The most famous ship that didn’t sink
I feel the need to reiterate my explanation of carbon dating. We had a recent quiz which was entirely based on carbon dating, that my students have cleverly manipulated into a warning flare to alert me to the fact that we need to slow down and be sure that everyone’s aboard before the ship goes sailing away.
Earlier, I posted this example of radiocarbon dating as a simplified exercise in determining how long it has been since a carbonbased organism was alive.
Here, I’m going to just walk through our recent quiz:
You are involved in an archaeological dig site of prehistoric humans. You find some samples from several of the people you suspect lived in the site and do radiometric dating.
1. Assuming an original steady state ratio of 1 part ^{14}C: 100 parts ^{12}C, and a halflife of Carbon14 of 5700 years, how old is the site if your samples have a ^{14}C:^{12}C ratio of 1:800?
What’s your starting point? — an original steady state ratio of 1 part ^{14}C: 100 parts ^{12}C. This means, when this archeological site had people living in it, they had a 1:100 carbon ratio. This comes from their continued input of carbon sources from their environment all containing that 1:100 ratio.
what’s the endpoint? — your samples have a ^{14}C:^{12}C ratio of 1:800. Over time, the radioactive carbon in these remains has decayed, so there is less ^{14}C over time. However, the amount of ^{12}C remains constant because this isotope of carbon is stable.
how do we get from 1:100 –> 1:800? the halflife of Carbon14 of 5700 years. Every 5700 years, half of the ^{14}C decays. After the first halflife (5700 years), the original ratio of 1 part ^{14}C: 100 parts ^{12}C changes. Now we have 0.5 part ^{14}C: 100 parts ^{12}C –or– 1 part ^{14}C: 200 parts ^{12}C.
follow this for two more halflives…
1:200 becomes…
1:400, which becomes…
1:800.
How many halflives is that?
count the arrows (each is a halflife) 1:100 –> 1:200 –> 1:400 –> 1:800
3 halflives x 5700 yrs / halflife = 17,100 years.
2. in 5700 another years, what will the ^{14}C:^{12}C ratio be?
Tack on one more halflife… 1:800 –> 1:1600
3. What is another method that you might employ to determine the age of this site ?
Here, I was asking for any answer that is consistent with the number of mechanisms we discussed that have been used to estimate time. I announced during the quiz that you could give any answer here, it did not matter whether that method was consistent with dating a sample of this approximate age.
Many of you chose dendrochronology – the means of using a daisychain of tree rings to walk back through time. This would require that someone has done the background work for this in the area and a sample of wood from the site from which tree rings could be identified… perfect.
You could have said, look at the geological strata if the site. – or mentioned that Paleomagnetism may also enable some reference for dating of rocks (despite the fact that these methods are likely out of scale for a timeperiod of 17,000 years.)
Extra Credit –

During the dig, one of your students falls down a well and is left for dead. Given the increased carbon in the atmosphere due to burning fossil fuels, if a future archeologist were to try to date this student’s remains assuming the original ratio of isotopes given in question #1, would this scientist overestimate or underestimate the time since your student died?
This question requires you to remember that fossil fuels are the result of very ancient carbon sources. because of their age, they are entirely depleted of ^{14}C. When these fuels are burned, combustion results in CO_{2} (all of which is ^{12}C) entering the atmosphere. This would skew the ^{14}C:^{12}C ratio in favor of ^{12}C. Therefore, out student would have a ratio of greater than 1:100 – perhaps 1:200 as his baseline at time of death. would this scientist overestimate or underestimate the time since your student died? They would overestimate – in fact, the student appears to be 5700 years old right away.
2. What would the atmospheric carbon ratio be today if these scientists thought that your student died at the same time as the other prehistoric humans?
1:800 – i.e. the student’s ratio of carbon isotopes would have to be the same as those found in the prehistoric remains. Quite a coincidence!
I hope these answers help you to understand the concept here and how to calculate answers for some basic problems.