A useful application of half-lives is radioactive dating.
This has to do with figuring out the age of ancient things.
For example, you can’t find the remaining amount of an isotope as 7.5 half-lives by finding the midpoint between 7 and 8 half-lives.
This decay is an example of an exponential decay, shown in the figure below.
Because the ratio of carbon 12 to carbon 14 present in all living organisms is the same, and because the decay rate of carbon 14 is constant, the length of time that has passed since an organism has died can be calculated by comparing the ratio of carbon 12 to carbon 14 in its remains to the known ratio in living organisms. Our Living Language : In the late 1940s, American chemist Willard Libby developed a method for determining when the death of an organism had occurred.
He first noted that the cells of all living things contain atoms taken in from the organism's environment, including carbon; all organic compounds contain carbon.
To change from an unstable atom to a completely stable atom may require several disintegration steps and radiation will be given off at each step.This procedure of radiocarbon dating has been widely adopted and is considered accurate enough for practical use to study remains up to 50,000 years old.Although the time at which any individual atom will decay cannot be forecast, the time in which any given percentage of a sample will decay can be calculated to varying degrees of accuracy.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: It’s important to realize that the half-life decay of radioactive isotopes is not linear.