## Radiometric Dating Applied – a simplified example

06 Dec

Radiometric dating has been used for about 60 years to determine the age of samples containing certain unstable elements. This technique was established as an accurate method for age determination by Arnold and Libby in 1949. As an example of how radiometric dating might be used to determine the age of a material, imagine that we are hiking the Himalayan mountains researching an ancient trade route when a particularly fierce storm sets sending us scurrying for shelter. By chance we find an opening in the rocks that we can squeeze into. When we bring out some lights and set up camp inside the small cavern we find that we are not the first to have been chased into shelter by the snow. Near the back of the cave we find the dried, frozen remains of several others that have the appearance of being here for a very long time.

An actual frozen / mummified body found in the Alps

Back in the laboratory several weeks later we decide to analyze samples from the mummies to determine if they might have been some of the very traders who used the pass through the mountains that we were looking for.

We know that there are several isotopes of Carbon occurring naturally. The most common isotope is Carbon-12, containing six protons, six neutrons and six electrons. This is a very stable form of carbon that does not break down and it accounts for 99%+ of all Carbon in the atmosphere.

There also exists a less stable form of Carbon, Carbon-14, that consists of six protons, eight neutrons and six electrons. The instability of this atom lends it to break down by beta decay  resulting in conversion of this Carbon atom into a Nitrogen atom.

Because the number of atoms in even a very small sample is vastly large, a decay rate can be measured. There is no way of knowing when any specific atom will decay, but on average, the decay rate will show you that one half of any sample will decay in a timeperiod called the halflife. The Halflife of every unstable element is different, for Carbon-14 it is 5730 years+/- 40 years.

We know that the ratio of Carbon-14 to Carbon-12 is 1:100 in the atmosphere and samples of living organisms reflect this ratio in their bodies. For ease of calculation let’s use the equivalent ratio of 8:800 instead, you’ll see why in a moment.

After analysis of our sample, we find it has 1 part Carbon-14 for every 800 parts Carbon-12.

We count backwards from the ratio in the atmosphere when the sample died:

8:800

after one halflife, half the Carbon-14 has decayed

4:800

after another halflife, half of that amount of carbon has decayed

2:800

after another halflife, half of that amount of carbon has decayed

1:800

This is the ratio we found in our sample, so we can stop here.

Three half-lives have passed to arrive at the ratio of Carbon-14 we see in our sample. 3 x 5730 years = 17,190 years.

Now we can ask ourselves, “How long ago was it that we thought traders used this pass? If this number is consistent, then this might have been one of those traders.

(Realistically, a trade route that is 17,000 years old is probably unlikely since trading suggests civilization and the oldest known civilizations were the Egyptians and Mesopotamians which date back only 5000 years. Then again, our estimates of the C-14:C-12 ratio is also absurd, but the concept is correct.)

Some assumptions and notes:

1. We know the ratio of Carbon-12 and Carbon-14 in the atmosphere at the time that the organism died.
2. We are measuring within a timeframe that is appropriate for the halflife of the element we are observing. i.e. Carbon-14’s halflife is 5730 years, it is not appropriate to use this to determine the time of death of something that died yesterday. Nor is it appropriate to use for samples expected to be millions of years old.
3. Realistically, a trade route that is 17,000 years old is probably unlikely since trading suggests civilization and the oldest known civilizations were the Egyptians and Mesopotamians which date back only 5000 years. Then again, our estimates of the C-14:C-12 ratio is also absurd, but the concept is correct.