I have a question about radio-carbon dating?

The relative amounts of carbon-12, C-13, and C-14 (ratios) are known. As plants breathe in CO2 they breathe in known ratios of these carbon isotopes. C-12 and C-13 are stable, but C-14 decays, so once the plant dies (for example, cut down if it is a tree) the C-14 cannot aculate further and decays. This decay has a half-life of 5700 years, so measuring the relative amounts of each isotope tells us how long ago the plant died, and consequently how old the artifact made from it is.