Carbon Dating

3 isotopes of carbon C-12 C-13 C-14 all have 6 protons but either 6,7 or 8 neutrons. C-14 is the isotope we are interested in.

Carbon 14 Formed in the upper atmosphere through bombardment by cosmic rays freeing neutrons in the atmosphere. 147N loses a proton through an interaction to become 146C. 147N + 10n  146C + 11p

Carbon 14 Carbon 14 produced in the upper atmosphere where it forms radioactive CO2. Through exchange with the atmosphere, plants take in radioactive CO2. This will also find its way into animals.

Radioactive CO2 Approximately 1 molecule in 1012 is radioactive CO2. A typical sample size for testing will be 1 gram. How many radioactive carbon atoms will there be in 1 g of carbon?

Half life As time progresses, the level of radioactive C-14 in a sample falls as it decays back to nitrogen through beta decay. Write a decay equation for this process.

Beta decay of C-14

Half life This element has t ½ = 5730 years. Calculate the decay constant for this element in appropriate units.

Activity Example: An Egyptian mummy of mass 50 kg contains 25 kg of carbon. What is its activity (Bq) when it is buried. What is its activity 3000 years later?

Mumm-Ra from Thundercats, legendary 1980s animation.

Example A woolly mammoth is found to contain 19 % of its original C-14. How old is this mammoth?

The Shroud of Turin

The Shroud of Turin Three independent tests carried out on the shroud in the late 1980s. All came up with a date of manufacture between 1260-1390. The uncertainty is due to the very small sample sizes the Vatican would allow to be taken.

Example Taking the date of the shroud’s production to be 1260, calculate the percentage of radioactive C-14 remaining in the shroud.

Contamination, smoke damage and bacterial growth adding more carbon have all been proposed as reasons why the shroud does not date to c.2000 years ago. The debate will rumble on for decades to come.