Formula for carbon dating
The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.
Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right).
After another 5,730 years, one-quarter of the original will remain.
On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is.
The number at the top is how many half-lives have elapsed.
In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay".In other words, the probability of a radioactive atom decaying within its half-life is 50%.For example, the image on the right is a simulation of many identical atoms undergoing radioactive decay.Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process.
Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statistical computer program.