Carbon-14 has a half-life of 5730 years. Human skeletal...

Carbon-14 has a half-life of 5730 years. Human skeletal fragments discovered in a cave are analyzed and found to have only $6.24 \%$ of the carbon- 14 that living tissue would have. How old are the remains?

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Key Concepts

Carbon Dating

Carbon dating is a technique used primarily in archaeology and geology to date organic materials by measuring the remaining amount of carbon-14, a radioactive isotope. By knowing the half-life and using exponential decay models, scientists can estimate the age of artifacts and remains that contain carbon.

Exponential Decay Equation

The exponential decay equation models how the quantity of a radioactive substance decreases over time. Generally expressed as N(t) = N0 * e^(-?t), it uses the decay constant and the initial quantity to calculate the remaining amount, enabling the determination of time elapsed from the percentage of substance remaining.

Half-life

Half-life is the period required for half of a given quantity of a radioactive substance to decay. It is an intrinsic property of the isotope and provides a practical measure for estimating how long a material has been decaying, allowing calculations of age or time elapsed.

Radioactive Decay

Radioactive decay is the process by which unstable atomic nuclei lose energy by emitting radiation. This process happens at a constant probabilistic rate and is a natural phenomenon that allows scientists to understand and model how radioactive substances diminish over time.

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