Radioactive dating in archaeology
Libby calculated the half-life of c14 as 5568 ± 30 years.
This means that half of the c14 has decayed by the time an organism has been dead for 5568 years, and half of the remainder has decayed by 11,136 years after death, etc.
A more recent innovation is the direct counting of c14 atoms by accelerator mass spectrometers (AMS).
The first measurements of radiocarbon were made in screen-walled Geiger counters with the sample prepared for measurement in a solid form.
Working with several collaboraters, Libby established the natural occurrence of radiocarbon by detecting its radioactivity in methane from the Baltimore sewer.
In contrast, methane made from petroleum products had no measurable radioactivity.
The ensuing atomic interactions create a steady supply of c14 that rapidly diffuses throughout the atmosphere.
Plants take up c14 along with other carbon isotopes during photosynthesis in the proportions that occur in the atmosphere; animals acquire c14 by eating the plants (or other animals).