Chemical Thermodynamics

Radioactive Decay and Half-Life

Radioactive decay is a process by which unstable atomic nuclei lose energy by emitting radiation. The half-life of a radioactive isotope is the time required for half of the radioactive atoms in a sample to decay. This concept is fundamental in nuclear chemistry and is used to date ancient objects, understand nuclear reactions, and manage radioactive materials.

• Half-life (t1/2): The time it takes for half of the original amount of a radioactive substance to decay.

• Decay curve: The amount of radioactive material decreases exponentially over time.

• Mathematical expression: The remaining amount of a radioactive isotope after time t can be calculated using: where is the initial amount, is the amount remaining after time t, and is the half-life.

• Application: Carbon-14 dating is used to determine the age of archaeological samples.

Examples and Calculations

• Example: If a sample contains 25% of its original radioactive isotope, it has undergone two half-lives.

• Example: The half-life of carbon-14 is 5,730 years. If a sample has 25% of its original carbon-14, it is approximately 11,460 years old.

• Graphical representation: Decay curves can be used to visually estimate the age or remaining quantity of a radioactive sample.

Half-Lives of Common Radioisotopes

Different isotopes have different half-lives, ranging from fractions of a second to millions of years. The choice of isotope depends on the application, such as medical imaging, dating, or power generation.

Radioactive Decay Simulation

Simulations and experiments, such as using balloons to represent decaying atoms, help visualize the random nature of radioactive decay. The number of undecayed 'atoms' decreases exponentially over time, matching the theoretical decay curve.

Nuclear Chemistry

Examples of Nuclear Processes

Nuclear processes involve changes in the nucleus of an atom and can result in the emission of different types of radiation. The main types of nuclear decay are:

• Alpha decay (α): Emission of an alpha particle (2 protons and 2 neutrons). Example:

• Beta emission (β): A neutron is converted to a proton, emitting an electron. Example:

• Positron emission: A proton is converted to a neutron, emitting a positron. Example:

• Electron capture: The nucleus captures an inner electron, converting a proton to a neutron. Example:

• Spontaneous fission: The nucleus splits into two smaller nuclei and emits neutrons. Example:

Key Terms

• Parent isotope: The original radioactive isotope.

• Daughter isotope: The product of radioactive decay.

• Decay constant (λ): The probability per unit time that a nucleus will decay. Related to half-life by

Applications of Nuclear Chemistry

• Radiometric dating: Determining the age of objects using isotopes with known half-lives.

• Medical uses: Radioisotopes are used in imaging and cancer treatment.

• Energy production: Nuclear fission is used in power plants to generate electricity.