Find the age t of a sample, if the total mass of carbon in the sample is me, the activity of the sample is A, the current ratio of the mass of C to the total mass of carbon in the atmosphere is r, and the decay constant of 14C is A. Assume that, at any time, C is a negligible fraction of the total mass of carbon and that the measured activity of the sample is purely due to 14C. Also assume that the ratio of mass of 14C to total carbon mass in the atmosphere (the source of the carbon in the sample) is the same at present and on the day when the number of 14C atoms in the sample was set

Find the age t of a sample, if the total mass of carbon in the sample is me, the activity of the sample is A, the current ratio of the mass of C to the total mass of carbon in the atmosphere is r, and the decay constant of 14C is A. Assume that, at any time, C is a negligible fraction of the total mass of carbon and that the measured activity of the sample is purely due to 14C. Also assume that the ratio of mass of 14C to total carbon mass in the atmosphere (the source of the carbon in the sample) is the same at present and on the day when the number of 14C atoms in the sample was set

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Nuclear Reactions

Nuclear reactions are processes in which the fundamental characteristics of a nucleus changes. They change into a completely different nucleus. These processes occur naturally in an unstable nucleus. Bombarding an energetic particle can induce nuclear reactions. In this article, both the naturally occurring nuclear reactions are termed as radioactive decay and the induced nuclear reactions are further categorized as nuclear fission and nuclear fusion.

Question

6
Carbon-14 (C) dating is a method for finding the age of an
organic artifact from the quantity of 14C it contains. Carbon-14,
an unstable isotope of carbon, follows a well-known sequence of
decay processes. The decay constants of these processes have
been well established, allowing researchers to determine the age
of an artifact knowing both the original amount of 14C and the
current amount.
In the lab, it is relatively easy to measure the activity of a sample
and to estimate the mass of carbon in the sample. From these
measurements, it is possible to find the age of the sample.

e
Part A
Find the age t of a sample, if the total mass of carbon in the sample is me, the activity of the sample is A, the current ratio of the mass of 14C to the total
mass of carbon in the atmosphere is r, and the decay constant of 14C is A Assume that, at any time, 14C is a negligible fraction of the total mass of
carbon and that the measured activity of the sample is purely due to 14C. Also assume that the ratio of mass of 14C to total carbon mass in the
atmosphere (the source of the carbon in the sample) is the same at present and on the day when the number of 14C atoms in the sample was set.
Express your answer in terms of the mass ma of a 14C atom, mc, A, r, and X.
View Available Hint(s)
t =
VE
ΑΣΦ
1 Ama
2
.
In
rmc
C
2.
?

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