Nuclear Energy: Mass Defect, Binding Energy, Fission and Fusion
Einstein’s mass-energy equivalence E = mc², atomic mass unit u, mass defect Δm, binding energy per nucleon curve, nuclear stability, nuclear fission chain reactions, and thermonuclear fusion.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Calculate nuclear mass defect Δm and binding energy E_b in MeV for various nuclides.
- Analyze the binding energy per nucleon curve to explain why fission releases energy for heavy nuclei and fusion releases energy for light nuclei.
Core Theory & Concepts
The mass of an assembled atomic nucleus is always strictly less than the total mass of its individual constituent free protons and neutrons. This missing mass—the mass defect Δm—is released as binding energy when the nucleus forms according to Einstein’s E = mc².
Mass Defect & Binding Energy
For a nucleus with atomic number Z and mass number A: Δm = [Z m_p + (A - Z) m_n] - M_nucleus. Total binding energy is E_b = Δm c² = Δm (in u) × 931.5 MeV.
Binding Energy per Nucleon Curve
Plot of E_b/A versus mass number A rises steeply from hydrogen, peaks near ⁵⁶Fe at ≈ 8.8 MeV/nucleon, and gradually decreases for heavy elements to ≈ 7.6 MeV/nucleon for Uranium. Fission of heavy nuclei and fusion of light nuclei both move toward the stable ⁵⁶Fe peak, releasing massive kinetic energy.
Common Misconceptions
A nucleus has more mass than its separated constituent protons and neutrons.
Syllabus Topic Outline
- 1Atomic mass unit u = 1.6605 × 10⁻²⁷ kg and energy equivalent 1 u = 931.5 MeV
- 2Nuclear mass defect Δm = [Z m_p + (A - Z) m_n] - M_nucleus
- 3Binding energy E_b = Δm c² and binding energy per nucleon (E_b / A)
- 4The E_b / A curve: peak at Iron-56 (8.8 MeV/nucleon), stability peak
- 5Induced nuclear fission of Uranium-235: chain reactions and moderator function
- 6Nuclear fusion: stellar proton-proton chain and tokamak plasma conditions