Chapter 11: Problem 13

How is carbon- 14 used to determine the ages of wood, bones, and other artifacts?

Short Answer

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Answer: The key steps for determining the age of an artifact using the carbon-14 dating technique are: 1) Understand the concept of carbon-14 and its decay, 2) Measure the remaining carbon-14 in the artifact, 3) Determine the artifact's amount of carbon-14 at the time of death, 4) Use the decay equation to calculate the age of the artifact, and 5) Estimate the age of the artifact considering possible uncertainties.

Step by step solution

Understand the concept of carbon-14 and its decay

Carbon-14 is a radioactive isotope of carbon that is formed in the upper atmosphere when cosmic rays interact with nitrogen molecules. This carbon-14 gets incorporated into carbon dioxide, which is then taken up by plants during photosynthesis. Animals eating these plants also incorporate carbon-14 into their bodies. The amount of carbon-14 in an organism remains constant during its lifetime, but after its death, the carbon-14 decays at a known rate called the half-life, which is approximately 5,730 years.

Measure the remaining carbon-14 in the artifact

To determine the age of an artifact containing organic material, one must first measure the amount of remaining carbon-14 isotopes in the sample. This can be done using several methods, such as accelerator mass spectrometry (AMS), which can accurately measure the relative amounts of carbon-12 and carbon-14 isotopes, even in very small samples.

Determine the artifact's amount of carbon-14 at the time of death

The proportion of carbon-14 to carbon-12 in the atmosphere remains relatively constant, which allows us to estimate the amount of carbon-14 in a living organism at any given time. To compare with the current proportion of remaining carbon-14 in the artifact, we use the modern standard, which is derived from high-precision measurements of atmospheric carbon-14 in the past. This modern standard, called "proportional pmC value," is represented as an artifact's percentage of modern carbon-14 content at the time of death.

Use the decay equation to determine the age of the artifact

Once the proportion of remaining carbon-14 is measured and the proportional pmC value is obtained, the age of the artifact (t) can be calculated using the decay equation: t = \frac{-ln(\frac{A}{A_0})}{\lambda}, where A is the remaining carbon-14 in the artifact, A_0 is the estimated initial carbon-14 amount (the proportional pmC value), λ is the decay constant, and ln is the natural logarithm. The decay constant (λ) can be determined from the half-life (t_{1/2}) of carbon-14 using the equation λ = \frac{ln(2)}{t_{1/2}}.

Estimate the age of the artifact

After calculating the artifact's age (t) using the decay equation, it is important to remember that the result is an estimate with a certain degree of uncertainty due to various factors, such as possible contamination or faulty measurements. However, carbon-14 dating is an essential tool for archaeologists, geologists, and other scientists to determine the age of ancient artifacts as accurately as possible within the limitations of the technique.

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How is carbon- 14 used to determine the ages of wood, bones, and other artifacts?

Short Answer

Step by step solution

Understand the concept of carbon-14 and its decay

Measure the remaining carbon-14 in the artifact

Determine the artifact's amount of carbon-14 at the time of death

Use the decay equation to determine the age of the artifact

Estimate the age of the artifact

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