Nuclear Physics
Fundamental Forces of Nature
Quantum Mechanics: Explores the fundamental forces at play in nature.
Forces Overview:
Strong Force:
Holds the nucleus together.
Strength: ~10^15 m.
Particles: Protons (mass > 0.1 GeV), Neutrons.
Weak Force:
Involved in processes like beta decay.
Particles: Intermediate vector bosons (W+, W, Z0) with mass > 80 GeV.
Electromagnetic Force:
Strength: 1, Range: Infinite.
Particle: Photon (mass = 0, spin = 1).
Gravity:
Strength: ~10^-39, Range: Infinite.
Particle: Graviton (current status ambiguous regarding mass).
Nuclear Physics
Scope of Nuclear Physics:
Study of nuclear properties and particles.
Investigation of interactions within the nucleus.
Focus on radioactivity and nuclear reactions.
Applications:
Medical radio-isotopes (imaging & therapy).
Magnetic Resonance Imaging (MRI).
Material identification (NAA, AMS).
Radiocarbon dating.
Power generation (fusion and fission).
Weapons of mass destruction (WMD).
Properties of Nuclei
Structure:
Nucleus: Extremely dense, positively charged center of the atom.
Contains protons (positive charge) and neutrons (no charge).
Isotopes:
Same number of protons, different number of neutrons.
Similar chemical properties, different physical properties.
Definitions:
Z = number of protons (atomic number).
N = number of neutrons.
A = Z + N (mass number).
Example: 16 8O ≡ AZO.
Isotopes Summary
Example Isotopes of Carbon:
12 6C:
A = 12, Z = 6, N = 6, Atomic Mass = 12.000000, Abundance = 98.90%.
13 6C:
A = 13, Z = 6, N = 7, Atomic Mass = 13.003355, Abundance = 1.10%.
14 6C:
A = 14, Z = 6, N = 8, Atomic Mass = 14.003242, Radioactive, Beta decay, Half-Life = 5730 y.
Nucleus Size and Mass
Radius Equation: R = R0 A^(1/3).
R0 = 1.2 x 10^-15 m.
Mass Calculation: m = A u (with u = 1.66 x 10^-27 kg).
Nuclear Density
Example of Iron Isotope (56 26Fe):
Parameters: R = 1.2 x 10^-15 m.
Volume Calculation: V = (4/3)πR^3 = 4.1 x 10^-43 m^3.
Mass Calculation: m = (56) * 1.66 x 10^-27 kg = 9.3 x 10^-26 kg.
Density: ρ = m / V = 2.3 x 10^17 kg/m^3 (compared to solid iron ≈ 7 x 10^3 kg/m^3).
Density remains roughly constant across all nuclei.
Nuclear Binding Energy
Definition: Energy gained in forming a nucleus from individual nucleons.
Binding Energy Equation:
E_B = (Z M_H + N m_N – A M) c^2.
Binding Energy per Nucleon
Characteristic:
E_B/A remains almost constant with varying A, indicating nuclear force saturation.
The Nuclear Force
Description: The force that binds protons and neutrons.
Characteristics:
Independent of charge.
Strong, but short-range (≈ 10^-15 m).
Saturated nature, interacting only with nearest neighbors.
Favors pairs with opposite spins.
Nuclear Stability
Criteria: Energy lowered when Z ≈ N.
Large A requirement: Need N ≥ Z to overcome electric repulsion.
N vs. Z Stability plot: Identifies stable versus non-stable nuclides.
Radioactivity Overview
Decay Types:
Alpha Decay: Emission of alpha particle for large nuclei (e.g., 238 92U → 234 90Th + α).
Gamma Decay: Transition between energy states leading to γ-ray emission.
Beta Decay: Emission of electrons or positrons, involves neutron-proton transitions.
Statistical Nature of Radioactivity
Decay Process: Unpredictable for individual nuclei; predictable for groups.
Decay Constant (λ): Probability of decay per unit time.
Mathematical Relationships:
N(t) = N0 exp(-λt).
Half-Life Concept
Definition: Time for half of radioactive nuclei to decay.
Mathematical Formula: T1/2 = ln(2) / λ.
Mean Lifetime: T_mean = 1 / λ.
Radioactivity Measurement
Activity (dN/dt): Measured in Curie (Ci), where 1 Ci = 3.7 x 10^10 decays/second.
Carbon-14 Dating
Mechanism: 14C produced in the atmosphere with cosmic ray interactions.
Decay: 14C → 14N + β- + ν, half-life = 5730 y.
Application: Measuring 14C/12C ratio to determine time since death.
Nuclear Reactions Overview
Definition: Rearrangement of nuclear components by particle bombardment.
Conservation Laws: Charge, momentum, energy, total nucleon number must be conserved.
Energy in Nuclear Reactions
Q-value: Energy released or absorbed in nuclear reactions.
Exoergic: Q > 0, where energy is released.
Endoergic: Q < 0, requiring additional energy input.
Particle Induced Nuclear Reactions
Applications: Used in nuclear physics research and analysis (e.g., detecting Lithium).
Neutron Induced Reactions
Use Cases:
Neutron activation analysis.
Energy generation (fission and fusion).
Reaction probability is influenced by neutron energy level (fast vs. slow neutrons).
Neutron Activation Analysis (NAA)
Application: Identifying elements in painting layers through emitted radiation signatures from neutron bombardment.
Fission and Fusion Principles
Binding Energy Per Nucleon: Peaks around A ~ 70.
Fission: Splitting heavy nucleus into medium mass nuclei.
Fusion: Fusing small nuclei into heavier ones, both processes release energy.
Fission Process
Uranium Isotopes: 238U (99.3% abundance), 235U (0.7% abundance).
Fission Reaction Example: n + 235U → 141Ba + 92Kr + 3n; releases ~200 MeV energy.
Chain Reaction in Fission
Sustainability Condition: Emitted neutrons must be captured by 235U for continuation of fission.
Reproduction Constant (k): Indicates reaction stability.
Nuclear Fission Reactor Design
Neutron Interaction: Moderators (water, graphite) slow down fast neutrons for effective fission.
Control Rod Function: Regulate fission inducing neutrons, typically made of materials like Cadmium.
Fusion Overview
Fusion Reaction Example: 2H + 3H → 4He + n + 17.6 MeV; higher energy release than in fission.
Potential: Abundance of fuel and lower risk compared to fission.
Challenges of Fusion Energy
Technical Challenges: Necessary to achieve high temperature (T > 10^7 K) and pressure for fusion to occur.