The Formation of Carbon-14

Every day, vast numbers of cosmic rays enter Earth’s atmosphere. For context, an individual is impacted by approximately half a million cosmic rays each hour.

It is quite common for a cosmic ray to collide with an atmospheric atom, resulting in a secondary cosmic ray composed of energized neutrons. These energized neutrons subsequently collide with nitrogen atoms.

When a neutron strikes, a nitrogen-14 atom (which comprises seven protons and seven neutrons) is transformed into a carbon-14 atom (with six protons and eight neutrons) alongside a hydrogen atom (one proton and no neutrons). Carbon-14 is radioactive, exhibiting a half-life of roughly 5,700 years.

Carbon-14 in Living Organisms

Carbon-14 atoms generated by cosmic rays combine with oxygen, forming carbon dioxide, which plants naturally absorb and incorporate into their structures through photosynthesis.

As animals and humans consume these plants, they also take in carbon-14. The ratio of normal carbon (carbon-12) to carbon-14 in the atmosphere and in all living organisms remains relatively constant over time.

In fact, approximately one in every trillion carbon atoms is a carbon-14 atom. While carbon-14 atoms continuously decay, new carbon-14 atoms replace them at a consistent rate. Presently, your body contains a specific percentage of carbon-14, mirroring that of all living plants and animals.

Dating Biological Remains

Upon the death of an organism, it ceases to absorb new carbon atoms. The ratio of carbon-12 to carbon-14 at the moment of death aligns with that of other living organisms, but from that point on, carbon-14 begins to decay without replacement.

In a sample, the half-life of carbon-14 is about 5,700 years, while carbon-12 levels remain unchanged. By analyzing the ratio of carbon-12 to carbon-14 in a sample and contrasting it with the ratio found in living beings, scientists can accurately determine the age of a specimen from the past.

The formula for calculating the age of a sample through carbon-14 dating is:

t = [ ln (Nf/No) / (-0.693) ] x t1/2

where ln represents the natural logarithm, Nf/No is the percentage of carbon-14 in the sample relative to that in living tissues, and t1/2 is the half-life of carbon-14 (5,700 years).

For instance, if a fossil contains 10% carbon-14 compared to a living sample, the fossil would be calculated as follows:

t = [ln (0.10)/(-0.693)] x 5,700 years

t = [(-2.303)/(-0.693)] x 5,700 years

t = [3.323] x 5,700 years

t = 18,940 years old

While the half-life of carbon-14 is 5,700 years, it is only effective for dating objects up to 60,000 years old.

However, the principles underlying carbon-14 dating can also be applied to other isotopes. For example, potassium-40 is another naturally occurring radioactive element found in the human body, with a half-life of 1.3 billion years. Other useful radioisotopes for dating include uranium-235 (half-life = 704 million years), uranium-238 (half-life = 4.5 billion years), thorium-232 (half-life = 14 billion years), and rubidium-87 (half-life = 49 billion years). The use of various radioisotopes enhances the precision of dating both biological and geological samples.

Is Carbon-14 Dating Trustworthy?

Indeed, carbon-14 dating is regarded as a highly reliable technique. However, challenges may arise in the future regarding its efficacy. Objects that perished after the 1940s, when nuclear bomb testing and reactors began to alter the environment, will be increasingly difficult to date accurately.

To delve deeper into this topic, visit the SEARA da Ciência link.