The amount of carbon- 14(^146 C) in a wooden artifact is measured to be 6.25 percent the amount

step 1 the number of nuclei remaining is given by n is equal to n0 e to the minus lambda t, where n0 is

The amount of carbon- 14(^146 C) in a wooden artifact is...

The amount of carbon- $14\left(^{14}_{6} \mathrm{C}\right)$ in a wooden artifact is measured to be 6.25 percent the amount in a fresh sample of wood from the same region. The half-life of carbon-14 is 5730 years. Assuming the same amount of carbon-14 was initially present in the artifact, determine the age of the artifact. (See Sample Problem 25C.)

Key Concepts

Radiocarbon Dating

Radiocarbon dating is a technique used to determine the age of carbon-containing materials by measuring the level of carbon-14, a radioactive isotope of carbon. Given the known half-life of carbon-14, scientists can calculate the time elapsed since the death of the organism, which is particularly useful in fields like archaeology and geology.

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting particles or electromagnetic waves. This process is random at the level of single atoms but predictable in large populations, allowing calculations of the remaining quantity of a radioactive substance over time.

Half-Life

Half-life is the time required for half of the atoms in a sample of a radioactive substance to decay. It is a characteristic property of each radioactive isotope and is crucial in determining the age of objects through methods such as radiocarbon dating.

Exponential Decay Equation

The exponential decay equation models the decrease of radioactive material over time, typically formulated as N(t) = N0 * e^(-?t), where N0 is the initial amount, N(t) is the amount remaining after time t, and ? is the decay constant. This formula is essential for calculating the elapsed time based on the remaining percentage of the substance.

Logarithmic Functions

Logarithmic functions are used to solve for time in exponential decay equations. By taking the logarithm of both sides of the decay equation, one can isolate the variable representing time, making it possible to calculate the age of an object when the remaining proportion of a radioactive substance is known.

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