The most stable nucleus in terms of binding energy per nucleon is \({ }^{56} \mathrm{Fe}\). If the atomic mass of \({ }^{56} \mathrm{Fe}\) is \(55.9349 \mathrm{u}\), calculate the binding energy per nucleon for \({ }^{56} \mathrm{Fe}\).

The mass defect is the difference between the mass of the separated nucleons and the actual mass of the nucleus. Since there are 56 nucleons in \({ }^{56}\mathrm{Fe}\), there are 26 protons and 30 neutrons. The mass of a proton is approximately 1.007276 u and the mass of a neutron is about 1.008665 u. We can calculate the mass defect using the following formula: Mass defect = (Number of protons × Mass of a proton) + (Number of neutrons × Mass of a neutron) - Actual mass of the nucleus Mass defect = (26 × 1.007276 u) + (30 × 1.008665 u) - 55.9349 u

We can convert the mass defect into energy using Einstein's famous equation \(E=mc^2\), where \(E\) is the energy, \(m\) is the mass, and \(c\) is the speed of light in a vacuum (approximately \(3 \times 10^8 \, \text{m/s}\)). But first, we need to convert the mass defect from atomic mass units (u) to kilograms (kg). 1 atomic mass unit (u) is approximately equal to \(1.6605 \times 10^{-27}\) kg. Thus, we can convert the mass defect into kilograms: Mass defect (in kg) = Mass defect (in u) × \(1.6605 \times 10^{-27}\mathrm{kg/u}\) Now, we can substitute the mass defect in kg into the Einstein's equation to calculate the total binding energy: Total Binding energy = Mass defect (in kg) × \((3 \times 10^8 \, \text{m/s})^2\)

To find the binding energy per nucleon, we divide the total binding energy by the number of nucleons (56 for \({ }^{56}\mathrm{Fe}\)): Binding energy per nucleon = Total Binding energy / 56 After calculating each step, we will obtain the binding energy per nucleon for \({ }^{56}\mathrm{Fe}\).