Lecture Notes: Nuclear Stability and Mass Parabolas

Introduction

• Lecture is ahead of schedule.
• Focus: Mass parabolas and nuclear stability.
• Time after class for questions will be allocated.

Review of Previous Material

• Semi-empirical mass formula: volume, surface, Coulomb, asymmetry, and pairing terms.
  • Coefficients in MeV from data.
• Nuclear Stability
  • Intuition: nucleus as a charged liquid drop.
  • Stability affected by neutron-proton balance.
  • Binding energy insights from theory vs. experiment.

Nuclear Stability Trends

• Odd vs. Even Mass Nuclei
  • Odd mass nuclei usually have fewer stable isotopes.
  • Even mass nuclei often more stable.
• Magic Numbers
  • Numbers of protons/neutrons that offer stability.

Mass Parabolas

• Mathematical derivation of semi-empirical mass formula.
• Graphing stability:
  • Example: A = 93 (Niobium stable isotope).
  • Mass parabolas: used for predicting nuclear decay paths.
• Decay Modes:
  • Positron emission vs. beta decay.
  • Energy considerations for decay modes.

Decay Energy and Stability

• Q-Value: Minimum energy for certain decay to occur (e.g., 1.022 MeV for positron decay).
• Decay Chains
  • Examples: Niobium 93, Potassium 40.
  • Stable isotopes at certain parabolic points, decay by various modes like beta or electron capture.

Analysis of Nuclear Charts and Examples

• Table of Nuclides
  • Visual representation of decay paths.
  • Stability and decay trends observed across elements.
• Practical Examples
  • Examination of stability using isotopes like Niobium 93, Potassium 40, and others.

Advanced Concepts

• Super Heavy Elements
  • Prediction of new elements and islands of stability.
  • Current research methods and what future elements might bring.

Open-Ended Discussion

• Problem-solving approaches:
  • Modifying semi-empirical mass formula for stability predictions.
  • Considerations of binding energy and half-life.

Questions and Clarifications

• Open floor for questions about complexity, stability, and applications.

Key Learning Points

• Understanding semi-empirical mass formula: Its components and applications.
• Interpreting mass parabolas: Predicting stability and decay modes.
• Recognizing trends: Odd vs. even nuclei stability, magic numbers.
• Future insights: Predicting super-heavy elements and their implications.