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The half-life of uranium-238, for example, is 4.5 billion years.By measuring the concentration of uranium-238 in comparison with the products of its decay (especially lead-206), a scientist can estimate the age of the rock in which the uranium was found.From Wikipedia, radioactive decay is the process in which an unstable atomic nucleus spontaneously loses energy by emitting ionizing particles and radiation.
So, Carbon-14 can only measure things up to just over 50,000 years old, great for determining when someone built a wood fire, but not good for determining the age of a meteorite. It occurs whenever an atom has an unbalanced number of protons and neutrons in its nucleus.
When we age date a planet, we are actually just dating the age of the surface, not the whole planet.
We can get absolute ages only if we have rocks from that surface.
It does burn in oxygen, and if you can pass the combusted gas through limewater, the carbon dioxide will turn the limewater milky by producing calcium carbonate.
While not a chemical test, the presence of carbon in a sample (like a meteorite) can be found by vaporizing the sample and passing it through a mass spectrometer.