How radioactive decay works
Radioactive atoms are unstable — they break down over time, emitting radiation as they transform into other elements. You can't predict when any single atom decays, but across billions of atoms the rate is perfectly consistent, and it's described by a single number: the half-life.
A half-life is the time for exactly half the atoms to decay. After one half-life, half remains; after two, a quarter; after three, an eighth. The amount never quite reaches zero — it halves again and again — which is why decay follows a smooth exponential curve rather than a straight line.
Why half-lives matter
Half-life spans an extraordinary range. Iodine-131, used in medicine, halves in about 8 days — handy, because it does its job then clears the body. Carbon-14 halves in 5,730 years, which is what makes radiocarbon dating possible. Uranium-238 halves in 4.5 billion years, roughly the age of the Earth. The same maths covers all of them.
This is also the concept behind nuclear waste: the longer the half-life, the longer a material stays radioactive. The fuel that drives the reactor output you can model elsewhere on the site, and the uranium in the fuel equivalence calculator, are governed by exactly these decay curves.
Frequently asked questions
What is the radioactive decay formula?
N = N₀ × (½)^(t / half-life). After one half-life half remains, after two a quarter, and so on.
What is a half-life?
The time for half of a radioactive substance to decay. It's constant for a given isotope, from fractions of a second to billions of years.
How many half-lives until a sample is effectively gone?
After about ten half-lives under 0.1% remains, so it's usually considered effectively decayed. Seven half-lives leave under 1%.