What Is the Radioactive Half-Life & Decay Calculator?
Radioactive half-life is the fundamental metric measuring the decay kinetics of radioactive isotopes.
It underpins nuclear medicine radiopharmaceutical dosing, archaeological radiometric dating, and nuclear waste storage management.
How Does the Radioactive Half-Life & Decay Calculator Work?
Each individual nucleus has a constant probability of decay per unit time.
Integrating the differential rate law dN/dt = -λN yields the exponential decay function N(t) = N₀ e^(-λt).
Radioactive Half-Life & Decay Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
First-order radioactive kinetics. After 1 half-life, 50% remains; after 2 half-lives, 25% remains; after n half-lives, (1/2)^n remains.
How to Use the Radioactive Half-Life & Decay Calculator
- Enter the starting quantity of radioisotope.
- Enter the known half-life and select its time unit (years, days, hours).
- Provide elapsed decay duration.
Step-by-Step Example Calculation
Two Half-Lives of Cesium-137
Input Values:
Understanding Your Result
Remaining Quantity: Amount of original parent isotope surviving.
Half-Lives Elapsed: Exact fractional number of half-life cycles completed.
Decayed Amount: Cumulative daughter product generated.
Factors That Affect the Result
- Elapsed Time: Exponential decrease over time.
- Isotope Identity: Half-lives range from fractions of a microsecond to billions of years (Uranium-238 = 4.47 billion years).
When Should You Use This Calculator?
- Nuclear medicine: Calculating radiotracer decay (e.g. Technetium-99m, t₁/₂ = 6 hours).
- Geochronology and archaeology dating.
Assumptions & Limitations
- Assumes a statistically large number of nuclei (stochastic fluctuations occur with very small sample counts).
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard exponential decay formulation with 100% mathematical precision.