The isotope 62₂₈Ni has the largest binding energy per nucleon of any isotope. Calculate this value from the atomic mass of nickel-62 (61.928345 amu) and compare it with the value given for iron-56 in Table 21.7.

Verified step by step guidance

1. Step 1: Understand the concept of binding energy per nucleon. Binding energy is the energy required to disassemble a nucleus into its component protons and neutrons. The binding energy per nucleon is the total binding energy divided by the number of nucleons in the nucleus.
2. Step 2: Calculate the mass defect for nickel-62. The mass defect is the difference between the mass of the completely separated nucleons and the mass of the nucleus. Use the formula: \( \Delta m = Zm_p + Nm_n - m_{\text{nucleus}} \), where \( Z \) is the number of protons, \( N \) is the number of neutrons, \( m_p \) is the mass of a proton, \( m_n \) is the mass of a neutron, and \( m_{\text{nucleus}} \) is the atomic mass of the isotope.
3. Step 3: Convert the mass defect from atomic mass units (amu) to energy using Einstein’s equation \( E = \Delta mc^2 \), where \( c \) is the speed of light. Note that 1 amu is equivalent to 931.5 MeV/c^2.
4. Step 4: Calculate the binding energy per nucleon by dividing the total binding energy by the number of nucleons in nickel-62. The number of nucleons is the sum of protons and neutrons, which is 62 for nickel-62.
5. Step 5: Compare the calculated binding energy per nucleon for nickel-62 with the value given for iron-56 in Table 21.7. This comparison will help you understand why nickel-62 has the largest binding energy per nucleon.