13.2 Nuclear stability and the chart of nuclides

Nuclear stability is all about balance. It's like a tug-of-war between forces inside the atom's core. The chart of nuclides is our map, showing which atoms are stable and which are ready to break apart.

Understanding nuclear stability helps us predict how atoms behave. We'll look at what makes some atoms steady and others unstable, and how this fits into the bigger picture of nuclear reactions. It's like learning the rules of a cosmic game of stability.

Nuclear stability factors

Fundamental forces and ratios

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• Nuclear stability results from balance between strong nuclear force and electrostatic repulsion between protons
• Neutron-to-proton ratio (N/Z ratio) crucially influences nuclear stability
  • Stable nuclei have specific N/Z ratios varying with atomic number
• Binding energy per nucleon (B/A) measures nuclear stability
  • Higher B/A values indicate greater stability
• Semi-empirical mass formula (SEMF) predicts nuclear stability quantitatively
  • Considers various contributions to binding energy

Nuclear structure and stability

• Magic numbers (2, 8, 20, 28, 50, 82, 126) represent especially stable configurations of protons or neutrons
• Pairing effects contribute to nuclear stability
  • Even-even nuclei more stable than odd-odd nuclei
• Nuclear shell model explains stability through energy levels and orbital filling
  • Analogous to electron shell model in atomic physics
  • Helps explain magic numbers and enhanced stability

Chart of nuclides interpretation

Chart structure and features

• Chart of nuclides (Segrè chart) plots neutron number (N) against proton number (Z) for all known nuclides
• Stable nuclides form "valley of stability"
  • Curved path from light to heavy elements
• Radioactive nuclides flank valley of stability
  • Neutron-rich nuclides below, proton-rich above
• Chart includes information on half-lives, decay modes, nuclear cross-sections
• Isobars form diagonal lines (same mass number A)
• Isotopes form horizontal lines (same Z)
• Isotones form vertical lines (same N)

Stability patterns and limits

• Chart reveals nuclear stability patterns
  • Preference for even-even nuclei
  • Existence of magic numbers
• Proton and neutron drip lines represent stability limits
  • Boundaries beyond which nuclei become unstable to immediate particle emission
• Islands of stability appear on chart
  • Regions of enhanced stability due to shell closures or magic numbers

Nuclear stability prediction

Position-based stability assessment

• Nuclei near valley of stability center generally more stable
• N/Z ratio of stable nuclei increases with atomic number
  • Follows curved path on chart
• Magic number nuclei (protons, neutrons, or both) show enhanced stability
  • Form local islands of stability on chart
• Nuclides above stability line tend towards β+ decay or electron capture
• Nuclides below stability line tend towards β- decay

Heavy and superheavy elements

• Very heavy nuclei (Z > 83) generally unstable
  • Prone to α decay or spontaneous fission
• Island of stability concept predicts potentially stable superheavy elements
  • Region beyond currently known nuclides
• Proximity to proton or neutron drip lines indicates extreme instability
  • Susceptible to immediate particle emission

Stability trends across the periodic table

Light and medium elements

• Light elements (Z < 20) most stable when N ≈ Z
  • Forms nearly straight line on nuclide chart
• N/Z ratio for stable nuclei increases with atomic number
  • Due to growing electrostatic repulsion between protons
• Stable isotope number per element generally increases up to mid-mass region
  • Peaks around iron (Fe-56)
  • Fe-56 has highest binding energy per nucleon

Heavy elements and beyond

• Elements with odd atomic numbers typically have fewer stable isotopes
  • Due to pairing effects
• Beyond lead (Z = 82), no completely stable isotopes exist
  • All nuclei radioactive to some degree
• Superheavy elements (Z > 104) have extremely short half-lives
  • Theoretical predictions suggest possible island of stability around Z = 114 to 126