Question

What range of ages can \({ }^{14} \mathrm{C}\) dating reliably determine?

Short answer

Carbon-14 dating can reliably determine ages from a few hundred years to about 50,000 years.

Step-by-step solution

Understanding Carbon-14 Dating

Carbon-14 dating is a method for determining the age of an object containing organic material by using the properties of radiocarbon, a radioactive isotope of carbon. The technique is based on measuring the amount of carbon-14 left in the sample and comparing it to the carbon-14 in the atmosphere.

Range of Effective Dating with Carbon-14

The effective range for carbon-14 dating is from a few hundred years to about 50,000 years. Below a few hundred years, the date can be very accurate. The limit of 50,000 years is due to the half-life of carbon-14, which is 5,730 years. After about 10 half-lives, the amount of carbon-14 remaining is often too small to be measured accurately.

Limitations of Carbon-14 Dating

Beyond 50,000 years, the amount of carbon-14 remaining is so small that it becomes difficult to obtain an accurate measure, thereby making carbon-14 dating unreliable for ages greater than approximately 50,000 years. Also, for dates more recent than a few hundred years, other factors like atmospheric variations in carbon-14 can affect the accuracy.

Key concepts

Radiocarbon Dating

Radiocarbon dating, also known as carbon-14 dating, is a technique used by scientists and archaeologists to determine the age of ancient objects that contain organic materials. This dating method is especially valuable for studying the history of our planet and human civilization. It works by measuring the amount of carbon-14, a radioactive isotope, that remains in these materials.

Radiocarbon is formed naturally in the atmosphere when cosmic rays interact with nitrogen. Once formed, carbon-14 combines with oxygen to create carbon dioxide, which then spreads throughout the atmosphere, is absorbed by plants during photosynthesis, and enters the food chain. When an organism dies, it stops absorbing carbon-14, and the isotope begins to decay at a known rate.

By comparing the carbon-14 levels in a sample to that of the atmosphere, scientists can estimate the time since the death of the organism. This method has been used to date objects as varied as dead sea scrolls, ancient charcoal from campfires, and linen wrappings from mummies.

Radioactive Isotope

A radioactive isotope, also known as a radioisotope, is an atom that has an unstable nucleus and releases energy in the form of radiation to reach a more stable state. Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons.

Carbon-14 is one such radioactive isotope and is of particular interest in archaeological and environmental studies. Unlike the most common carbon isotope, carbon-12, which has six protons and six neutrons, carbon-14 has two additional neutrons. This difference makes it unstable, so it decays over time. Radioactive decay is a random process, but for a large number of carbon-14 atoms, the rate at which decay occurs is relatively constant. The decay of radioisotopes like carbon-14 can be modelled mathematically and is used to measure the age of formerly living things.

Half-Life of Carbon-14

The half-life of a radioactive isotope is the amount of time it takes for half of the atoms in a sample to decay. For carbon-14, this time is approximately 5,730 years. Knowing this half-life allows scientists to perform carbon-14 dating because it provides a timeframe to calculate the age of a sample.

After one half-life, 50% of the original carbon-14 would remain in a sample. After two half-lives, about 25% would remain, and so on. By measuring the remaining carbon-14 in an object and comparing it to the expected amount in the atmosphere, the time that has passed since the object stopped exchanging carbon with the environment can be estimated. After about 10 half-lives, the amount of carbon-14 left is usually too small to be measured, making dating impossible. This is why carbon-14 dating is most effective for samples up to about 50,000 years old.