Carbon dating

Definition

Carbon dating is a method used to determine the age of an artifact or sample by measuring the amount of carbon-14 it contains. It relies on the exponential decay of carbon-14 over time.

5 Must Know Facts For Your Next Test

1. Carbon dating is based on the exponential decay formula $N(t) = N_0 e^{-kt}$, where $N(t)$ is the quantity of carbon-14 at time $t$, $N_0$ is the initial quantity, and $k$ is the decay constant.
2. The half-life of carbon-14 is approximately 5730 years, a key value needed for calculations.
3. The decay constant $k$ can be found using the relationship $k = \frac{\ln(2)}{T_{1/2}}$, where $T_{1/2}$ is the half-life.
4. Integration techniques are used to solve for unknowns in exponential growth and decay problems related to carbon dating.
5. Carbon dating is most effective for samples up to about 50,000 years old due to the diminishing amounts of carbon-14.

Review Questions

• What mathematical model describes the decay process in carbon dating?
• How do you calculate the decay constant for carbon-14?
• Why does carbon dating become less accurate for samples older than 50,000 years?

Related terms

Exponential Decay: A process where a quantity decreases at a rate proportional to its current value, often described by $y(t) = y_0 e^{-kt}$.

Half-Life: The time required for half of a radioactive substance to decay. For carbon-14, this period is approximately 5730 years.

Decay Constant: $k$ in the exponential decay formula; calculated as $k = \frac{\ln(2)}{T_{1/2}}$, where $T_{1/2}$ represents the half-life.