The black rectangle above symbolizes a piece of carbon, mostly consisting of C-12 and C-13, but containing some C-14 atoms (yellow dots; initial concentration 10 thousand atoms). Because C-14 is radioactive, as time goes on the C-14 atoms will decay, or in other words disappear. When exactly an individual atom will decay cannot be predicted; it could happen within a few seconds, but it could also survive several tens of thousands of years (the average lifetime is 8033 years). The survival-time of the atoms is modelled through randomly selecting 10,000 values from an exponential distribution with a Libby half-life of 5568 yr (8803*ln(2); red line), and then plotting the remaining atoms for each 50-yr time slice of the animation. It is easy to see that dating of old samples is difficult, as only few C-14 atoms remain. Modern natural carbon contains many more C-14 atoms than the 10 thousand shown here (some 50 million per mg); this number was chosen for illustration purposes only.

You're welcome to use/adapt this video for teaching/research purposes. It can be downloaded as mp4 (good for e.g. presentations) and as webm (good for webpages), and is also available on vimeo and youtube.

The R code for this animation can be dowloaded here. This R script produces lots of .png files, which are then made into an animation (default in .webm and .mp4 formats, but this can be changed) outside of R. To produce the animation, ffmpeg has to be installed.