Chemistry
Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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Directions: Read about how radioactive carbon-14 is use in estimating the age of a
fossil. Then try to answer the sample exercises below. Use a separate sheet of paper.
Archaeologist use the exponential, radioactive decay of carbon 14 to estimate
the age of fossils. The half-life of a radioactive isotope describes the amount of time
it takes half of the isotope in a sample to decay. For example, if you had a 2 kg of
carbon 14 it would take 5,730 years for that sample to decay, and you would be left
with 1 kg of carbon 14. (Therefore, the half-life of carbon 14 is 5730 years.)
Ex: a wooden artifact from ancient tomb contains 50% of the carbon-14 that is
present in living trees. Using the half-life of carbon 14 (5730 years), calculate for the
age of artifact.
A(t) = A-e*t
A(t) = Final Amount
A. = Initial amount
k = rate of decay
t = time
Assume we have an initial amount of 1 g and A(t) = 5730, lets solve first for the rate
of decay.
A. = 1g
A157 30) = % g
1/2 = 1 e5730k
In 1/2 = In 1 e5730k
k = - 0.000120968
To solve for the age,
A(t) = Aet
A. = 1 g
A(t) = 50% or .5
.5 = 1 e-0.000120968t
In (.5) = In le 0.000120968t
A(t) = 573 yrs. Old
The age of wooden artefact with 50% of carbon-14 is 573 yrs. old
Solve for the following problems:
1. You have just discovered a fossil and tested it to discover it contains 35% of
the original carbon 14, about how old is it?
2. If you know a sample is 2715 years old, what percent of carbon 14 would you
expect to find in the fossil?
3. If a sample of the isotope is 1744 years old, what percent of the isotope would
you expect to find in the fossil?
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Transcribed Image Text:Directions: Read about how radioactive carbon-14 is use in estimating the age of a fossil. Then try to answer the sample exercises below. Use a separate sheet of paper. Archaeologist use the exponential, radioactive decay of carbon 14 to estimate the age of fossils. The half-life of a radioactive isotope describes the amount of time it takes half of the isotope in a sample to decay. For example, if you had a 2 kg of carbon 14 it would take 5,730 years for that sample to decay, and you would be left with 1 kg of carbon 14. (Therefore, the half-life of carbon 14 is 5730 years.) Ex: a wooden artifact from ancient tomb contains 50% of the carbon-14 that is present in living trees. Using the half-life of carbon 14 (5730 years), calculate for the age of artifact. A(t) = A-e*t A(t) = Final Amount A. = Initial amount k = rate of decay t = time Assume we have an initial amount of 1 g and A(t) = 5730, lets solve first for the rate of decay. A. = 1g A157 30) = % g 1/2 = 1 e5730k In 1/2 = In 1 e5730k k = - 0.000120968 To solve for the age, A(t) = Aet A. = 1 g A(t) = 50% or .5 .5 = 1 e-0.000120968t In (.5) = In le 0.000120968t A(t) = 573 yrs. Old The age of wooden artefact with 50% of carbon-14 is 573 yrs. old Solve for the following problems: 1. You have just discovered a fossil and tested it to discover it contains 35% of the original carbon 14, about how old is it? 2. If you know a sample is 2715 years old, what percent of carbon 14 would you expect to find in the fossil? 3. If a sample of the isotope is 1744 years old, what percent of the isotope would you expect to find in the fossil?
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