Radiocarbon dating

Definition

Radiocarbon dating is a method used to determine the age of an object containing organic material by measuring its carbon-14 content. It is based on the principles of radioactive decay and exponential functions.

5 Must Know Facts For Your Next Test

1. Radiocarbon dating relies on the exponential decay of carbon-14, which has a half-life of approximately 5730 years.
2. The formula for radiocarbon dating is $N(t) = N_0 e^{-kt}$, where $N(t)$ is the remaining quantity of carbon-14 at time $t$, $N_0$ is the initial quantity, and $k$ is the decay constant.
3. The decay constant $k$ can be found using the relationship $k = \frac{\ln(2)}{5730}$.
4. Radiocarbon dating can be used to date objects up to about 50,000 years old.
5. In logarithmic terms, radiocarbon dating allows us to solve for time by rearranging the equation: $t = \frac{1}{k} \ln(\frac{N_0}{N(t)})$.

Review Questions

• What is the half-life of carbon-14 and how does it relate to radiocarbon dating?
• Write the exponential decay formula used in radiocarbon dating and explain each variable.
• How do you solve for time ($t$) in radiocarbon dating using logarithms?

Related terms

Exponential Decay:

A process where a quantity decreases at a rate proportional to its current value, often modeled with the function $y = y_0 e^{-kt}$.

Half-Life: The time required for half of a given amount of a radioactive substance to decay.

Logarithmic Function:

$y = \log_b(x)$ is the inverse function of an exponential function; it determines how many times one number must be multiplied by itself to obtain another number.