That is a number between 1 followed by zeros and 1 followed by zeros. Assuming of course that no extra Carbon has got into the sample in the mean time, and that is pretty much impossible in a sample that old, because a very small amount of Carbon is almost bound to result from background radiation. Basically the original sample could be as massive as the observable universe and you still could not expect to find any original Carbon atoms left.
Why is that 40, years limit for carbon dating methods? Carbon makes up about 1 part per trillion of the carbon atoms around us, and this proportion remains roughly constant due to continual production of carbon from cosmic rays. The half life datjng carbon is about 5, years, so if we measure the proportion of C in a sample and discover it's half a part per trillion, i.
So by measuring the C level we work out how many half lives old the sample is and therefore how old it is. This isn't a ove limit as more accurate measurements could go further back, but at some point you'd simply run out of C atoms. With our current kit K vetermine is about the limit. However, given that the half life of carbon 14 is years, then there really isn't much carbon 14 left in a sample that is 40, years old. Of course, these small traces probably could be found with modern techniques, with some uncertainty, but then you have to factor in systematic uncertainties - for example associated with present-day contamination the air contains carbon 14!
Any small uncertainty in the measurements, in the amount of contamination or any other source of small error such as fluctuations in the naturally occurring 14 to 12 C ratio could easily be magnified into a huge age error in an old sample with a very small amount of carbon 14 present.
Why is carbon dating limit only 40, years? Derfder 1 5 John Rennie k 41 Damn, the two of you have made me feel guilty for posting such a brief answer, so I've fleshed it out a bit: You missed adding why the carbon 14 level is "frozen-in". Assigning a reasonable value and a reasonable uncertainty and pointing out that this would fail to distinguish between "30 kyr" and "infinity" is a very nice way of showing why people say that carbon dating stops working js a few tens of thousands of years.