Radioactive Decay Calculator
Find the amount remaining and decay constant.
Model exponential radioactive decay using the decay constant.
How the Math Works
The Radioactive Decay Calculator uses the formula N = N₀ · e^(−λt) to determine the remaining quantity of a substance over time. Here, N₀ is the initial amount, e is Euler's number (~2.71828), λ is the decay constant, and t is elapsed time. The decay constant λ is calculated from the half-life using λ = ln(2) ÷ half-life, where ln(2) (~0.693) represents the natural logarithm of 2. This relationship ensures that after one half-life period, exactly half the original quantity remains, as e^(−ln(2)) = 1/2. The exponential model captures how decay accelerates initially and slows over time, reflecting the probabilistic nature of individual atom decay events.
Practical Applications
To use this calculator, input the initial quantity (N₀) of the radioactive substance, its half-life, and the elapsed time (t) you wish to analyze. For example, if you have 100 grams of Carbon-14 with a half-life of 5,730 years, after 1,000 years the remaining amount would be calculated by first determining λ = 0.693 ÷ 5,730 ≈ 0.0001209 per year, then applying N = 100 · e^(−0.0001209·1,000) ≈ 88.6 grams. This method is essential in archaeology for carbon dating artifacts, in medicine for determining safe radiation exposure durations, and in nuclear engineering for managing fuel decay chains in reactors.
Day-to-Day Use
While most people don't calculate decay daily, this principle underpins technologies you encounter regularly. Medical imaging like PET scans relies on controlled radioactive decay to produce diagnostic images. Smoke detectors use Americium-241, whose decay emits alpha particles to detect fires. Even in environmental science, understanding decay rates helps monitor nuclear waste storage safety and assess radiation risks from natural sources like granite countertops or airline flights. By predicting how quickly radioactive materials diminish, these calculations ensure safety protocols for everyday items and critical infrastructure.
Worked example
100 over half a half-life → ~70.7 remaining.
FAQ
Vs half-life calc?
Same physics — this also reports the decay constant λ.