If a number of samples are analyzed and the results are shown to define a straight line within error, then a precise age is defined because this is only possible if each is a closed system and each has the same initial ratio and age.The uncertainty in determining the slope is reduced because it is defined by many points.Where do nature's building blocks, called the elements, come from? Her job is to figure out how much gold is in them there rocks. I don't see any more rocks in here, but the bad news is, I don't see any gold in here, either. Final steps: cool and clean the bars, stamp them with their unique serial numbers and their weights. The ancients first learned how to heat rocks to extract copper, at least 7,000 years ago. Traders in New York, London and Shanghai buy and sell more than 20 million tons a year. Copper has been prized for millennia for its unique properties: it conducts electricity better than any metal except silver; it's malleable and has a moderate melting temperature; it even scares away bacteria. Even with all the other modern materials available, they still choose bronze. Hasn't something better come along, after all these years? The quality of the sound depends on the atomic structure of the material.They're the hidden ingredients of everything in our world, from the carbon in our bodies to the metals in our smartphones. The good news is that we haven't finished; there may be still gold hiding in the mix. And, today, it's one of the most widely bought and sold metals in the world. Copper is in wire, electronics and computer chips, plumbing and other building materials. These guys can trade their copper futures; I've got to unload my copper today. In pure metals, the atoms are arranged in orderly rows and columns.and graphitisation lines in 2010 has enabled us to quadruple our throughput and reduce our turnaround time for AMS (now averaging 6 weeks), while maintaining our quality control, improving our background limits and reducing sample size requirements.
Isotope separation is pretty expensive, even because a big improvement in the field can be really dangerous at political-military level.
Lawrence during WWII used calutrons to separate Uranium 238 and 235, but it was really expensive and inefficient.
To back up @Curious One - the detection limits are pretty darn small (Purdue's lab lists detecting one part in 3E14 of C14 vs C12).
My understanding of the limitation of radiometric dating is that background radiation swamps the radiation from C14 once the remaining atoms get few enough in number.
Accelerator mass spectrometry seems to actually count every atom in the sample, meaning background radiation doesn't matter.