A group of scientists use carbon dating to date a piece of wood to be 3 billion years old. Why doesn't this make sense?

Radioactive isotope decay is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. In the context of carbon dating, we are particularly interested in the decay of Carbon-14 (C-14), a radioactive isotope of carbon. It's naturally present in the atmosphere and absorbed by living organisms during their life cycles. Once an organism dies, it no longer absorbs C-14, and the already absorbed C-14 begins to decay at a predictable rate. This decay is measured in terms of a 'decay curve' that scientists use to estimate the time elapsed since the organism's death.

Carbon-14 decays by a process called beta decay, where a neutron in the C-14 nucleus transforms into a proton while emitting an electron (beta particle) and an antineutrino. This changes the C-14 into nitrogen-14, a stable and non-radioactive isotope. By measuring the remaining C-14 in a once-living object, scientists can ascertain when that organism stopped exchanging carbon with its environment, thus estimating its age.

The half-life of a radioactive isotope is the amount of time it takes for half of the isotope in a sample to decay. In the case of Carbon-14, its half-life is approximately 5,730 years. This reliable measure allows scientists to calculate the age of organic materials by comparing the ratio of Carbon-14 to Carbon-12 in a sample. Since this ratio should be constant while an organism is alive, deviations from this ratio in dead matter signify the time that has elapsed since death.

Understanding the half-life of C-14 is crucial for researchers in archaeology, geology, and environmental science to determine the approximate age of carbon-containing materials up to about 50,000 - 60,000 years old. Mathematically expressed, if we started with 100% of C-14, after 5,730 years, we would expect to have about 50% of the original C-14 left in a sample. It's important to note that the half-life remains constant over time, even though the amount of radioactive material decreases.

While radiocarbon dating is a powerful tool for reconstructing the chronology of the past, it has its limitations. One key limitation, as highlighted in the exercise, is its age limit. Techniques involving C-14 are effective up to around 50,000 - 60,000 years ago, due to the detectable limits of the remaining C-14 in a sample. Beyond this time frame, the fraction of C-14 is so small that it's difficult to measure and date accurately.

Another limitation is contamination. The results can be skewed by the presence of modern carbon introduced during the collection or conservation of the specimen. Also, the initial concentration of C-14 in the atmosphere may vary over time, which can lead to inaccuracies if not properly accounted for. Lastly, radiocarbon dating is only applicable to samples that were once part of a living organism - it cannot be used for rocks or other inorganic materials. Due to these constraints, scientists must often employ other methods, like potassium-argon dating or uranium-lead dating, for objects believed to be older than the C-14 range, ensuring more accurate results for the study of our planet's ancient history.