Problem 2 - Biology: A Global Approach

Question

Recall that \({ }^{14} \mathrm{C}\) has a half-life of 5,730 years. To calibrate the \(x\)-axis for \({ }^{14} \mathrm{C}\) decay, write the time before present in years below each half-life.

Step-by-Step Solution

Answer

The time below each half-life is: 5730, 11460, 17190 years BP.

Step 1: Understand the concept of half-life

The half-life of a radioactive isotope is the time it takes for half of the substance to decay. Given, \(^{14}\mathrm{C}\) has a half-life of 5730 years, meaning that every 5730 years, the amount of carbon-14 will be reduced by half.

Step 2: Set up initial point

The starting point on the \(x\)-axis for carbon-14 decay calibration is the present, labeled 0 years before present (BP). This is the initial time when no decay has occurred.

Step 3: First half-life

After one half-life, which is 5730 years, we label the point on the \(x\)-axis as 5730 years BP. This represents the point at which 50% of the original \(^{14}\mathrm{C}\) remains.

Step 4: Second half-life

After two half-lives, which is 2 × 5730 = 11460 years BP, we mark the point where 25% of the original \(^{14}\mathrm{C}\) remains.

Step 5: Third half-life

After three half-lives, which is 3 × 5730 = 17190 years BP, label the point where 12.5% of the original \(^{14}\mathrm{C}\) remains. Continue this pattern for further calculations if needed.

Key Concepts

Understanding Carbon-14

Carbon-14, denoted as \(^{14} ext{C}\), is a radioactive isotope of carbon. In nature, carbon can be found in various forms, with the most stable and abundant being \(^{12} ext{C}\). However, \(^{14} ext{C}\) is crucial for understanding processes such as radiocarbon dating.

• Carbon-14 is formed in the atmosphere through the interaction of nitrogen and cosmic rays.
• Its radioactive nature means it slowly decays over time, releasing particles and energy in the process.

Living organisms continually exchange carbon with their environment. As long as an organism is alive, the level of \(^{14} ext{C}\) remains stable. But once it dies, the intake of carbon stops, and \(^{14} ext{C}\) starts to decay. This decay provides archaeologists and scientists with a way to measure and date organic materials.

What is Half-Life?

The term 'half-life' refers to the time required for half of a radioactive substance to decay. This concept is pivotal in understanding radioactive materials, including \(^{14} ext{C}\).For \(^{14} ext{C}\), the half-life is 5730 years. This means that after 5730 years, only half of the initial amount of \(^{14} ext{C}\) remains.

• For example, if you start with 10 grams of \(^{14} ext{C}\), in one half-life (5730 years), you'd have 5 grams left.
• After another half-life (a total of 11460 years), only 2.5 grams would be left.

This predictable decay pattern makes it easier for scientists to understand and calculate the age of ancient artifacts.

The Process of Radiocarbon Dating

Radiocarbon dating, also known as carbon dating, is a technique used to determine the age of an organic object by measuring the amount of \(^{14} ext{C}\) it contains. The method was developed in the late 1940s and has since become a fundamental tool in archaeology.

• It is based on the consistent rate of decay of \(^{14} ext{C}\).
• Scientists measure the remaining \(^{14} ext{C}\) in a sample and compare it to the expected amount in a living organism.

By understanding how much \(^{14} ext{C}\) remains in a sample and using the half-life of 5730 years, researchers can calculate how long it has been since the organism's death. This allows for dating from as recent as a couple of hundred years ago to as far back as 50,000 years, making it invaluable for historical and environmental research.