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.
Related Calculators & Financial Tools
Explore complementary calculators to plan your loans, investments, taxes, and savings.
Ohm's Law & Electrical Power Calculator
Calculate voltage (V), current (I), resistance (R), and electrical power (P) instantly using Ohm's Law.
Kinetic Energy & Momentum Calculator
Calculate kinetic energy in Joules, kilojoules, and foot-pounds from object mass and velocity.
Kinematics Motion Equations Calculator
Solve kinematic motion equations for displacement, initial velocity, final velocity, and acceleration.
Newton's Universal Gravitation Calculator
Calculate universal gravitational attraction force in Newtons between two celestial or physical masses.
Density, Mass & Volume Calculator
Calculate density, mass, or volume instantly with unit conversions and buoyant float-or-sink determination.
Simple Pendulum Period & Frequency
Calculate simple pendulum oscillation period (T), frequency (Hz), and length using harmonic motion physics.