If it takes 10,000 atoms detected to make a measurement accurate to 1% of the current abundance, starting with 1 miligram of carbon in which 1% by number is¹⁴C, what would be the maximum age at which dating could be made and what would be the error in the dating when the sample measurement error is 1%? Explain your work.

In practice this is far longer than can be achieved accurately, not because the atoms cannot be found, but because samples mix with their environment, and the intial levels of radiocarbon are variable and cannot be established with high accuracy. Instead, for ages over about 50,000 years radioactive isotopes of other elements are used to date samples that have been isolated well from sources that could change their concentration.