Half-life, decay constant, applications of radioactivity

The half-life of a radioactive substance is the time taken for half of its nuclei to decay.
It is denoted by T_1/2.
Formula: T_1/2 = ln(2)/λ, where λ is the decay constant.
Different isotopes have different half-lives, ranging from fractions of a second to billions of years.
Example: The half-life of Uranium-238 is approximately 4.5 billion years.
The concept of half-life is critical in understanding the stability of isotopes.

The decay constant (λ) is the probability per unit time that a nucleus will decay.
Relation with activity: Activity (A) = λ · N, where N is the number of undecayed nuclei.
Higher decay constants correspond to shorter half-lives and more rapid decay.
Measured in inverse time units (e.g., s^-1).
Decay constant is a fundamental property of a radioactive isotope.

Medical Applications:
- Cancer treatment: Using radioactive isotopes like Cobalt-60 for radiotherapy.
- Imaging: Positron Emission Tomography (PET) scans use isotopes like Fluorine-18.
- Diagnosis: Tracers like Technetium-99m help in detecting abnormalities.
Industrial Applications:
- Thickness measurement: Radioactive sources are used to monitor thickness in manufacturing.
- Welding inspection: Gamma radiography detects flaws in welded joints.
Energy Production:
- Nuclear power plants use fission reactions of uranium and plutonium.
Scientific Research:
- Radiocarbon dating (C-14 dating) estimates the age of organic materials.
- Isotopes like Deuterium and Tritium are used in fusion research.
Agricultural Applications:
- Radioisotopes are used to study plant metabolism and control pests.

Radioactive decay is a first-order reaction, meaning its rate depends on the number of undecayed nuclei.
The activity of a radioactive material decreases exponentially over time.
The decay constant and half-life are inversely proportional.
All radioactive isotopes eventually decay into stable isotopes.