Lecture on Radioactivity and Kinetics

Alpha Decay

• Definition: Alpha (α) decay is the emission of an α particle from the nucleus.
• Alpha Particle Composition: 2 protons and 2 neutrons; can also be represented as He.
• Daughter Nuclide: Formed product is lighter by two protons and two neutrons than the parent nuclide.

Beta Decay

• Definition: Beta (β) decay involves the emission of a β particle (electron) from the nucleus.
• Mechanism: Conversion of a neutron into a proton accompanied by the emission of a β particle.
• Effects on Nucleus: No change in mass number; increases the number of protons and decreases the number of neutrons.

Gamma Emission

• Definition: Gamma (γ) emission occurs when a nuclide in an excited state transitions to a ground state, releasing a γ ray.
• Indication of Excited State: Often shown by an asterisk (*) in notation.

Stability of Nuclei

• Isotopes: Atoms with the same atomic number but different mass numbers are termed nuclides. Representation notation is AZX (e.g., ^{13}C for carbon-13).
• Nucleons: Comprising protons and neutrons in the nucleus.
• Nuclear Instability: Higher proton counts lead to instability, manifested as radioactivity. All isotopes beyond atomic number 83 are radioactive.
• Radioactive Decay: Spontaneous change from an unstable parent nuclide to a daughter nuclide, releasing various particles and possibly forming stable nuclei.
• Decay Types: Include alpha, beta, and gamma decay.

Effects of Radiation

• Alpha Particles: Can be stopped by a few sheets of paper or skin; non-dangerous externally but hazardous when inhaled or ingested.
• Beta Particles: Penetrate paper and thin layers of material; stopped by metals.
• Gamma Radiation: Very penetrating; requires dense materials for shielding (e.g., lead).

Reaction Rates

• Definition: Change in amount of reactant or product per unit of time.
• Measurement: Can be determined experimentally through changes in properties (e.g., absorbance, concentration).
• Factors Affecting Rate:
  • Identity of Reactants: Physical states impact reactivity; solids react less readily than liquids or gases.
  • Temperature: Higher temperatures typically increase reaction rates.
  • Concentration: Higher concentrations of reactants lead to faster reactions.
  • Catalysis: The presence of a catalyst speeds up the reaction without undergoing permanent change.

Rate Laws

• Zero-Order, First-Order, and Second-Order Reactions:
  • Rate laws express how concentration of reactants affects the rate.
  • Integrated forms show relationships over time:
  • For zero-order: [A]t = -kt + [A]0.
  • Examination of concentration plots helps determine reaction order.

Half-Life

• Definition: Time required for the concentration of a reactant to decrease by half.
• Applications: Useful in pharmacokinetics to calculate remaining drug concentrations in the body over time.

Measurement Accuracy and Precision

• Measurement: Process and tools used to quantify variables.
• Precision: The reproducibility of measurements.
• Accuracy: Closeness of a measurement to the true value.
• Error: Deviation of measured value from true value, quantifiable as range ext{range} = ext{max} - ext{min} .

Beer’s Law

• Concentration: Measurement of solute in relation to solution volume; expressed in various units.
• Dilution Equation: M1V1 = M2V2 describes how concentrations change when diluting solutions.
• Spectrophotometer: Instrument for measuring light intensity at various wavelengths to quantify solute concentrations.
• Absorbance: Measured normally in a spectrophotometer; helps quantify the concentration of solutes in a solution.

Electromagnetic Radiation and Spectroscopy

• Photon: Fundamental unit of light; packets of electromagnetic energy.
• Wavelength and Frequency:
  • Wavelength (λ): Distance between successive peaks; measured in nm.
  • Frequency (ν): Number of cycles per second; related to wavelength by c = λν .
• Electromagnetic Spectrum: Range from low to high energy radiation.

Equilibrium**

• Reversible Reactions: Can occur in both forward and reverse directions, reaching balance.
• Equilibrium Constant (K): Describes concentrations/pressures at equilibrium.
• Le Châtelier’s Principle: States that if a system at equilibrium is disturbed, it reacts to restore equilibrium.

Titration and pH Analysis

• Definitions:
  • Titrant: Known concentration solution used in titrations.
  • Analyte: Unknown concentration solution analyzed.
• Equivalence Point: Moles of titrant equal moles of analyte.
• Indicators: Substances signaling endpoints during titrations; each has specific pH transition colors.

Buffer Solutions**

• Definitions:
  • Buffer: Mix of weak acid/base and its conjugate prevents significant pH changes.
  • Henderson-Hasselbalch Equation: pH = pK_a + ext{log}rac{[ ext{base}]}{[ ext{acid}]} .
• Buffer Capacity: Effectiveness in maintaining pH, impacted by concentrations of components.

Thermodynamics and Spontaneity

• Entropy (S): Measure of disorder within a system.
• Gibbs Free Energy Change (ΔG): Determines spontaneity; negative ΔG indicates spontaneity.
• Second Law of Thermodynamics: All spontaneous processes increase universal entropy.