Introduction to GAMOS Theory of Alpha Decay and Giger-Nuttal Law

Overview of Alpha Decay

• Definition: A spontaneous radioactive decay process where a large nucleus (mass number > 210) emits an alpha particle.
• Alpha Particle: A helium nucleus consisting of 2 protons and 2 neutrons (mass number = 4).

Why Does Alpha Decay Occur?

• Nuclear Forces:
  • Attractive force between neutrons and protons.
  • Coulombic force: A repulsive force acting between protons.
• Stability of Nuclei:
  • Small and medium nuclei have stable configurations due to dominant nuclear forces at small distances (1-3 femtometers).
  • Large nuclei experience overpowering Coulombic repulsion as distances between nucleons increase, leading to instability.
• Decay Process: Large nuclei lose protons and neutrons to stabilize (alpha decay).

Kinetic Energy of Alpha Particles

• Range: Typical kinetic energy of emitted alpha particles ranges from 4 to 9 mega electron volts (MeV).
• Energy vs. Potential Height:
  • Potential height for nuclear configurations: 25 to 30 MeV.
  • Puzzles arise: How can alpha particles escape potential barriers higher than their kinetic energy?

Quantum Tunneling Explanation

• Classical Analogy:
  • Example of throwing a chalk upwards: It must exceed escape velocity to leave Earth's gravitational influence.
  • If the chalk escapes despite insufficient energy, it seems puzzling.
• Quantum Mechanics:

  • Quantum tunneling allows particles to penetrate barriers that exceed their kinetic energy.

  • Probability of tunneling: Given by the formula:

    [ T \propto e^{-2kL} \text{ , where } k = \sqrt{\frac{2m(V - E)}{\hbar^2}} ]

  • The alpha particle can escape due to wave behavior and tunneling probability.

GAMOS Theory of Alpha Decay

• Application of Quantum Tunneling:
  • Gamow applied quantum tunneling to explain alpha decay.
  • Alpha particle in a potential well has a probability of escaping even if its energy is less than the potential height.

Relationship to Giger-Nuttal Law

• Comparison of Alpha Particles:
  • Different kinetic energies (E1 and E2) lead to different tunneling probabilities.
  • Higher energy alpha particles have increased transmission probability and shorter half-lives.
• Conclusions:
  • Higher half-life correlates to lower kinetic energy alpha particles.
  • Lower half-life correlates to higher kinetic energy alpha particles.

Giger-Nuttal Law

• Experimental Evidence:
  • Plotting logarithm of half-life against square root of kinetic energy shows proportional relationship.
  • Formula: [ \log_{10}(t_{1/2}) = \frac{Z}{\sqrt{E}} + C ] (where Z = atomic number, E = kinetic energy)
• Implications:
  • Experimental observations validate GAMOS theory and quantum tunneling.

Conclusion

• Summary: GAMOS theory explains alpha decay through quantum tunneling while the Giger-Nuttal law provides experimental validation.
• Next Steps: In the next video, a derivation of Giger-Nuttal law from quantum tunneling will be provided.