General Chemistry II Unit 9 Review: Radioactivity and Reactions

Fundamentals of Nuclear Chemistry

• Atomic structure consists of protons, neutrons, and electrons
  • Protons have a positive charge and are located in the nucleus
  • Neutrons have no charge and are also located in the nucleus
  • Electrons have a negative charge and orbit the nucleus in shells
• Isotopes are atoms of the same element with different numbers of neutrons (carbon-12, carbon-13, carbon-14)
• 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
• Mass-energy equivalence relates mass and energy through Einstein's equation $E=mc^2$
• Binding energy holds protons and neutrons together in the nucleus
  • Binding energy per nucleon varies with the size of the nucleus (iron-56 has the highest binding energy per nucleon)

Types of Radioactivity

• Alpha decay involves the emission of an alpha particle (two protons and two neutrons, or a helium-4 nucleus)
  • Alpha particles have a positive charge and low penetrating power
  • Alpha decay typically occurs in heavy nuclei (uranium, radium)
• Beta decay involves the emission of a beta particle (an electron or positron) and an antineutrino or neutrino
  • Beta minus ($\beta^-$) decay occurs when a neutron converts into a proton, releasing an electron and an antineutrino
  • Beta plus ($\beta^+$) decay occurs when a proton converts into a neutron, releasing a positron and a neutrino
• Gamma decay involves the emission of high-energy photons called gamma rays
  • Gamma rays have no charge or mass and high penetrating power
  • Gamma decay often accompanies alpha or beta decay as the nucleus releases excess energy
• Electron capture occurs when a proton captures an inner shell electron, converting into a neutron and emitting a neutrino
• Spontaneous fission is the splitting of a heavy nucleus into two smaller nuclei and neutrons (uranium-235, plutonium-239)

Nuclear Equations and Notation

• Nuclear equations represent nuclear reactions and decays
  • Reactants are written on the left side, and products are written on the right side
  • Mass number (A) and atomic number (Z) are conserved in nuclear reactions
• Nuclide notation: $^A_Z\text{X}$, where X is the chemical symbol, A is the mass number, and Z is the atomic number
• Alpha particle notation: $^4_2\alpha$ or $^4_2\text{He}$
• Beta particle notation: $^0_{-1}\beta^-$ or $^0_{-1}\text{e}^-$ for beta minus, $^0_1\beta^+$ or $^0_1\text{e}^+$ for beta plus
• Gamma ray notation: $\gamma$
• Neutron notation: $^1_0\text{n}$
• Example nuclear equation for alpha decay: $^{238}_{92}\text{U} \rightarrow ^{234}_{90}\text{Th} + ^4_2\alpha$

Radioactive Decay Processes

• Radioactive decay is a random process governed by probability
• Decay constant ($\lambda$) represents the probability of a nucleus decaying per unit time
  • Decay constant is unique to each radioisotope and relates to half-life: $\lambda = \frac{\ln 2}{t_{1/2}}$
• Decay modes include alpha decay, beta decay, gamma decay, electron capture, and spontaneous fission
• Decay series are sequences of radioactive decays that occur until a stable nucleus is reached (uranium series, thorium series, actinium series)
• Secular equilibrium occurs when the half-life of the parent isotope is much longer than the half-life of the daughter isotope
  • In secular equilibrium, the activity of the daughter isotope equals the activity of the parent isotope (radium-226 and radon-222)
• Transient equilibrium occurs when the half-life of the parent isotope is longer than the half-life of the daughter isotope, but not by a significant margin
  • In transient equilibrium, the activity of the daughter isotope initially increases, then decreases as the parent isotope decays (strontium-90 and yttrium-90)

Half-Life and Decay Rates

• Half-life ($t_{1/2}$) is the time required for half of a given quantity of a radioactive substance to decay
  • Half-life is constant for a specific radioisotope and does not depend on the initial amount
  • Half-life can range from fractions of a second to billions of years (carbon-14 has a half-life of 5,730 years)
• Decay rate is the number of decays per unit time
  • Decay rate is proportional to the number of radioactive nuclei present: $\frac{dN}{dt} = -\lambda N$
• Exponential decay describes the decrease in the number of radioactive nuclei over time: $N(t) = N_0 e^{-\lambda t}$
  • $N(t)$ is the number of radioactive nuclei at time $t$, $N_0$ is the initial number of radioactive nuclei, and $\lambda$ is the decay constant
• Radiometric dating uses the half-life of radioactive isotopes to determine the age of objects (carbon dating, uranium-lead dating)
• Activity (A) is the rate of decay and is measured in becquerels (Bq) or curies (Ci)
  • One becquerel equals one decay per second, and one curie equals $3.7 \times 10^{10}$ decays per second
  • Activity decreases exponentially over time: $A(t) = A_0 e^{-\lambda t}$, where $A_0$ is the initial activity

