A sample of organic material is found to contain 18 g of carbon. Based on samples of pottery fou

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A sample of organic material is found to contain 18 g of...

A sample of organic material is found to contain $18 \mathrm{g}$ of carbon. Based on samples of pottery found at the site, investigators believe the material is about 23000 years old. Estimate what percentage of the material's carbon-14 has decayed. (See Sample Problem 25C.)

Key Concepts

Radioactive Decay

Radioactive decay refers to the process by which unstable atomic nuclei lose energy by emitting radiation. This decay is a random process at the level of single atoms, but it leads to predictable behavior when large numbers of atoms are involved. The decay rate is characterized by a decay constant or half-life, and it follows an exponential decay law.

Half-Life

The half-life of a radioactive substance is the time required for half of the initial quantity of the substance to decay. It is a constant for any given isotope and is a critical parameter in determining how the amount of a radioactive material decreases over time.

Exponential Decay Equation

The exponential decay equation models the decrease in quantity of a substance over time. It is given by N(t) = N0 * e^(-?t) or, equivalently, using half-life, N(t) = N0 * (1/2)^(t/T_half). This equation allows one to calculate the remaining fraction of a substance after a given time.

Carbon-14 Dating

Carbon-14 dating is a method used in archaeology and geology to determine the age of organic materials. It is based on measuring the remaining amount of the radioactive isotope carbon-14, which decays over time with a known half-life. By comparing the current amount of carbon-14 to the expected initial amount, scientists can estimate the time that has elapsed since the organism's death.

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