Physics of Carbon Dating

Physics of Carbon Dating

The story of dinosaurs of movie Jurassic park must have amused most of us. Do you know that it all started when people found out the skeletal remains of dinosaurs in the process of excavation? Dinosaurs appeared on earth 225 million years ago and they were extinct 65 million years ago. There are theories that state that mass extinction of the dinosaurs is caused by a meteorite collision; since the meteorite collision is timed back to this region in the timeline. But how do we precisely state that dinosaurs walked on earth 225 million years ago? All that we have is the bones of these organisms. So how do we use these bones to calculate the time period they belonged to? The answer is carbon dating. Let’s discuss what carbon dating is and how it works in this essay.

Carbon exists in three different isotopic forms each of which weighs differently. One mole (6 x 1023) of carbon atoms of C-12 type weighs 12 grams, C-13 weighs 13 grams and that of C-14 weighs 14 grams. C-14 decays into C-12 since it is radioactive. The process of conversion of 1 gram of C-14 to 0.5 grams takes approximately 6000 years. Interestingly, for the 0.5 grams of isotope to convert into C-12, it also takes 5000 years. As we have learnt during our Physics tuition class on Nuclear Physics, this means that 5000 years is the half-life of C-14. For a given amount of C-14 to convert into half of the initial amount, it takes 5000 years, irrespective of the amount of C-14 initially taken.

Both C-14 and C-12 are present in the earth’s atmosphere in the form of carbon dioxide or sugars or other organic molecules that living organisms possess. When an organism dies it stops consuming C-14 or C-12 and because of the radioactive nature of C-14, it gets converted to C-12 as time passes. Based on the ratio of the content of C-14 and C-12, one can estimate the age of the fossil assuming that the ratio of these two remains constant in time in the atmosphere.

Let’s say the ratio of C-14 and C-12 in the atmosphere is 2:1 (hypothetically). Assume that it remains constant in time. If a plant dies today and stops the intake of carbon, neither C-14 nor C-12 enter it or gets out of it (as it is fossilized). Assume that the plant has a total of 30 grams of carbon with C-14 and C-12 being 20 and 10 grams respectively. As the time passes, the C-14 gets decayed, let’s say after 12000 years the amount of C-14 will be decreased to 5 grams (20 -> 10 -> 5). And the ratio of C-14 to C-12 changes from 2:1 to 1:5. So based on this ratio, a person looking at the fossil 12000 years later can estimate the age of the fossil.