Nuclear Physics Revision

Einstein's Mass-Energy Equivalence

• Equation: ∆E = ∆mc²
  • ∆E: Energy released or absorbed
  • ∆m: Change in mass
  • c: Speed of light (3.0 × 10⁸ m/s)
• Highlights the massive energy from small mass changes

Beta Decay Example

• Carbon-14 decays into Nitrogen-14 via beta-minus decay
• Emitted Particles: Electron (beta-minus) and an anti-neutrino
• Calculations:
  • Mass of carbon-14: 2.3253914 × 10⁻²⁶ kg
  • Mass of nitrogen-14: 2.3252723 × 10⁻²⁶ kg
  • Mass of electron: 9.10938356 × 10⁻³¹ kg
• Mass Change (∆m): -2.8 × 10⁻³¹ kg
• Energy Calculation (∆E): 2.52 × 10⁻¹⁴ J (using ∆m c²)

Electron-Positron Annihilation

• Produce two gamma-ray photons
• Total Mass: 2 times electron mass (9.11 × 10⁻³¹ kg)
• Energy (∆E): 8.2 × 10⁻¹⁴ J
• Photon Frequency (f): ∆E / h ≈ 1.24 × 10²⁰ Hz

Key Definitions

• Binding Energy: Energy required to separate nucleus into protons & neutrons
• Mass Defect: Difference between mass of separated nucleons and original nucleus
• Binding Energy Per Nucleon: Minimum energy to remove a nucleon
  • Calculated using E = ∆mc² / number of nucleons

Nuclear Fusion and Fission

• Fusion: Light nuclei combine to form a heavier nucleus
  • Requires high temperature and pressure
  • Releases more energy than fission
• Fission: Heavy nucleus splits into smaller nuclei
• Binding Energy Graph: (binding energy per nucleon vs nucleon number)
  • Most stable element: Iron (increases stability for fusion/fission)

Nuclear Fission Chain Reaction

• Slow thermal neutron absorbed -> unstable nucleus splits -> releases more neutrons
• Components of a Nuclear Reactor:
  • Fuel Rods: Contain uranium fuel
  • Control Rods: Absorb neutrons to control reaction rate
  • Moderator: Slows down neutrons (e.g., water)

Nuclear Fusion Conditions

• Requires high temperature and pressure to overcome electrostatic repulsion
• Example: Fusion in stars
• Probability of Fusion: Higher with higher temperature; affected by the charge and repulsion of involved particles (e.g., deuterium-tritium vs deuterium-helium)

Practice Problems & Examples

• Bind Energy Per Nucleon (Beryllium-8)
  • Mass defect calculated: 1.020 × 10⁻²⁸ kg
  • Binding energy: 9.18 × 10⁻¹² J
  • Binding energy per nucleon: ≈1.148 × 10⁻¹² J/nucleon

Next Steps

• Review the nuclear atom and strong nuclear force
• Revise beta plus and beta minus decay

Note: Refer to suggested revision videos for enhanced understanding.