How this calculation works
The Radioactive Half-Life & Decay Calculator models exponential nuclear decay, calculating remaining isotope fraction, total decayed mass, elapsed half-life cycles, and decay constant (λ) for radiocarbon dating and nuclear medicine.
Mathematical formula and logic
N(t) = N₀ × (0.5)^(t / t½) = N₀ × e^(-λ·t), where Decay Constant λ = ln(2) / t½ = 0.693147 / t½.
Worked example
Starting with 100 grams of Carbon-14 (t½ = 5,730 years) after 11,460 years (exactly 2 half-lives): Exactly 25.0 grams (25%) remain, and 75.0 grams have decayed into Nitrogen-14.
Calculation assumptions
- First-order exponential nuclear decay kinetics.
- Time units for half-life and elapsed time must match (years, days, or hours).
Frequently asked questions
What is a radioactive half-life?
The half-life of a radioactive isotope is the time required for exactly half of the radioactive atomic nuclei in a sample to undergo nuclear decay into stable daughter isotopes.
How does Carbon-14 dating work?
Living organisms absorb Carbon-14 from the atmosphere. Upon death, C-14 intake ceases, and existing C-14 decays with a half-life of 5,730 years. Measuring the remaining C-14 ratio allows scientists to date organic artifacts up to ~50,000 years old.
How much sample remains after 4 half-lives?
After 4 half-lives, (1/2)⁴ = 1/16 = 6.25% of the original radioactive substance remains.
What is the half-life of medical isotopes like Technetium-99m?
Technetium-99m has a short half-life of approximately 6 hours, making it ideal for diagnostic medical imaging scans without leaving long-term radiation in the patient.
What is the decay constant (lambda)?
The decay constant (λ = ln(2) / t½) is the instantaneous probability per unit time that a given nucleus will decay.