Radiocarbon dating

Definition

Radiocarbon dating is a method used to determine the age of an object containing organic material by measuring the amount of carbon-14 it contains. This technique relies on the known half-life of carbon-14 and uses exponential decay models.

5 Must Know Facts For Your Next Test

1. Radiocarbon dating uses the exponential decay formula $N(t) = N_0 e^{-\lambda t}$, where $N(t)$ is the quantity of carbon-14 at time $t$, $N_0$ is the initial quantity, and $\lambda$ is the decay constant.
2. The half-life of carbon-14 is approximately 5730 years, which is crucial for calculating ages using logarithmic models.
3. To find the age of a sample, you often need to solve for $t$ using logarithms: $t = \frac{1}{\lambda} \ln(\frac{N_0}{N(t)})$.
4. Radiocarbon dating assumes that the initial ratio of carbon-14 to carbon-12 in a living organism remains constant until death.
5. The decay constant $\lambda$ can be found using the relation $\lambda = \frac{\ln(2)}{T_{1/2}}$, where $T_{1/2}$ is the half-life.

Review Questions

• What is the formula used in radiocarbon dating to model exponential decay?
• How do you calculate the age of a sample using its remaining amount of carbon-14?
• What assumption about carbon ratios does radiocarbon dating rely on?

Related terms

Exponential Decay: A process where quantities decrease at a rate proportional to their current value, often modeled with functions like $N(t) = N_0 e^{-kt}$.

Half-Life: The time required for a quantity to reduce to half its initial amount. For carbon-14, this period is about 5730 years.

Logarithm: \A mathematical function that is the inverse operation to exponentiation, used extensively in solving equations involving exponential growth or decay.