Nuclear Reactions and Energy

• Nuclear reactions involve changes in the composition of atomic nuclei
  • Fusion reactions combine light nuclei to form heavier nuclei (hydrogen fusion in the sun)
  • Fission reactions split heavy nuclei into lighter nuclei (uranium-235 fission in nuclear reactors)
• Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons
  • Binding energy is released when nuclei with lower binding energy per nucleon fuse or nuclei with higher binding energy per nucleon fission
• Mass defect is the difference between the mass of a nucleus and the sum of the masses of its constituent protons and neutrons
  • Mass defect relates to binding energy through Einstein's equation: $E = \Delta mc^2$
• Nuclear cross section is a measure of the probability of a nuclear reaction occurring
  • Cross section depends on the type of reaction, energy of the incident particle, and target nucleus (barn is a unit of cross section)
• Nuclear fusion powers stars and is the basis for fusion energy research (ITER, NIF)
• Nuclear fission is used in nuclear power plants to generate electricity
  • Fission chain reactions are controlled using moderators, control rods, and coolants

Applications of Nuclear Chemistry

• Nuclear power plants generate electricity through controlled nuclear fission reactions
  • Pressurized water reactors (PWRs) and boiling water reactors (BWRs) are common types of nuclear reactors
  • Nuclear fuel, typically uranium dioxide (UO2), is encased in fuel rods and arranged in a reactor core
• Radioisotopes are used in medical imaging and therapy
  • Positron emission tomography (PET) uses radioisotopes that emit positrons (fluorine-18)
  • Radiation therapy uses high-energy radiation to treat cancer (cobalt-60, iridium-192)
• Radioisotopes are used as tracers in environmental and biological research
  • Tracers help study chemical reactions, metabolic processes, and environmental transport (phosphorus-32, sulfur-35)
• Radiometric dating determines the age of objects based on the decay of radioactive isotopes
  • Carbon-14 dating is used for organic materials up to ~50,000 years old
  • Uranium-lead dating is used for rocks and minerals up to billions of years old
• Nuclear batteries use radioactive decay to generate electricity for long-duration, low-power applications (space probes, pacemakers)
• Radiation is used in food preservation to kill bacteria and extend shelf life (cobalt-60, cesium-137)

Safety and Environmental Considerations

• Radiation exposure can cause health effects, including radiation sickness and increased cancer risk
  • Acute radiation syndrome occurs when a person receives a high dose of radiation over a short period (nausea, skin burns, organ damage)
  • Chronic radiation exposure increases the risk of cancer and genetic mutations
• Radiation protection principles: time, distance, and shielding
  • Minimize time spent near radiation sources
  • Maximize distance from radiation sources (inverse square law)
  • Use appropriate shielding materials (lead, concrete, water)
• Radiation dosimetry quantifies the amount of radiation absorbed by a person or object
  • Absorbed dose is measured in grays (Gy), and equivalent dose is measured in sieverts (Sv)
  • Effective dose accounts for the type of radiation and the sensitivity of different tissues (whole-body dose)
• Nuclear waste management involves the safe handling, storage, and disposal of radioactive waste
  • Low-level waste (LLW) includes contaminated clothing, tools, and medical supplies
  • High-level waste (HLW) includes spent nuclear fuel and byproducts from nuclear weapons production
• Nuclear accidents and incidents can release radioactive material into the environment (Chernobyl, Fukushima)
  • Containment structures and emergency response plans help mitigate the consequences of nuclear accidents
• Nuclear nonproliferation efforts aim to prevent the spread of nuclear weapons and materials
  • International Atomic Energy Agency (IAEA) monitors nuclear facilities and materials worldwide
  • Treaties and agreements, such as the Nuclear Non-Proliferation Treaty (NPT), promote peaceful uses of nuclear technology