This technique bombards the sample, slowly drawing material out and then sending it through to an ion counter.
The half life of carbon-14 is about 5,700 years, so if we measure the proportion of C-14 in a sample and discover it's half a part per trillion, i.e.
half the original level, we know the sample is around one half life or 5,700 years old.
For example, you may want to date the same zircon crystals using the U-Pb method.
In order to do this, you need to measure various isotopes of uranium .
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This question requires a very extensive answer to be able to cover all bases here but I'm going to attempt to explain the salient facts.
So you can never have perfect running conditions and certain parameters will change over time, this is just the nature of high-tech machinery.
A small shift in a parameter can affect your final outcome.
Analytical limitations encompass the limitations of the machinery that is being used to date a material.
For example, you may want to date a zircon crystal using a secondary ion microprobe (SIMS).
For an example, when they tried to get the carbon dating for presence of Aboriginal people in Australia they get to the number 40,000. Why is that 40,000 years limit for carbon dating methods?