A well-known illustration of a first order process is radioactive decay.
Uses of Radioactivity
Applications in medicine include:
- Medical Imaging: Discussing the substance Cardiolite, which is used to image the heart.
- Cardiolite, a transition metal with octahedral geometry and potent cyanide ligands, is used in medical imaging.
- Alan Davidson, a professor at MIT, contributed to the design of Cardiolite, which is used roughly 7 million times annually. It utilizes Technetium-99m, a metastable isotope of Technetium.
- The search for the next great imaging agent is still ongoing in the field of medical imaging.
Nuclear Energy
The potential and present applications of nuclear energy are discussed.
Nuclear Energy Challenges
There are many obstacles to overcome, especially regarding:
- Disposal of nuclear waste.
- The proposed project in Finland to store 12,000 metric tonnes of waste for 100,000 years in a three-mile tunnel.
- Durability of storage containers and the necessity of protecting the facility for millennia.
- The best way to alert future generations to the danger.
Sociology, politics, the natural sciences, and engineering are all intertwined in the discussion of waste storage.
Radioactive Decay Fundamentals
A nucleus decays regardless of the number of nearby nuclei, making it a first order process.
First-Order Kinetics
Radioactive decay can be explained by:
- The integrated rate laws for first-order processes.
- The equation N(t) = N₀ * e^(-kt), where N₀ is the initial number of nuclei and k is the decay constant.
- Using the atomic mass number of the isotope to determine the number of nuclei.
- Measurement of decay events, unlike chemical kinetics which measures concentration.
Measurement of Decay
A Geiger counter is the most widely used instrument for measuring decay events.
- It detects radiation, ionizing internal gases and causing clicks.
- Hans Geiger was a participant in the well-known gold foil experiment and the inventor of the Geiger counter.
Terminology
Decay rate is also known as activity, represented by the letter A.
- A = kN is the rate law for activity, which is the change in the number of nuclei over time.
- A(t) = A₀ * e^(-kt), where A₀ is the initial activity.
- The becquerel (Bq) is the SI unit for activity.
- The curie (Ci) is an older unit of activity, with a disintegration rate of 3.7 x 10¹⁰/s.
- The curie unit is named after Marie Curie, but may also honor Pierre Curie.
- The discovery of radioactivity earned Marie Curie, Pierre Curie, and Henri Becquerel a share of the Nobel Prize in 1903.
- History: Pierre Curie died in 1906 after being struck by a horse and wagon.
Types of Nuclear Radiation
Nuclear radiation can be classified into three types:
- Beta decay, which involves an electron.
- Gamma decay, which involves a photon.
- Alpha particles, equivalent to a helium-4 nucleus.
Half-Life
The half-life is contingent upon the particular material and its rate of decay, varying from milliseconds to gigayears (Ga).
Decay Series
Some decay processes involve a lengthy and intricate sequence of distinct decay events, such as that of uranium 238.
The poem "The Days of Our Half-Lives" by Mala Radakrishan provides a scientific description of the Uranium 238 decay series.
The poem narrates the Uranium 238 Decay Series, detailing the transitions through various isotopes until reaching stable Lead 206.
Transition
After discussing first-order nuclear decay, the lecture moves on to:
Second-Order Kinetics
For a second-order process with a single reactant A, the integrated rate law is 1/[A]t = kt + 1/[A]₀, where [A]t is the concentration at time t, k is the rate constant, and [A]₀ is the initial concentration.
A straight line is produced when 1/[A] is plotted against time in second-order kinetics.
Key Features of Second-Order Kinetics
- The 1/[A] vs. t plot has a slope of k
- The y-intercept is 1/[A]₀
Second-Order Half-Life
The formula for a second-order process's half-life is t₁/₂ = 1/(k[A]₀. The second-order half-life depends on the starting concentration, which is a significant distinction from the first-order half-life.
Determining Reaction Order
An experiment is required to ascertain the order of a reaction. To do this:
- Plot kinetic data using the integrated rate laws for various orders
- Use 1/[A] vs t for second order
- Use ln[A] vs t for first order
- Determine which plot produces a straight line
The Connection Between Equilibrium and Kinetics
The connection between rate constants and equilibrium constants is examined in the lecture. At equilibrium:
- The forward and reverse reaction rates are equal
Kinetics and Equilibrium Relationship
For a reversible reaction, the equilibrium constant K is equal to the ratio of the forward reaction's rate constant (K₁) to the reverse reaction's rate constant (K₋₁), meaning that:
- K = K₁/K₋₁
- If K > 1, there are more products than reactants at equilibrium
- If K < 1, there are more reactants than products at equilibrium
Reaction Mechanisms
The majority of reactions take place in multiple steps, referred to as elementary steps or elementary reactions.
The rate law and order can be directly predicted from its stoichiometry for an elementary reaction, in contrast to overall reactions. Elementary reactions are recorded in real time.
Molecularity
The quantity of reactant species that collide and unite in a single elementary step is referred to as molecularity.
Types of Molecularity
Three types of molecularity are discussed:
- Termolecular (three reactants)
- Bimolecular (two reactants)
- Unimolecular (one reactant)
Unimolecular processes include radioactive decay and the breakdown of a molecule into its constituent elements.
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