Concept explainers
(a)
The number of carbon atoms in the given sample.
(a)
Answer to Problem 24P
The number of carbon atoms in the given sample is
Explanation of Solution
Write the equation to find the number of carbon atoms.
Here,
Conclusion:
Substitute
Therefore, the number of carbon atoms in the given sample is
(b)
The number of carbon atoms in the given sample.
(b)
Answer to Problem 24P
The number of carbon-14 atoms in the given sample is
Explanation of Solution
Write the equation to find the number of carbon-14 atoms.
Here,
Conclusion:
Substitute
Therefore, the number of carbon-14 atoms in the given sample is
(c)
The decay constant for carbon-14 in inverse seconds.
(c)
Answer to Problem 24P
The decay constant for carbon-14 in inverse seconds is
Explanation of Solution
Write the equation to find the half-life time of carbon-14.
Here,
Conclusion:
Substitute
Therefore, the decay constant for carbon-14 in inverse seconds is
(d)
The number of initial number of decays in a week immediately after the death of species.
(d)
Answer to Problem 24P
The number of initial number of decays in a week immediately after the death of species is
Explanation of Solution
Write the equation to find the decay rate.
Here,
Write the equation to find
Here,
Rewrite the equation for
To find the
Conclusion:
Substitute
Therefore, the number of initial number of decays in a week immediately after the death of species is
(e)
The new number of decays in a week in the current sample.
(e)
Answer to Problem 24P
The new number of decays in a week in the current sample is
Explanation of Solution
Write the equation to find the new number of decays in a week in the current sample.
Here,
Conclusion:
Substitute
Therefore, the new number of decays in a week in the current sample is
(f)
Lifetime of specimen in years using the results from part (c) and (d).
(f)
Answer to Problem 24P
Lifetime of specimen is
Explanation of Solution
Write the equation to find the fraction of decay.
Apply logarithm on both sides.
Rewrite the above equation in terms of
Conclusion:
Substitute
Therefore, the lifetime of specimen is
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Chapter 30 Solutions
Principles of Physics: A Calculus-Based Text
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