Carbon Dating

Carbon Dating

Carbon dating, or radiocarbon dating, is a method for estimating the age of organic materials by analyzing the decay of the radioactive isotope carbon-14 (¹⁴C). Here's how it works:

What is Carbon-14?

• ¹⁴C is a radioactive isotope of carbon formed in the atmosphere by cosmic rays.
• It is incorporated into living organisms through carbon dioxide during photosynthesis and the food chain.

The Process

1. While alive, organisms maintain a stable ratio of ¹⁴C to ¹²C by exchanging carbon with the environment.
2. When the organism dies, it stops taking in carbon, and the ¹⁴C begins to decay into nitrogen-14 (¹⁴N) at a fixed rate, known as its half-life (5,730 years).

The Decay Equation

The relationship between the remaining ¹⁴C in a sample and its age is given by the equation:

Where:

• N: Amount of ¹⁴C remaining in the sample.
• N0: Original amount of ¹⁴C.
• λ: Decay constant, calculated as λ = ln(2) / half-life.
• t: Time since the organism died (the age we want to determine).

Example Calculation

Problem: A piece of ancient wood has 25% of its original ¹⁴C remaining. How old is the wood? (Assume the half-life of ¹⁴C is 5,730 years.)

Step 1: Decay Constant (λ)

Step 2: Solve for Time (t)

The ratio N / N0 = 0.25. Substituting into the formula:

Step 3: Calculate

• ln(1 / 0.25) = ln(4) ≈ 1.386
• t = 1.386 / 0.000121 ≈ 11,462 years

Conclusion

The wood is approximately 11,462 years old.