Nuclear stability is all about the delicate balance of protons and neutrons in an atom's core. As elements get heavier, they need more neutrons to stay stable. This balance is key to understanding how atoms behave and change.

The chart of nuclides is like a map of all known atomic nuclei. It shows which combinations of protons and neutrons make stable atoms and which ones decay. This visual tool helps scientists predict and study nuclear behavior.

Nuclear Stability

Stability Belt and Neutron-to-Proton Ratio

• Stability belt represents region of stable nuclides on chart of nuclides
• Follows diagonal line from lighter to heavier elements
• Neutron-to-proton ratio increases as atomic number increases
• For lighter elements (Z < 20), stable nuclei have approximately equal numbers of protons and neutrons
• Heavier stable nuclei require more neutrons than protons to counteract electrostatic repulsion
• Neutron-to-proton ratio for stable heavy nuclei approaches 1.5

Decay Processes for Unstable Nuclei

• Beta decay occurs when nucleus has excess neutrons or protons
• Beta minus (β-) decay converts neutron to proton, emits electron and antineutrino
• Beta plus (β+) decay converts proton to neutron, emits positron and neutrino
• Alpha decay involves emission of helium-4 nucleus (two protons and two neutrons)
• Typically observed in heavy nuclei with atomic number greater than 82 (lead)
• Spontaneous fission splits heavy nucleus into two or more lighter nuclei
• Occurs in very heavy elements (atomic number > 90)
• Releases neutrons and significant energy

Chart of Nuclides

Structure and Organization of the Chart

• Chart of nuclides graphically represents all known nuclides
• Horizontal axis shows number of neutrons (N)
• Vertical axis shows number of protons (Z)
• Each square represents a specific nuclide with given Z and N
• Color-coding indicates stability and decay modes (black for stable, others for various decay types)
• Provides visual representation of nuclear landscape and trends in stability

Island of Stability and Nuclear Shell Model

• Island of stability refers to predicted region of superheavy elements with increased stability
• Located beyond currently known elements on chart of nuclides
• Based on nuclear shell model and magic numbers of protons and neutrons
• Magic numbers (2, 8, 20, 28, 50, 82, 126) correspond to filled nuclear shells
• Nuclei with magic numbers of protons or neutrons exhibit enhanced stability
• Predicted island centered around elements with proton numbers near 114, 120, or 126

Binding Energy and Nuclear Stability

• Binding energy per nucleon (B/A) measures average energy required to remove a nucleon from nucleus
• Calculated using mass defect and Einstein's mass-energy equivalence ($E = mc^2$)
• Plotted against mass number (A) reveals characteristic curve
• Peak of curve occurs around iron (Fe-56), indicating most stable nuclei
• Explains trends in nuclear stability and energy release in fusion and fission reactions
• Higher B/A values indicate greater nuclear stability

Radioactive Decay

Decay Chains and Modes of Decay

• Radioactive decay chains describe series of successive decays from parent to stable daughter nucleus
• Include multiple decay modes (alpha, beta, gamma)
• Uranium-238 decay chain ends with stable lead-206 after 14 decay steps
• Thorium-232 decay chain produces stable lead-208 after 10 decay steps
• Branching ratios indicate probability of different decay modes for a given nuclide
• Decay chains important for understanding natural radioactivity and dating methods

Half-Life and Decay Kinetics

• Half-life defines time required for half of radioactive sample to decay
• Characteristic property of each radionuclide, ranging from fractions of a second to billions of years
• Exponential decay law describes decrease in number of radioactive nuclei over time
• Activity (A) represents rate of decay, measured in becquerels (Bq) or curies (Ci)
• Decay constant (λ) relates half-life to activity: $λ = \ln(2) / t_{1/2}$
• Used in radiometric dating techniques (carbon-14, potassium-40, uranium-lead)
• Applications in medicine for diagnostic imaging and radiation therapy