Half-Life Calculator

In short Half-life is the time for half of a radioactive sample to decay, and the amount remaining is N₀ × ½ raised to the power of elapsed time divided by half-life. After one half-life 50% is left, after two 25%, after ten 0.0977% — under a thousandth, which is the working rule for how long a source must be stored before it is effectively background. After twenty half-lives about one part in a million remains. There is no point at which decay is mathematically complete; there is only a point where what is left stops mattering. The decay constant λ is ln2 divided by the half-life, and it has a physical meaning the half-life hides: it is the chance that any one nucleus decays in the next instant, and it is the same for every nucleus regardless of age. Decay has no memory. An atom that has survived a billion years is no more likely to go in the next second than one created a moment ago, which is exactly why the curve is exponential rather than a countdown. A consequence worth knowing is that the average atom does not last one half-life. The mean lifetime is 1/λ, which is the half-life divided by ln2 — about 1.4427 half-lives. The long tail of survivors drags the mean above the median. Half-life is also a property of the nucleus alone: it is unaffected by temperature, by pressure, and by what the atom is chemically bonded to. That total independence from conditions is what makes it usable as a clock, from caesium-137 at 30.08 years to uranium-238 at 4.468 billion.