) * 931.5 MeV/c^2 = 0.00285667 amu * 931.5 MeV/c^2 = 2.6631 MeV

We have now calculated the binding energy per nucleon for both deuterium and tritium: Binding Energy per Nucleon (Deuterium) = 0.8621 MeV Binding Energy per Nucleon (Tritium) = 2.6631 MeV