chm 12901 general chemistry with a biological focus unit 8 study guides

Key Concepts and Definitions

• Atomic number ($Z$) represents the number of protons in an atom's nucleus and determines the element's identity
• Mass number ($A$) is the sum of the number of protons and neutrons in an atom's nucleus
• Isotopes are atoms of the same element with different numbers of neutrons (varying mass numbers)
  • Isotopes have the same chemical properties but different physical properties (radioactive decay rates)
• Radioactivity is the spontaneous emission of radiation from an unstable atomic nucleus
• Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation
• Half-life ($t_{1/2}$) is the time required for half of a given quantity of a radioactive substance to decay
• Radiation can be in the form of alpha particles ($\alpha$), beta particles ($\beta$), or gamma rays ($\gamma$)

Atomic Structure and Nuclear Stability

• Protons and neutrons, collectively called nucleons, reside in the nucleus of an atom
• Protons have a positive charge, neutrons have no charge, and electrons have a negative charge
• The strong nuclear force holds protons and neutrons together in the nucleus, overcoming the electrostatic repulsion between protons
• Nuclear stability depends on the ratio of protons to neutrons in the nucleus
  • Stable nuclei generally have a 1:1 ratio of protons to neutrons for lighter elements and a slightly higher ratio of neutrons to protons for heavier elements
• The band of stability is a region on the chart of nuclides where stable isotopes are found
• Isotopes outside the band of stability are radioactive and undergo decay to reach a more stable configuration
• Magic numbers (2, 8, 20, 28, 50, 82, 126) represent the number of protons or neutrons that result in increased nuclear stability

Types of Radioactive Decay

• Alpha decay ($\alpha$) involves the emission of an alpha particle (two protons and two neutrons, equivalent to a helium-4 nucleus) from the parent nucleus
  • Alpha decay decreases the mass number by 4 and the atomic number by 2
• Beta minus decay ($\beta^-$) involves the conversion of a neutron into a proton, an electron (beta particle), and an antineutrino
  • Beta minus decay increases the atomic number by 1 while the mass number remains constant
• Beta plus decay ($\beta^+$) involves the conversion of a proton into a neutron, a positron (antielectron), and a neutrino
  • Beta plus decay decreases the atomic number by 1 while the mass number remains constant
• Gamma decay ($\gamma$) involves the emission of high-energy photons (gamma rays) from an excited nucleus
  • Gamma decay does not change the mass number or atomic number but releases excess energy
• Electron capture is a process where a proton captures an inner shell electron, converting into a neutron and emitting a neutrino
  • Electron capture decreases the atomic number by 1 while the mass number remains constant

Nuclear Equations and Balancing

• Nuclear equations represent the changes in atomic structure during radioactive decay or nuclear reactions
• In a nuclear equation, the sum of the mass numbers (top numbers) and the sum of the atomic numbers (bottom numbers) must be equal on both sides of the arrow
• When writing nuclear equations, include the chemical symbol, mass number, and atomic number for each species involved
  • Example: ${}^{14}_6\text{C} \rightarrow {}^{14}7\text{N} + {}^0{-1}\text{e} + \bar{\nu}$ (beta minus decay of carbon-14)
• To balance a nuclear equation, ensure that the total mass number and total atomic number are conserved on both sides of the arrow
• Identify the type of decay based on the changes in mass number and atomic number between the parent and daughter nuclei

Half-Life and Decay Rates

• The half-life ($t_{1/2}$) is the time required for half of a given quantity of a radioactive substance to decay
• The decay constant ($\lambda$) is the probability of decay per unit time and is related to the half-life by the equation: $\lambda = \frac{\ln 2}{t_{1/2}}$
• 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
• The activity ($A$) of a radioactive sample is the number of decays per unit time and is related to the number of nuclei by: $A = \lambda N$
  • The SI unit for activity is the becquerel (Bq), which is one decay per second
• The half-life and decay constant are intrinsic properties of a radioactive isotope and cannot be altered by external factors (temperature, pressure, chemical state)
• Radioactive dating techniques (carbon-14 dating) rely on comparing the ratio of a radioactive isotope to its stable daughter product to determine the age of a sample

Applications in Biology and Medicine

• Radioactive isotopes are used as tracers in biological research to study metabolic processes, protein synthesis, and drug distribution
  • Example: Carbon-14 is used to trace the path of carbon in photosynthesis and respiration
• Radioisotopes are used in medical imaging techniques such as positron emission tomography (PET) and single-photon emission computed tomography (SPECT)
  • These techniques provide functional information about organ systems and can help diagnose diseases (cancer, Alzheimer's)
• Radiation therapy uses high-energy radiation (gamma rays or X-rays) to kill cancer cells and shrink tumors
  • The goal is to deliver a high dose of radiation to the tumor while minimizing damage to surrounding healthy tissue
• Radioimmunoassay (RIA) is a sensitive technique that uses radioactive isotopes to measure the concentration of specific antigens or antibodies in a sample
  • RIA is used to diagnose hormonal disorders, monitor therapeutic drug levels, and detect infectious diseases
• Radioactive isotopes are used in sterilization processes for medical equipment, food, and consumer products
  • Gamma radiation from cobalt-60 or cesium-137 is used to kill bacteria and other microorganisms without leaving residual radioactivity

Safety and Environmental Considerations

• Radiation exposure can cause damage to living tissues, leading to acute radiation syndrome, increased cancer risk, 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 principles of radiation protection are time, distance, and shielding
  • Minimize time spent near a radiation source, maximize distance from the source, and use appropriate shielding materials (lead, concrete)
• Occupational radiation exposure is monitored using personal dosimeters (film badges, thermoluminescent dosimeters) to ensure that workers stay within safe limits
• Environmental contamination can occur from the improper disposal of radioactive waste or accidental releases from nuclear facilities (Chernobyl, Fukushima)
• The safe handling, storage, and disposal of radioactive materials are regulated by national and international agencies (Nuclear Regulatory Commission, International Atomic Energy Agency)
• The use of radioactive isotopes in research and medicine is subject to strict safety protocols and oversight to minimize risks to workers, patients, and the public

Problem-Solving Strategies

• Identify the type of radioactive decay based on the changes in mass number and atomic number between the parent and daughter nuclei
• Write balanced nuclear equations by ensuring that the total mass number and total atomic number are conserved on both sides of the arrow
• Use the exponential decay equation ($N(t) = N_0 e^{-\lambda t}$) to calculate the number of radioactive nuclei remaining after a given time
  • Rearrange the equation to solve for the initial number of nuclei, decay constant, or time, depending on the given information
• Convert between half-life and decay constant using the equation: $\lambda = \frac{\ln 2}{t_{1/2}}$
• Calculate the activity of a radioactive sample using the equation: $A = \lambda N$
  • Remember to express activity in becquerels (Bq) or other appropriate units (curies, disintegrations per minute)
• Apply the principles of radiation protection (time, distance, shielding) when solving problems related to radiation safety
• Analyze data from radioactive dating techniques (carbon-14 dating) to determine the age of a sample based on the ratio of the radioactive isotope to its stable daughter product
• Interpret data from medical imaging techniques (PET, SPECT) and radioimmunoassay (RIA) to diagnose diseases or monitor treatment efficacy