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Chapter 11: Problem 14

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

Short Answer

Expert verified
Question: Explain how radiocarbon dating using the radioactive decay of Carbon-14 can be used to determine the age of an artifact. Answer: Radiocarbon dating involves measuring the remaining amount of Carbon-14 in a sample and comparing it with the initial amount that should have been present. Carbon-14 is a radioactive isotope that decays into Nitrogen-14 at a constant rate with a half-life of about 5,730 years. By using the radioactive decay formula, we can calculate the time elapsed, which gives the age of the artifact. This method is reliable for artifacts up to around 50,000 years old.

Step by step solution

01

Understand what Carbon-14 is

Carbon-14 is a radioactive isotope of carbon with 6 protons and 8 neutrons. It occurs naturally in trace amounts and is produced in the upper atmosphere when cosmic rays interact with nitrogen. Carbon-14 mixes with other carbon isotopes like carbon-12 and carbon-13 and enters the carbon cycle, thus becoming part of all living organisms. When an organism dies, it stops exchanging carbon with its environment, and the Carbon-14 present in its body begins to decay into Nitrogen-14 at a known rate.
02

Learn the concept of half-life

Half-life is the time it takes for half of the atoms in a radioactive sample to decay. Every radioactive element, including carbon-14, has a unique half-life which is constant and unchangeable. The half-life of carbon-14 is approximately 5,730 years. In other words, after 5,730 years, half of the carbon-14 atoms in a sample will have decayed into nitrogen-14.
03

Understand the decay equation for Carbon-14

We use the radioactive decay formula to determine the age of an artifact based on the remaining amount of carbon-14 in the sample. The formula is: \[N_t = N_0 \times (1/2)^{\frac{t}{t_{1/2}}}\] Where: - \(N_t\) is the remaining amount of carbon-14 at time t - \(N_0\) is the initial amount of carbon-14 - \(t\) is the time elapsed (in years) - \(t_{1/2}\) is the half-life of carbon-14 (approximately 5,730 years)
04

Determine the ratio of remaining Carbon-14 to the initial amount

To date an artifact or a sample, scientists first measure the amount of remaining carbon-14 (\(N_t\)) and compare it with the initial amount of carbon-14 that should have been present (\(N_0\)). Typically, the ratio of carbon-14 to carbon-12 is used to determine the initial amount of carbon-14, as carbon-12 remains constant after the organism's death.
05

Solve the decay equation for the elapsed time t

To find the age of the artifact, we need to solve the decay equation for t: \[t = t_{1/2} \times \frac{\log(\frac{N_t}{N_0})}{\log(1/2)}\] By plugging in the ratio of remaining carbon-14 to the initial amount and the half-life of carbon-14 (5,730 years), we can calculate the time elapsed (t) and determine the age of the artifact.
06

Interpret the result

After finding the time elapsed (t) using the decay equation, we can now determine the age of the artifact. Keep in mind that radiocarbon dating has its limitations, as it has a maximum age limit of around 50,000 years. Beyond this age, the remaining carbon-14 amount becomes too small to measure accurately. However, for artifacts within this age range, radiocarbon dating provides a reliable method to determine their age and better understand historical events and the evolution of life on Earth.

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