Radiocarbon dating is possible because

When the organism dies, the ratio of C-14 within its carcass begins to gradually decrease.

The rate of decrease is 1/2 the quantity at death every 5,730 years. The animation provides an example of how this logarithmic decay occurs.

This process of ingesting C-14 continues as long as the plant or animal remains alive.

The C-14 within an organism is continually decaying into stable carbon isotopes, but since the organism is absorbing more C-14 during its life, the ratio of C-14 to C-12 remains about the same as the ratio in the atmosphere.

However, when the organism dies, the amount of c14 declines such that the longer the time since death the lower the levels of c14 in organic tissue.

This is the clock that permits levels of c14 in organic archaeological, geological, and paleontological samples to be converted into an estimate of time.

Because it reacts identically to C-12 and C-13, C-14 becomes attached to complex organic molecules through photosynthesis in plants and becomes part of their molecular makeup.

During the lifetime of an organism, the amount of c14 in the tissues remains at an equilibrium since the loss (through radioactive decay) is balanced by the gain (through uptake via photosynthesis or consumption of organically fixed carbon).

As the Earth's upper atmosphere is bombarded by cosmic radiation, atmospheric nitrogen is broken down into an unstable isotope of carbon - carbon 14 (C-14).

The unstable isotope is brought to Earth by atmospheric activity, such as storms, and becomes fixed in the biosphere.

Libby, a Professor of Chemistry at the University of Chicago, predicted that a radioactive isotope of carbon, known as carbon-14, would be found to occur in nature.

Working with several collaboraters, Libby established the natural occurrence of radiocarbon by detecting its radioactivity in methane from the Baltimore sewer.