Nuclear binding energy is the energy released when protons and neutrons join to form a nucleus. It also equals the energy needed to pull that nucleus completely apart into separate nucleons. This idea matters because it explains why some nuclei are very stable while others can release energy through nuclear reactions.
The key clue is that a bound nucleus has slightly less mass than the total mass of its separate protons and neutrons.
Key Facts
- Mass defect: Δm = Zmp + Nmn - mnucleus
- Binding energy: Eb = Δmc^2
- Binding energy per nucleon: Eb/A, where A = Z + N
- Higher Eb/A usually means a more stable nucleus.
- The binding-energy-per-nucleon curve peaks near iron-56 and nickel-62 at about 8.8 MeV per nucleon.
- Fusion releases energy for light nuclei below iron, while fission releases energy for very heavy nuclei above iron.
Vocabulary
- Binding energy
- The energy required to separate a nucleus into its individual protons and neutrons.
- Mass defect
- The difference between the mass of separate nucleons and the smaller mass of the bound nucleus.
- Nucleon
- A proton or neutron found in an atomic nucleus.
- Binding energy per nucleon
- The total binding energy of a nucleus divided by the number of nucleons in that nucleus.
- Nuclear stability
- A measure of how strongly a nucleus is held together and how unlikely it is to change by radioactive decay or nuclear reaction.
Common Mistakes to Avoid
- Using atomic mass without accounting for electrons is wrong because nuclear binding energy refers to the nucleus, not the neutral atom unless electron masses are handled consistently.
- Thinking missing mass is destroyed is wrong because mass is converted into energy according to E = mc^2, conserving total mass-energy.
- Assuming the largest total binding energy means the most stable nucleus is wrong because stability is better compared using binding energy per nucleon.
- Saying fusion always releases energy is wrong because fusion releases energy mainly for nuclei lighter than iron, while fusion of heavier nuclei generally requires energy input.
Practice Questions
- 1 A nucleus has a mass defect of 0.030 u. Using 1 u = 931.5 MeV/c^2, calculate its binding energy in MeV.
- 2 An isotope has total binding energy 492 MeV and mass number A = 56. Calculate its binding energy per nucleon.
- 3 Use the binding-energy-per-nucleon curve to explain why fusing two light hydrogen isotopes can release energy, but fusing two iron nuclei would not release energy.