Nuclear Physics Unit 4 ReviewRadioactivity and Radioactive Decay

Key Concepts and Terminology

• Radioactivity the spontaneous emission of radiation from unstable atomic nuclei
• Radioactive decay process by which an unstable atomic nucleus loses energy by emitting radiation
• Alpha decay emission of an alpha particle (two protons and two neutrons) from the nucleus
• Beta decay 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 emission of high-energy photons (gamma rays) from the nucleus
• Half-life time required for half of the radioactive nuclei in a sample to decay
• Activity measure of the rate of radioactive decay, expressed in becquerels (Bq) or curies (Ci)

Types of Radioactive Decay

• Alpha decay occurs in heavy nuclei with too many protons, such as uranium and thorium
  • Alpha particles have a positive charge and are highly ionizing but have low penetrating power
• Beta decay occurs when there is an imbalance between the number of protons and neutrons in the nucleus
  • Beta minus decay results in the emission of an electron and an antineutrino
  • Beta plus decay results in the emission of a positron and a neutrino
• Gamma decay often accompanies alpha or beta decay, as the daughter nucleus releases excess energy
  • Gamma rays are high-energy electromagnetic radiation with no charge and high penetrating power
• Electron capture a proton captures an inner shell electron, converting into a neutron and emitting a neutrino
• Spontaneous fission heavy nuclei split into two smaller nuclei, releasing neutrons and energy
• Cluster decay emission of a small cluster of nucleons (e.g., carbon-14) from the nucleus, rarer than alpha decay

Radioactive Decay Equations

• General decay equation: $N(t) = N_0 e^{-\lambda t}$, where $N(t)$ is the number of radioactive nuclei at time $t$, $N_0$ is the initial number of nuclei, and $\lambda$ is the decay constant
• Decay constant $\lambda$ represents the probability of a nucleus decaying per unit time, related to the half-life $t_{1/2}$ by $\lambda = \frac{\ln 2}{t_{1/2}}$
• Activity equation: $A(t) = \lambda N(t) = A_0 e^{-\lambda t}$, where $A(t)$ is the activity at time $t$ and $A_0$ is the initial activity
• Relationship between half-life and mean lifetime: $\tau = \frac{t_{1/2}}{\ln 2}$, where $\tau$ is the mean lifetime of the radioactive nuclei
• Secular equilibrium occurs when the half-life of the parent nuclide is much longer than that of the daughter nuclide, resulting in a constant ratio of their activities

Half-Life and Decay Rates

• Half-life the time required for half of the radioactive nuclei in a sample to decay
  • Each radionuclide has a characteristic half-life, ranging from fractions of a second to billions of years
• Decay rate the number of radioactive decays per unit time, proportional to the number of radioactive nuclei present
• Exponential decay radioactive decay follows an exponential function, with the number of nuclei decreasing by half every half-life
• Radiometric dating technique that uses the known decay rates of radioactive isotopes to determine the age of materials
  • Carbon-14 dating used for organic materials up to ~50,000 years old
  • Uranium-lead dating used for rocks and minerals up to billions of years old
• Decay chains series of radioactive decays that occur until a stable nucleus is reached (e.g., uranium-238 decay chain)

Radiation Detection and Measurement

• Geiger-Müller counter gas-filled detector that measures ionizing radiation by producing electrical pulses
• Scintillation detector uses a scintillator material that emits light when exposed to ionizing radiation, which is then detected by a photomultiplier tube
• Semiconductor detector uses a semiconductor material (e.g., silicon or germanium) to detect ionizing radiation by producing electron-hole pairs
• Ionization chamber measures the ionization of a gas caused by radiation, used for high-intensity radiation fields
• Thermoluminescent dosimeter (TLD) measures accumulated radiation dose using a material that emits light when heated after exposure to radiation
• Radiation units
  • Becquerel (Bq) SI unit of radioactivity, one decay per second
  • Curie (Ci) non-SI unit of radioactivity, 3.7 × 10^10 decays per second
  • Gray (Gy) SI unit of absorbed dose, one joule of energy absorbed per kilogram of matter
  • Sievert (Sv) SI unit of equivalent dose, accounts for the biological effects of different types of radiation

Biological Effects and Safety

• Ionizing radiation can cause damage to living cells and DNA, leading to health effects such as cancer and genetic mutations
• Linear no-threshold (LNT) model assumes that any exposure to ionizing radiation increases the risk of health effects, with no safe threshold
• Acute radiation syndrome (ARS) occurs when a person is exposed to a large dose of radiation over a short period, causing symptoms such as nausea, hair loss, and decreased blood cell counts
• Radiation protection principles
  • Time minimize the time spent in radiation fields
  • Distance maintain a safe distance from radiation sources, as dose decreases with the square of the distance
  • Shielding use appropriate materials (e.g., lead, concrete) to block or attenuate radiation
• Occupational dose limits set by regulatory agencies to protect workers exposed to radiation (e.g., 50 mSv per year for whole-body exposure)
• ALARA principle (As Low As Reasonably Achievable) minimize radiation exposure while considering social and economic factors

Applications in Science and Medicine

• Radioisotope thermoelectric generators (RTGs) use the heat from radioactive decay to generate electricity, used in space probes and remote locations
• Nuclear medicine uses radioactive tracers for diagnostic imaging and treatment of diseases
  • Positron emission tomography (PET) uses positron-emitting radionuclides to image metabolic processes
  • Radioimmunotherapy uses antibodies labeled with radioactive isotopes to target and destroy cancer cells
• Radiation therapy uses high-energy radiation (e.g., gamma rays, X-rays) to kill cancer cells and shrink tumors
• Food irradiation uses ionizing radiation to sterilize and preserve food by killing bacteria and other pathogens
• Radioactive tracers used in environmental studies to track the movement of water, sediment, and contaminants
• Carbon dating uses the radioactive decay of carbon-14 to determine the age of organic materials

Advanced Topics and Current Research

• Neutrino physics studying the properties and interactions of neutrinos, which are emitted during beta decay
  • Neutrino oscillations the phenomenon of neutrinos changing between their three flavors (electron, muon, and tau) as they travel
• Double beta decay rare nuclear decay process in which two beta decays occur simultaneously, used to study neutrino properties and test conservation laws
• Superheavy elements research into the synthesis and properties of elements beyond the current periodic table (atomic numbers > 118)
• Nuclear astrophysics studying the nuclear processes that occur in stars and the universe
  • Nucleosynthesis the formation of elements through nuclear reactions in stars and supernovae
• Accelerator mass spectrometry (AMS) using particle accelerators to measure rare isotopes for dating and tracing applications
• Radiation hormesis hypothesis that low doses of ionizing radiation may have beneficial effects on health, stimulating repair mechanisms
• Targeted alpha therapy (TAT) using alpha-emitting radionuclides attached to targeting molecules (e.g., antibodies) to selectively kill cancer cells while minimizing damage to healthy tissue