The isotope 62₂₈Ni has the largest binding energy per ...

Question

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.

Accepted Answer

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.. 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.. 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.. 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.. 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.

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.

Key Concepts

Binding Energy

Mass Defect

Atomic Mass Unit (amu)

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.

Key Concepts

Binding Energy

Mass Defect

Atomic Mass Unit (amu)

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.