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.