College Physics I – Introduction Unit 31 Review: Radioactivity and Nuclear Physics

Fundamentals of Atomic Structure

• Atoms consist of protons, neutrons, and electrons
  • Protons have a positive charge and are located in the nucleus
  • Neutrons are electrically neutral and reside in the nucleus alongside protons
  • Electrons have a negative charge and orbit the nucleus in shells
• The number of protons in an atom determines its element (atomic number)
• Isotopes are atoms of the same element with different numbers of neutrons
  • Isotopes have the same chemical properties but different physical properties (mass)
• Atomic mass is the sum of the protons and neutrons in an atom's nucleus
• Electrons are arranged in energy levels (shells) around the nucleus (K, L, M, etc.)
• The outermost electron shell is called the valence shell and determines an atom's chemical properties
• Atoms tend to gain, lose, or share electrons to achieve a stable electronic configuration (octet rule)

Radioactivity Basics

• Radioactivity is the spontaneous emission of radiation from an unstable atomic nucleus
• Radioactive decay occurs when an unstable nucleus releases energy in the form of particles or electromagnetic waves
• The three main types of radioactive decay are alpha, beta, and gamma decay
• Radioactivity is a random process, and the decay rate is constant for a given isotope
• The activity of a radioactive source is measured in becquerels (Bq) or curies (Ci)
  • One becquerel equals one decay per second
  • One curie equals 3.7 × 10^10 decays per second
• Radioactive materials can be found naturally in the environment (uranium, radon) or produced artificially (medical isotopes)

Types of Radioactive Decay

• Alpha decay involves the emission of an alpha particle (two protons and two neutrons)
  • Alpha particles have a positive charge and are relatively heavy
  • They have low penetrating power but high ionizing ability
  • Examples of alpha emitters include uranium-238 and radon-222
• Beta decay involves the emission of a beta particle (electron or positron)
  • Beta minus (β⁻) decay occurs when a neutron converts into a proton, emitting an electron and an antineutrino
  • Beta plus (β⁺) decay occurs when a proton converts into a neutron, emitting a positron and a neutrino
  • Beta particles have moderate penetrating power and ionizing ability
  • Examples of beta emitters include carbon-14 and strontium-90
• Gamma decay involves the emission of high-energy photons (gamma rays)
  • Gamma rays have high penetrating power but low ionizing ability
  • They often accompany alpha or beta decay as the nucleus releases excess energy
  • Examples of gamma emitters include cobalt-60 and cesium-137

Nuclear Reactions and Equations

• Nuclear reactions involve changes in the composition of atomic nuclei
• Fusion reactions combine light nuclei to form heavier nuclei, releasing energy (stars, hydrogen bombs)
  • Example: $^2_1H + ^3_1H → ^4_2He + ^1_0n + \text{energy}$
• Fission reactions split heavy nuclei into lighter fragments, releasing energy (nuclear reactors, atomic bombs)
  • Example: $^{235}_{92}U + ^1_0n → ^{141}_{56}Ba + ^{92}_{36}Kr + 3^1_0n + \text{energy}$
• Nuclear equations must balance mass number (A) and atomic number (Z)
  • Mass number is conserved: $A_{\text{reactants}} = A_{\text{products}}$
  • Atomic number is conserved: $Z_{\text{reactants}} = Z_{\text{products}}$
• Nuclear binding energy is the energy required to break a nucleus into its constituent protons and neutrons
  • Binding energy per nucleon is highest for elements near iron-56, making them the most stable

Half-Life and Decay Rates

• Half-life is the time required for half of a given quantity of a radioactive isotope to decay
  • Each isotope has a unique half-life ranging from fractions of a second to billions of years
  • Examples: carbon-14 (5,730 years), uranium-238 (4.5 billion years), and radon-222 (3.8 days)
• The decay rate is the number of decays per unit time and is proportional to the number of radioactive nuclei present
  • Decay rate follows an exponential decay curve: $N(t) = N_0e^{-λt}$, where $N(t)$ is the number of nuclei at time $t$, $N_0$ is the initial number of nuclei, and $λ$ is the decay constant
• The decay constant ($λ$) is related to the half-life ($t_{1/2}$) by the equation: $λ = \frac{\ln 2}{t_{1/2}}$
• The activity of a radioactive sample decreases exponentially with time, following the same decay curve as the number of nuclei

Radiation Detection and Measurement

• Radiation detectors measure the presence and intensity of ionizing radiation
• Geiger-Müller counters detect ionizing radiation by measuring electrical pulses created by ionization in a gas-filled tube
  • They are sensitive to alpha, beta, and gamma radiation but do not distinguish between them
• Scintillation detectors use materials that emit light when exposed to ionizing radiation (sodium iodide, plastic)
  • The light is then converted into an electrical signal by a photomultiplier tube
  • Scintillation detectors are more sensitive and can distinguish between different types of radiation
• Semiconductor detectors (silicon, germanium) measure ionization in a solid-state material
  • They have high energy resolution and can identify specific radioisotopes based on their energy spectra
• Dosimeters measure an individual's exposure to ionizing radiation over time (film badges, thermoluminescent dosimeters)

Applications of Nuclear Physics

• Nuclear power plants generate electricity by harnessing the energy released from controlled nuclear fission reactions
  • Fission of uranium-235 or plutonium-239 heats water to produce steam, which drives turbines to generate electricity
• Radioisotopes are used in medical imaging and therapy
  • Technetium-99m is used in bone scans and other diagnostic procedures
  • Iodine-131 is used to treat thyroid disorders and thyroid cancer
  • Cobalt-60 and linear accelerators are used in external beam radiation therapy for cancer treatment
• Radiocarbon dating uses the decay of carbon-14 to determine the age of organic materials (up to ~50,000 years old)
  • Living organisms have a constant ratio of carbon-14 to carbon-12, which begins to decrease after death
• Nuclear weapons rely on uncontrolled fission (atomic bombs) or fusion (hydrogen bombs) reactions to create devastating explosions
  • The Manhattan Project during World War II led to the development of the first atomic bombs
• Radioisotope thermoelectric generators (RTGs) use the heat from radioactive decay to generate electricity for spacecraft and remote installations

Safety and Environmental Considerations

• Ionizing radiation can cause damage to living tissues, leading to health effects such as radiation sickness and increased cancer risk
  • The severity of the effects depends on the type and amount of radiation, as well as the duration of exposure
• The principles of radiation protection are time, distance, and shielding
  • Minimize time spent near radioactive sources
  • Maximize distance from radioactive sources (inverse square law)
  • Use appropriate shielding materials (lead, concrete) to reduce exposure
• Radioactive waste must be properly managed to prevent environmental contamination and human exposure
  • Low-level waste (contaminated clothing, tools) is typically stored in sealed containers and buried in licensed facilities
  • High-level waste (spent nuclear fuel, reactor components) requires long-term storage in deep geological repositories
• Nuclear accidents (Chernobyl, Fukushima) can release radioactive materials into the environment, contaminating air, water, and soil
  • Emergency response plans and environmental monitoring are crucial for mitigating the consequences of such accidents
• The International Atomic Energy Agency (IAEA) promotes the peaceful use of nuclear technology and establishes safety standards and guidelines
  • The International Nuclear and Radiological Event Scale (INES) is used to communicate the severity of nuclear incidents to the public