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Nuclear Physics
Table of Contents
Unit 9 Overview: Nuclear Fission and Nuclear Reactors
9.1 Fission process and energy release
9.2 Chain reactions and critical mass
9.3 Nuclear reactor types and components
9.4 Reactor safety and waste management

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9.1 Fission process and energy release

Citation:

Nuclear fission is a process where heavy atomic nuclei split, releasing energy and neutrons. This phenomenon forms the basis of nuclear power and weapons, with key fissile isotopes like uranium-235 and plutonium-239 playing crucial roles in chain reactions.

The energy released in fission comes from the difference in binding energy between the original nucleus and its fragments. This massive energy output, typically around 200 MeV per fission event, is distributed among various forms, including kinetic energy and radiation.

Nuclear Fission Process

Fission Fundamentals and Isotopes

  • Nuclear fission involves splitting heavy atomic nuclei into lighter nuclei
  • Process releases energy and neutrons, enabling chain reactions
  • Fissile isotopes undergo fission when bombarded with low-energy neutrons
  • Common fissile isotopes include uranium-235, plutonium-239, and uranium-233
  • Neutron-induced fission occurs when a nucleus absorbs a neutron, becoming unstable
  • Unstable nucleus splits into two or more lighter nuclei called fission fragments
  • Fission fragments typically have mass numbers between 70 and 160

Neutron Production and Characteristics

  • Prompt neutrons emerge immediately during fission process (within 10^-14 seconds)
  • Average of 2-3 prompt neutrons released per fission event
  • Delayed neutrons emitted by certain fission products seconds to minutes after fission
  • Delayed neutrons crucial for controlling nuclear reactors
  • Neutron emission probability varies among fissile isotopes (uranium-235: ~0.0158, plutonium-239: ~0.0061)
  • Energy spectrum of emitted neutrons ranges from 0.1 MeV to 10 MeV
  • Neutron multiplicity (average number of neutrons per fission) depends on incident neutron energy

Fission Chain Reactions and Applications

  • Chain reaction occurs when neutrons from one fission event trigger subsequent fissions
  • Critical mass required to sustain chain reaction
  • Controlled chain reactions used in nuclear power plants for energy generation
  • Uncontrolled chain reactions form the basis of nuclear weapons
  • Neutron moderators (water, graphite) slow down neutrons to increase fission probability
  • Neutron absorbers (control rods) regulate chain reaction in nuclear reactors
  • Applications of nuclear fission include medical isotope production and neutron radiography

Energy Release in Fission

Binding Energy and Mass-Energy Equivalence

  • Binding energy represents the energy required to break apart a nucleus into its constituent nucleons
  • Calculated using Einstein's mass-energy equivalence equation: E=mc2E = mc^2
  • Mass defect measures the difference between the mass of a nucleus and the sum of its constituent nucleon masses
  • Mass defect directly related to binding energy through E=Δmc2E = \Delta mc^2
  • Binding energy per nucleon peaks around iron-56, explaining why fission of heavy nuclei releases energy
  • Typical binding energy per nucleon for uranium-235: ~7.6 MeV, for fission products: ~8.5 MeV

Energy Distribution in Fission Reactions

  • Total energy released in fission reaction distributed among various forms
  • Kinetic energy of fission fragments accounts for ~80% of total energy release
  • Prompt neutrons carry ~2-3% of total energy
  • Gamma radiation emitted during fission process contributes ~7% of energy
  • Beta decay of fission products releases ~7% of total energy
  • Neutrinos produced during beta decay carry away ~10 MeV per fission (not typically recoverable)
  • Energy distribution varies slightly depending on fissile isotope and incident neutron energy

Q-Value and Energy Calculations

  • Q-value represents the total energy released in a nuclear reaction
  • For fission, Q-value calculated as difference between initial and final rest masses: Q=(mi−mf)c2Q = (m_i - m_f)c^2
  • Typical Q-value for uranium-235 fission: ~200 MeV
  • Energy release per fission event significantly higher than chemical reactions (factor of ~10^7)
  • Q-value used to determine energy output of nuclear reactors and weapons
  • Fission energy yield often expressed in terms of TNT equivalent (1 kg U-235 ≈ 20 kilotons TNT)
  • Efficiency of energy conversion in nuclear reactors typically 30-40% due to thermodynamic limitations