What is radioactive dating?
Radioactive dating uses the concept of half life to determine the age of something.
The general idea is that elements exist naturally as a combination of isotopes. Some isotopes are stable while others decay radioactively. The half-life of a radioactive isotope is the time required to reduce the initial quantity of the isotope by 50% through the process of radioactive decay.
Carbon 14 dating works this way. A tree growing in the past would have an equilibrium mixture of C-12 and C-14 atoms in proportions consistent with living matter today. We know this value.
When that tree dies, it no longer accumulates new carbon atoms from carbon dioxide in the atmosphere (through photosynthesis). At this point, the proportion of C-14 in the organic matter that was the tree decreases due to the decay of C-14 to an isotope of nitrogen.
When we dig up the remnants of the tree today, we can measure the proportion of C-14 to C-12 and see how much it has been reduced. From this we can calculate backwards using the half life of C-14 (5730 years) to estimate how old the remains of the tree are.
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