1.3 Basic principles of nuclear reactions

Nuclear reactions are the heart of radiochemistry, involving changes in atomic nuclei. Fission splits heavy nuclei, while fusion combines light ones. Both release massive energy, powering stars and nuclear plants.

Reaction energetics are key, with Q-values showing energy changes and binding energies indicating nuclear stability. Cross-sections measure reaction probabilities, crucial for reactor design and radiation applications.

Nuclear Reaction Types

Fission and Fusion Reactions

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• Nuclear fission reactions involve the splitting of a heavy nucleus into two or more lighter nuclei
  • Typically induced by the absorption of a neutron by a heavy nucleus (uranium-235)
  • Releases a large amount of energy, additional neutrons, and fission fragments
  • Forms the basis for nuclear power generation and nuclear weapons
• Nuclear fusion reactions involve the combining of light nuclei to form a heavier nucleus
  • Requires extremely high temperatures and pressures to overcome the electrostatic repulsion between positively charged nuclei
  • Releases even more energy per nucleon compared to fission
  • Powers the sun and other stars through the fusion of hydrogen into helium

Neutron Activation

• Neutron activation is a process where a stable nucleus absorbs a neutron, becoming a radioactive isotope
  • The resulting radioactive isotope can then undergo radioactive decay, emitting various types of radiation
  • Commonly used in neutron activation analysis (NAA) to determine the elemental composition of a sample
  • Can also be used to produce radioisotopes for medical and industrial applications (cobalt-60 for radiation therapy)

Nuclear Reaction Energetics

Q-value and Mass Defect

• The Q-value represents the amount of energy released or absorbed in a nuclear reaction
  • Calculated as the difference between the total mass-energy of the reactants and the total mass-energy of the products
  • Positive Q-values indicate an exothermic reaction (energy released), while negative Q-values indicate an endothermic reaction (energy absorbed)
• The mass defect is the difference between the sum of the masses of the individual nucleons and the actual mass of the nucleus
  • Arises from the conversion of mass into binding energy, according to Einstein's equation $E = mc^2$
  • The greater the mass defect, the more stable the nucleus

Nuclear Binding Energy

• Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons
  • Represents the energy that holds the nucleus together, overcoming the electrostatic repulsion between protons
  • Can be calculated from the mass defect using Einstein's equation $E = mc^2$
  • Binding energy per nucleon varies with the mass number, with iron-56 having the highest binding energy per nucleon

Nuclear Reaction Probability

Cross-section

• The cross-section is a measure of the probability of a specific nuclear reaction occurring
  • Represents the effective area of interaction between the incident particle and the target nucleus
  • Measured in units of barns (1 barn = $10^{-24}$ cm$^2$)
  • Depends on factors such as the energy of the incident particle, the type of reaction, and the properties of the target nucleus
• Different types of nuclear reactions have different cross-sections
  • Fission reactions typically have larger cross-sections compared to fusion reactions
  • Neutron capture cross-sections vary widely depending on the target nucleus and the neutron energy (thermal neutrons vs. fast neutrons)
• Knowledge of cross-sections is essential for designing nuclear reactors, optimizing neutron activation analysis, and understanding the behavior of materials in high-radiation environments