Carbon- 14 dating is used to date a bone found at an...

Carbon- 14 dating is used to date a bone found at an archaeological excavation. If the ratio of $\mathrm{C}-14$ to $\mathrm{C}-12$ atoms is $3.25 \times 10^{-13}$, how old is the bone? [Hint: Note that this ratio is $\frac{1}{4}$ the ratio of $1.3 \times 10^{-12}$ that is found in a living sample.]

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Key Concepts

Radiometric Dating

Radiometric dating is a technique used to determine the age of materials by measuring the decay of radioactive isotopes. It relies on knowing the original amount of a radioactive substance and its known decay rate, allowing scientists to calculate the time elapsed since the material was last in equilibrium.

Exponential Decay

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. This mathematical model is used in radioactive decay to represent how the number of radioactive atoms diminishes over time, following a predictable decay law.

Half-life

The half-life is the time required for half of a radioactive isotope to decay. This concept is fundamental in radiometric dating because it allows the calculation of the age of a sample by comparing the remaining quantity of the radioactive isotope to its initial amount.

Isotopic Ratio

The isotopic ratio refers to the proportion of a radioactive isotope to a more stable or non-radioactive isotope in a sample. In dating methods, comparing the measured ratio in a sample to the known initial ratio helps determine how much time has passed since the sample ceased exchanging isotopes with its environment.

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