The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.
The idea behind radiocarbon dating is straightforward, but years of work were required to develop the technique to the point where accurate dates could be obtained.
Count the remaining objects and repeat the process until half of them have decayed. It took a while, but we finally got pretty close to 40 tiles left.
This is called the half-life—the amount of time required for one-half of a given number of atoms to disintegrate. The plot of the number of tiles as a function of the number of turns looks like this: Again, I made radioactive spheres disappear when they decayed.
The method was developed by Willard Libby in the late 1940s and soon became a standard tool for archaeologists.
Libby received the Nobel Prize in Chemistry for his work in 1960.
Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly.
Since all living organisms on Earth are made up of organic molecules that contain Carbon atoms derived from the atmosphere, they therefore contain Carbon-14 atoms.
The Carbon-14 within a living organism is continually decaying, but as the organism is continuously absorbing Carbon-14 throughout its life the ratio of Carbon-14 to Carbon-12 atoms in the organism is the same as the ratio in the atmosphere.
Of course, the best way to understand something is to model it, because the last thing you want to do at home is experiment with something radioactive. Before doing any modeling, you must first understand one key idea: Each atom in a sample of material has an essentially random chance to decay.
The rate of decay depends upon the number of atoms you have.