# Carbon dating and half life

*30-Jul-2015 13:00*

This has to do with figuring out the age of ancient things.

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.

Scientists look at half-life decay rates of radioactive isotopes to estimate when a particular atom might decay.

A useful application of half-lives is radioactive dating.

It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.

It takes a certain amount of time for half the atoms in a sample to decay.

The rule is that a sample is safe when its radioactivity has dropped below detection limits. So, if radioactive iodine-131 (which has a half-life of 8 days) is injected into the body to treat thyroid cancer, it’ll be “gone” in 10 half-lives, or 80 days.

Radioactive dating is helpful for figuring out the age of ancient things.Carbon-14 (C-14), a radioactive isotope of carbon, is produced in the upper atmosphere by cosmic radiation.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.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.

Knowing about half-lives is important because it enables you to determine when a sample of radioactive material is safe to handle.