How to do carbon dating problems
There are two techniques for dating in archaeological sites: relative and absolute dating.Relative dating stems from the idea that something is younger or older relative to something else.
All sorts of interesting data are being uncovered that challenge the supposedly “rock-solid” idea that the earth is billions of years old.
It decays with a half life of 5700 years into nitrogen 14 and electron and an electron antineutreno. So for that reason, every living thing that is interacting with its environment is expected to have this natural abundance of carbon 14. But when something dies, now it's not interacting with the environment anymore. We know that the amount at time t is equal to the initial amount times one half to the time over the half life, alright?
So this is just an ordinary beta decay process and this carbon fourteen's half life is way way way too short for any carbon to just kind of exist naturally in the atmosphere, you'd think, not quite right. So that mean that 1.3 times 10 to the -12 carbon 14 atoms, exist for each and every carbon 12 atom in nature. So you'd think that if you got this 1.3 times 10 to the -12 carbon 14 atoms for each carbon 12 atom at some time, well then 5700 years later, half of the carbon 14 will have decayed. But in fact what happens is, cosmic rays from the sun interact with the upper atmosphere and they actually create carbon 14, at this rate so that in equilibrium, 1.3 times 10 to the -12 carbon 14 atoms will exist for every carbon 12 atom. It's no longer replenishing its carbon 14 supply. This is our standard radioactive decay formula, always works.
We know that it is older than Christendom, but whether by a couple of years or a couple of centuries, or even by more than a millenium, we can do no more than guess." [Rasmus Nyerup, (Danish antiquarian), 1802 (in Trigger, 19)].
The person who wrote these words lived in the 1800s, many years before archaeologists could accurately date materials from archaeological sites using scientific methods.