What does a half-life actually tell us?
What is actually halved?
For a particular radioactive isotope, one half-life is the time in which about half of a large population of parent atoms decays. The atoms change into daughter products; the material does not simply vanish.
Parent atoms become daughter products
Start
100%1 half-life
50%2 half-lives
25%What happens in the next half-life?
After two half-lives, one quarter of the original parent population remains. After three, one eighth remains. Each interval removes the same fraction of the remaining population, rather than the same amount of the starting population.
How do we calculate what remains?
For a large population of a single isotope with a constant half-life and no new parent atoms being added, the expected fraction remaining is 2 raised to the power of minus the elapsed time divided by the half-life. The interactive example uses hypothetical values.
Does that tell us when the material is safe?
Actual used fuel contains many isotopes and decay chains. A fraction of parent atoms remaining is not a calculation of dose, total heat, or the time when fuel can be handled. Those questions require additional information about the material and its surroundings.
Still to understand
How do the individual decay chains combine into the changing heat output of real used fuel?