14.1 Nuclear fission process and chain reactions

Nuclear fission is the process of splitting heavy atomic nuclei, releasing energy and neutrons. This phenomenon forms the basis for nuclear power and weapons, hinging on the concept of critical mass and chain reactions.

Understanding fission mechanics, neutron behavior, and factors affecting reaction rates is crucial. This knowledge allows us to harness nuclear energy safely in reactors while also grasping the devastating potential of uncontrolled fission in weapons.

Nuclear Fission Process

Fission Mechanics and Energy Release

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• Nuclear fission splits heavy atomic nuclei into lighter nuclei, releasing energy and neutrons
• Binding energy per nucleon curve explains fission's energetic favorability for heavy nuclei
  • Peak occurs around iron-56
• Fission energy release stems from mass defect described by Einstein's equation $E = mc²$
• Typical fission reaction releases 2-3 neutrons
  • Triggers further fission events in nearby nuclei, leading to chain reaction

Role of Neutrons in Fission

• Neutrons initiate fission by colliding with fissile nuclei (uranium-235, plutonium-239)
  • Collision causes nuclei to become unstable and split
• Neutron multiplication factor (k) determines chain reaction behavior
  • Subcritical: $k < 1$
  • Critical: $k = 1$
  • Supercritical: $k > 1$
• Neutron moderators slow down fast neutrons
  • Increases fission probability in thermal reactors
  • Common moderators include water and graphite

Critical Mass in Fission

Defining Critical Mass

• Critical mass represents minimum amount of fissile material needed for sustained nuclear chain reaction
• Depends on various factors
  • Type of fissile material (uranium-235, plutonium-239)
  • Material purity
  • Geometry of the fissile mass
  • Presence of neutron moderators or reflectors
• Below critical mass, neutron loss rate exceeds production rate
  • Results in subcritical reaction that cannot sustain itself
• At critical mass, neutron production rate equals loss rate
  • Leads to self-sustaining chain reaction
• Above critical mass, reaction becomes supercritical
  • Potential for rapid, uncontrolled energy release

Significance in Nuclear Applications

• Critical mass concept underpins nuclear reactor design and nuclear weapons development
• Nuclear reactors manipulate effective critical mass using control mechanisms
  • Control rods
  • Coolant flow
  • Fuel arrangement
• Weapons design aims to rapidly achieve supercritical mass
  • Uses techniques like implosion or gun-type assembly

Factors Affecting Fission Rates

Neutron Characteristics and Material Properties

• Neutron flux influences reaction rate
  • Represents number of neutrons passing through given area per unit time
• Neutron cross-section of fissile material determines capture and fission probability
  • Larger cross-section increases reaction likelihood
• Neutron energy spectrum plays crucial role
  • Thermal neutrons (low energy) more effective for U-235 fission
  • Fast neutrons (high energy) required for some breeder reactor concepts
• Neutron leakage from system boundary affects reaction sustainability
  • Larger systems generally have lower leakage rates

Environmental and Compositional Factors

• Temperature impacts reaction rates through Doppler broadening
  • Changes effective neutron cross-section of fuel
• Neutron poisons significantly impact reaction rates and reactor stability
  • Xenon-135 buildup can cause temporary reactor shutdown
• Fuel composition affects long-term sustainability
  • Ratio of fissile to fertile isotopes influences breeding potential
  • Plutonium-239 production in uranium-238 fuel extends reactor life

Controlled vs Uncontrolled Fission

Characteristics and Applications

• Controlled fission maintains criticality at $k ≈ 1$
  • Used in nuclear power plants for electricity generation
  • Employed in research reactors for radioisotope production (medical imaging, cancer treatment)
• Uncontrolled fission rapidly becomes supercritical with $k > 1$
  • Forms basis for nuclear weapons design
  • Used in pulse reactors for studying material behavior under extreme conditions
• Energy release time scale differs significantly
  • Controlled reactions release energy steadily over long periods (years)
  • Uncontrolled reactions release energy explosively in microseconds

Safety and Engineering Considerations

• Controlled reactions require sophisticated engineering for stability
  • Control rods for neutron absorption
  • Moderators for neutron speed control
  • Coolant systems for heat removal
• Multiple safety systems prevent runaway reactions in nuclear power plants
  • Automatic shutdown mechanisms
  • Containment structures
  • Emergency core cooling systems
• Environmental and safety implications vary greatly
  • Controlled reactions pose manageable risks under normal operation
  • Uncontrolled reactions present catastrophic potential (nuclear weapons, severe accidents)