Which statement is true about radiocarbon dating?

• A. It is effective for dating materials older than 10 million years.
• B. It measures the ratio of \(^{12}ext{C}\) to \(^{13}ext{C}\) in a sample.
• C. It is used to determine the age of once-living materials by measuring the decay of \(^{14}ext{C}\).
• D. It can be used to date rocks that are billions of years old.

Answer: (C)

Verified step by step guidance

1. Understand the concept of radiocarbon dating: Radiocarbon dating is a method used to determine the age of once-living materials by measuring the decay of the radioactive isotope carbon-14 (\(^{14}\text{C}\)). It is effective for dating materials up to about 50,000 years old, not millions or billions of years.
2. Clarify the isotopes involved: Radiocarbon dating specifically measures the ratio of \(^{14}\text{C}\) to \(^{12}\text{C}\) in a sample, not \(^{12}\text{C}\) to \(^{13}\text{C}\). \(^{14}\text{C}\) is radioactive and decays over time, while \(^{12}\text{C}\) and \(^{13}\text{C}\) are stable isotopes.
3. Explain the decay process: \(^{14}\text{C}\) undergoes beta decay to form nitrogen-14 (\(^{14}\text{N}\)) over time. The half-life of \(^{14}\text{C}\) is approximately 5,730 years, which limits its effectiveness to dating relatively recent materials.
4. Discuss the limitations: Radiocarbon dating is not suitable for dating rocks or materials that are millions or billions of years old because \(^{14}\text{C}\) would have decayed completely over such long timescales. Other methods, such as uranium-lead dating, are used for older geological samples.
5. Identify the correct statement: The correct answer is that radiocarbon dating is used to determine the age of once-living materials by measuring the decay of \(^{14}\text{C}\). This aligns with the scientific principles of the method.