16. What is the decay rate of carbon 147 Express your answer in yr. 17. In dating using radiocarbon, the amount of 1C re- maining at the time of measurement is expressed as a percentage of modern carbon. For example, for a sample that has 30% modern carbon, N/N, would be 0.3. Using equation (2.2) and the k value deter- mined in problem 16, what is the age of the sample in years?
16. What is the decay rate of carbon 147 Express your answer in yr. 17. In dating using radiocarbon, the amount of 1C re- maining at the time of measurement is expressed as a percentage of modern carbon. For example, for a sample that has 30% modern carbon, N/N, would be 0.3. Using equation (2.2) and the k value deter- mined in problem 16, what is the age of the sample in years?
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Solve problem 17 by using equation (2,2) and the k value determined by solving 16.
Transcribed Image Text:hall-life is the amount of time required for the decay of half of any amount of a particular
isotope. For example, the half-life of uranium 235 is 0.7 billion years. After this amount of
time, only one-half of the original amount of uranium 235 will remain. After two half-lives,
only one-fourth of the original amount will be left.
Radioactive decay is an exponential process and as such can be explained by the same
mathematical expression as equation (1.1), with one modification: In equation (2.2), N be-
comes the number of molecules of the radioactive isotope of an element at time t, instead
of the number of people in a population, and No is the original number of isotopes prior to
decay, rather than the number of people at the beginning of the time interval.
N = Nekt
(2.2)
The one difference in the two equations is that the term k represents the decay rate instead
of the growth rate, and it is negative in this case because molecules of the radioactive iso-
tope are declining instead of increasing like people in a growing population. Half-life is
70
Chapter 2
The Earth and Its Systems
analogous to doubling time and can be determined as follows, Since after on
Transcribed Image Text:16. What is the decay rate of carbon 147 Express your
answer in yr.
17. In dating using radiocarbon, the amount of 1C re-
maining at the time of measurement is expressed as
a percentage of modern carbon. For example, for a
sample that has 30% modern carbon, N/N, would
be 0.3. Using equation (2.2) and the k value deter-
mined in problem 16, what is the age of the sample
in years?
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Solution:
16. The decay rate is given in terms of half-life of radioactive material is given by,
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