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## Homework Statement

Background info: The first order rate of nuclear decay of an isotope depends only upon the isotope, not its chemical form or temperature. The half-life for decay of carbon-14 is 5730 years. Assume that the amount of C-14 present in the atmosphere as CO2 and therefore in a living organism has been constant for the last 50,000 years. An ancient sample containing C-14 will show fewer disintegrations of the C-14 that is present than a modern sample because the concentration of C-14 is lower in the ancient sample.

If a 1.00 gram sample of wood found in an archaelogical site in Arizona underwent 7.90x10

^{3}

disintegrations in a given time period (e.g., 20 h) and a modern sample underwent 1.84x10

^{4}disintegrations in the same time period, how old is the ancient sample?

## Homework Equations

First order:

ln[A]

_{t}= -kt + ln[A]

_{o}

[A]

_{t}= e

^{-kt}[A]

_{o}

ln(([A]

_{o}/2)/[A]

_{o}) = -kt

_{1/2}= ln(1/2)

or ln2 = kt

_{1/2}= 0.693

## The Attempt at a Solution

kt

_{1/2}= 0.693

k = 0.693/5730 = 1.21x10

^{-4}

ln[A]

_{t}= -kt + ln[A]

_{o}

ln[A]

_{t}= ?

ln[A]

_{o}= ?

Solve for t?

Is this the right equation to use?

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