Radioactive Decay Calculator
Calculate the remaining amount of a radioactive substance after a given time period. Uses the exponential decay formula N = N₀e^(-λt), where λ = ln(2)/t½. Supports multiple time units and displays the decay constant, fraction remaining, and number of half-lives elapsed.
Radioactive decay is a first-order process where unstable atomic nuclei spontaneously transform, emitting radiation. The rate of decay is characterized by the half-life (t½), the time for half the atoms to decay.
Key Equations:
- N = N₀ × e^(-λt): Amount remaining after time t
- λ = ln(2) / t½: Decay constant (probability of decay per unit time)
- Activity = λ × N: Disintegrations per unit time (Bq or Ci)
- After n half-lives: N = N₀ / 2^n
Common Radioactive Isotopes:
- Carbon-14: t½ = 5,730 years (radiocarbon dating)
- Iodine-131: t½ = 8.02 days (thyroid treatment)
- Cobalt-60: t½ = 5.27 years (radiation therapy)
- Uranium-238: t½ = 4.47 × 10⁹ years (geological dating)
- Technetium-99m: t½ = 6.01 hours (medical imaging)
Practical Applications:
Radioactive decay is used in carbon dating (archaeology), radiometric dating (geology), nuclear medicine (diagnosis and treatment), smoke detectors (Am-241), and nuclear power generation. Understanding decay kinetics is essential for radiation safety and waste management.