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Nuclear Binding Energy Overview

Aug 14, 2025

Overview

This lecture introduces the concept of binding energy in atomic nuclei, explaining mass defect, energy conversion, and the stability of elements using key equations and examples.

Energy Units: Joules and Electron Volts

  • 1 electron volt (eV) is the energy gained by an electron accelerated by 1 volt; 1 eV = 1.602 × 10⁻¹⁹ joules (J).
  • To convert eV to J, multiply by 1.6 × 10⁻¹⁹; to convert J to eV, divide by 1.6 × 10⁻¹⁹.
  • Joules are used for larger energies; electron volts are used for very small energies.

Atomic Mass Unit (amu) and Mass-Energy Equivalence

  • Atomic mass unit (amu or u) is used in nuclear physics instead of kilograms.
  • 1 amu = 1.6605 × 10⁻²⁷ kg.
  • Masses of subatomic particles: proton ≈ 1.00728 u, neutron ≈ 1.00867 u, electron ≈ 0.00055 u.
  • Mass-energy equivalence: E = mc² allows conversion of mass to energy.
  • 1 u = 931.5 MeV (million electron volts, or mega electron volts) of energy.

Binding Energy and Mass Defect

  • Mass defect is the difference between the summed masses of separate nucleons and the actual mass of the nucleus.
  • Binding energy is the energy required to hold the nucleus together, equal to the mass defect converted using E = mc².
  • Example: Chlorine atom’s measured mass is less than the mass of its individual protons, neutrons, and electrons; the difference is the binding energy.

Binding Energy per Nucleon and Nuclear Stability

  • Binding energy per nucleon = total binding energy divided by number of nucleons.
  • Greater binding energy per nucleon indicates a more stable nucleus.
  • The graph of binding energy per nucleon versus mass number peaks at iron (Fe), indicating maximum stability.
  • Small nuclei fuse to form larger ones (fusion), releasing energy; large nuclei split into smaller ones (fission), also releasing energy.

Key Terms & Definitions

  • Binding Energy — Energy required to hold the nucleus of an atom together.
  • Mass Defect — Difference between the mass of a nucleus and the sum of its individual nucleons’ masses.
  • amu (atomic mass unit) — Standard unit of mass in nuclear physics; 1 amu = 1.6605 × 10⁻²⁷ kg.
  • Electron Volt (eV) — A small unit of energy used in atomic and nuclear physics; 1 eV = 1.602 × 10⁻¹⁹ J.
  • Binding Energy per Nucleon — Binding energy divided by the number of nucleons; measures stability.
  • Fusion — Process where light nuclei combine to form a heavier nucleus, releasing energy.
  • Fission — Process where a heavy nucleus splits into lighter nuclei, releasing energy.

Action Items / Next Steps

  • Review the scanned notes and PowerPoint slides.
  • Prepare for numericals on binding energy and mass defect in the next class.
  • Remember the mass defect percentage formula: (initial mass – final mass) / initial mass × 100.