Half-Lives and Radioactive Dating

If you could watch a single atom of a radioactive isotope, U-238, for example, you wouldn’t be able to predict when that particular atom might decay. It may take a millisecond, or it may take a century. There’s simply no way to tell.

But if you have a large enough sample — what mathematicians call a statistically significant sample size — a pattern begins to emerge. It takes a certain amount of time for half the atoms in a sample to decay. It then takes the same amount of time for half the remaining radioactive atoms to decay, and the same amount of time for half of those remaining radioactive atoms to decay, and so on. The amount of time it takes for one-half of a sample to decay is called the half-life of the isotope, and it’s given the symbol t_1/2. Table 1.1 shows this process.

Table 1.1Half-Life Decay of a Radioactive Isotope