⚛️Intro to Applied Nuclear Physics Unit 2 – Radioactivity and Nuclear Decay

Key Concepts and Definitions

• Radioactivity is the spontaneous emission of radiation from unstable atomic nuclei
• Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation
• Isotopes are atoms of the same element with different numbers of neutrons in their nuclei
• Radioisotopes are isotopes that undergo radioactive decay
• Activity is the rate of decay of a radioactive substance, measured in becquerels (Bq) or curies (Ci)
  • 1 Bq = 1 decay per second
  • 1 Ci = 3.7 × 10^10 decays per second
• Ionizing radiation is radiation with sufficient energy to ionize atoms or molecules, including alpha particles, beta particles, and gamma rays

Types of Radioactive Decay

• Alpha decay involves the emission of an alpha particle (two protons and two neutrons) from the nucleus
  • Alpha particles have a positive charge and are relatively heavy
  • They have low penetrating power but high ionizing power
• Beta decay involves the emission of a beta particle (an electron or positron) from the nucleus
  • Beta minus ($\beta^-$) decay occurs when a neutron transforms into a proton, emitting an electron and an antineutrino
  • Beta plus ($\beta^+$) decay occurs when a proton transforms into a neutron, emitting a positron and a neutrino
• Gamma decay involves the emission of a gamma ray (high-energy photon) from the nucleus
  • Gamma rays have no charge or mass and have high penetrating power
• Electron capture is a process where an inner shell electron is captured by the nucleus, causing a proton to transform into a neutron
• Spontaneous fission is the spontaneous splitting of a heavy nucleus into two smaller nuclei, releasing neutrons and energy

Nuclear Stability and Decay Rates

• Nuclear stability depends on the ratio of protons to neutrons in the nucleus
  • Stable nuclei have a specific range of proton-to-neutron ratios
  • Nuclei with too many or too few neutrons are unstable and undergo radioactive decay
• The nuclear binding energy is the energy required to break apart a nucleus into its constituent protons and neutrons
  • Nuclei with higher binding energies per nucleon are more stable
• The decay rate is the number of radioactive decays per unit time
  • Decay rate is proportional to the number of radioactive nuclei present
• The decay constant ($\lambda$) is the probability of a single atom decaying per unit time
  • $\lambda = \frac{\ln 2}{t_{1/2}}$, where $t_{1/2}$ is the half-life

Radioactive Half-Life

• The half-life ($t_{1/2}$) is the time required for half of a given quantity of a radioactive substance to decay
• The number of radioactive nuclei remaining after a given time can be calculated using the exponential decay equation:
  • $N(t) = N_0 e^{-\lambda t}$, where $N_0$ is the initial number of nuclei and $t$ is the elapsed time
• The activity of a radioactive sample decreases by half after each half-life
• The mean lifetime ($\tau$) is the average time a radioactive nucleus exists before decaying
  • $\tau = \frac{1}{\lambda} = \frac{t_{1/2}}{\ln 2}$
• Carbon-14 dating is a method for determining the age of organic materials based on the ratio of carbon-14 to carbon-12

Radiation Detection and Measurement

• Geiger-Müller (GM) counters detect ionizing radiation by measuring the ionization of a gas in a sealed tube
  • GM counters are sensitive to alpha, beta, and gamma radiation
• Scintillation detectors use materials that emit light when exposed to ionizing radiation
  • The light is then converted into an electrical signal by a photomultiplier tube
• Semiconductor detectors (silicon or germanium) create electron-hole pairs when exposed to ionizing radiation
  • The number of electron-hole pairs is proportional to the energy of the incident radiation
• Thermoluminescent dosimeters (TLDs) measure accumulated radiation dose using materials that emit light when heated after exposure to ionizing radiation
• Radiation dose is measured in units of gray (Gy) or sievert (Sv)
  • 1 Gy = 1 joule of energy absorbed per kilogram of matter
  • 1 Sv = 1 joule of energy absorbed per kilogram of tissue, weighted by the biological effectiveness of the radiation type

Applications of Radioactivity

• Medical imaging techniques use radioactive tracers to visualize internal structures and functions
  • Positron emission tomography (PET) uses positron-emitting radioisotopes to create 3D images of metabolic processes
  • Single-photon emission computed tomography (SPECT) uses gamma-emitting radioisotopes to create 3D images of organ function
• Radiation therapy uses targeted ionizing radiation to destroy cancer cells
  • External beam radiation therapy (EBRT) delivers radiation from an external source
  • Brachytherapy involves placing radioactive sources directly inside or near the tumor
• Radioisotopes are used as tracers in biological and environmental research to study processes such as nutrient uptake, gene expression, and pollutant transport
• Radiocarbon dating is used to determine the age of organic materials by measuring the ratio of carbon-14 to carbon-12
• Industrial radiography uses high-energy gamma rays to inspect materials for defects, such as cracks or voids in welds or castings

Safety and Environmental Considerations

• Ionizing radiation can cause damage to living tissues, leading to health effects such as radiation sickness, cancer, and genetic mutations
• The biological effects of radiation depend on the type and energy of the radiation, the dose received, and the sensitivity of the exposed tissue
• The ALARA principle (As Low As Reasonably Achievable) is used to minimize radiation exposure to workers and the public
  • Time: Minimize the time spent in radiation areas
  • Distance: Maximize the distance from radiation sources
  • Shielding: Use appropriate shielding materials to reduce radiation exposure
• Radioactive waste management involves the safe handling, storage, and disposal of radioactive materials
  • Low-level waste (LLW) has low concentrations of radioactivity and short half-lives
  • High-level waste (HLW) has high concentrations of radioactivity and long half-lives, requiring long-term isolation
• Environmental monitoring is used to detect and quantify the presence of radioactive materials in air, water, soil, and biota
• Nuclear accidents (Chernobyl, Fukushima) can release radioactive materials into the environment, leading to contamination and potential health risks

Calculations and Problem-Solving

• Radioactive decay calculations involve determining the number of radioactive nuclei remaining after a given time or the time required for a specific fraction of the original nuclei to decay
  • $N(t) = N_0 e^{-\lambda t}$, where $N_0$ is the initial number of nuclei, $\lambda$ is the decay constant, and $t$ is the elapsed time
  • $t = \frac{\ln (N_0/N(t))}{\lambda}$, where $N(t)$ is the number of nuclei remaining after time $t$
• Activity calculations involve determining the rate of radioactive decay or the number of radioactive nuclei present based on the activity
  • $A(t) = \lambda N(t) = A_0 e^{-\lambda t}$, where $A_0$ is the initial activity and $A(t)$ is the activity after time $t$
  • $N(t) = \frac{A(t)}{\lambda}$
• Dosimetry calculations involve determining the absorbed dose, equivalent dose, or effective dose based on the type and energy of the radiation and the properties of the exposed material or tissue
  • Absorbed dose (Gy) = Energy absorbed (J) / Mass of material (kg)
  • Equivalent dose (Sv) = Absorbed dose (Gy) × Radiation weighting factor (WR)
  • Effective dose (Sv) = Σ (Equivalent dose to organ × Tissue weighting factor)
• Shielding calculations involve determining the thickness of shielding material required to reduce the radiation dose to a specific level
  • $I(x) = I_0 e^{-\mu x}$, where $I_0$ is the initial radiation intensity, $\mu$ is the linear attenuation coefficient of the shielding material, and $x$ is the thickness of the shielding