Carbon dating is a method used to determine the age of an object containing organic material by measuring the amount of carbon-14 it contains. It utilizes the principles of exponential decay.
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Carbon dating relies on the radioactive decay of carbon-14 (C-14) into nitrogen-14 (N-14).
The half-life of C-14 is approximately 5730 years, which is crucial for calculating ages.
The exponential decay formula $A(t) = A_0 e^{-kt}$ is used, where $A_0$ is the initial amount and $k$ is the decay constant.
The decay constant $k$ can be found using $k = \frac{\ln(2)}{5730}$.
A carbon-dated sample must be calibrated with other dating methods for accuracy due to fluctuations in atmospheric C-14 levels.
Review Questions
What is the half-life of carbon-14 and why is it important in carbon dating?
How do you express the decay constant $k$ in terms of the half-life?
Explain how the exponential decay formula applies to carbon dating.
Related terms
Exponential Decay: A process where quantities decrease at a rate proportional to their current value, often modeled by $y = y_0 e^{-kt}$.
Half-Life: The time required for a quantity to reduce to half its initial value. In carbon dating, this refers to the time taken for half of C-14 to decay.
Radioactive Isotope: $An isotope whose nucleus decays over time, releasing radiation. Carbon-14 is one such isotope used in radiometric dating.$