Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This process occurs at a predictable exponential rate measured by its "half-life"—the exact amount of time required for half of the radioactive atoms in a sample to decay into a stable isotope. Understanding half-life calculations is critical for archaeological carbon dating, managing nuclear waste, and administering proper dosages in radiopharmaceuticals.
Exponential Decay Formula
N(t) = N₀ × (1/2)^(t / t₁/₂)
Where N(t) = remaining quantity, N₀ = initial quantity, t = time elapsed, and t₁/₂ = half-life of the substance.
How to Use This Calculator
- Enter the Initial Quantity (mass or percentage) of the radioactive substance.
- Input the specific Half-Life constant for the isotope you are analyzing.
- Enter the Time Elapsed (ensure the time unit matches the half-life unit).
- Click Calculate to find the remaining quantity and the calculated decay constant (λ).
Frequently Asked Questions (FAQ)
Does a radioactive substance ever completely disappear?
Mathematically, exponential decay never truly reaches zero; the amount just gets infinitely smaller (a concept known as an asymptote). However, in practical physical terms, the quantity eventually becomes so microscopic that it is virtually undetectable and negligible.
How is half-life used in Carbon Dating?
Living organisms constantly absorb Carbon-14. When they die, absorption stops, and the C-14 begins to decay into Nitrogen-14 with a half-life of roughly 5,730 years. By measuring the remaining ratio of C-14 in an archaeological sample, scientists can calculate exactly how much time has passed since the organism died.