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What is the limitations if carbon dating and what is a example of the materials for which the technique cannot be used?

"Carbon dating" is the technique used to calculate how long ago a living organism died. Here's how it works. Cosmic rays from space hit atoms in the atmosphere, and in some cases will generate thermal neutrons. Nitrogen-14 atoms in the upper atmosphere absorb a few of those neutron, become unstable, and then emit a proton. This changes the Nitrogen-14 (atomic number 7) to carbon-14 (atomic number 6). This process has been going on for a very long time, so there's a relatively constant - but low - percentage of carbon 14 in the atmosphere. Living things breathe in the carbon-14 (along with oxygen and ordinary nitrogen) and the biological processes incorporate this carbon-14. Carbon-14 is slightly radioactive, and decays with a half-life of 5760 years. As long as you are alive, you keep replenishing your supply of carbon-14. But when you (or any other living thing) dies, it's no longer getting fresh carbon-14, and the existing carbon-14 continues to decay. By measuring the amount of carbon-14 remaining in any organic material, we can calculate approximately how long ago the organism died. It's fairly accurate back to about 10,000 years, and sort-of accurate back to about 60,000 years. After that, the proportion of carbon-14 that remains is too tiny for accurate analysis. This only works with living things, and only within the past 60,000 years. This also assumes that there have been no discontinuities in the formation of carbon-14 in the atmosphere. If there had been a supernova explosion within about 50 light years, a spike in cosmic rays might have caused a spike in carbon-14 production, and carbon-dating analysis might indicate that the sample was younger than it really was.