Energy and Human Ambitions on a Finite Planet, 2021a

15 Nuclear <strong>Energy</strong> 270
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3. How many neutrons does the isotope Fe contain?
12 13
4. Use the information in the boxes for C <strong>and</strong> C in Figure 15.4
to determine the weighted composite mass of a natural blend of
carbon—showing work—<strong>and</strong> compare this to the number in the
left-most box for carbon in the same figure.
5. In Figure 15.4, what are the only mass numbers, A, for which no
stable nuclei exist?
6. What are the only three long-lived radioactive isotopes in the
portion of the Chart of the Nuclides appearing in Figure 15.4, <strong>and</strong>
which one lives the longest (how long)?
7. Cosmic rays impinging on our atmosphere generate radioactive
14
C from
14 N nuclei. 78 14
These C atoms soon team up with oxygen 78: Nitrogen is the principal constituent in
to form CO 2 , so that plants absorbing CO 2 from the air will have Earth’s atmosphere.
about one in a trillion of their carbon atoms in this form. Animals
eating these plants 79 will also have this fraction of carbon in their 79: . . . <strong>and</strong>/or eating the animals that eat
bodies, until they die <strong>and</strong> stop cycling carbon into their bodies. At these plants
14
this point, the fraction of carbon atoms in the form of C in the The wording is long because without context,
it’s just math. The real learning is in
body declines, with a half life of 5,715 years. If you dig up a human
skull, <strong>and</strong> discover that only one-eighth of the usual one-trillionth
the application of math to the world.
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of carbon atoms are C, how old do you deem the skull to be?
8. If a friend creates a nucleus whose half-life is 4 hours <strong>and</strong> gives it
to you at noon, what is the probability that it will not have decayed
by noon the following day?
235 238
9. In close analog to the half-lives of U <strong>and</strong> U, let’s say two
elements have half lives of 4.5 billion years <strong>and</strong> 750 million years. 80
If we start out having the same number of each (1:1 ratio), what
will the ratio be after 4.5 billion years? Express as x:1, where x is
the larger of the two.
10. Control rods in nuclear reactors tend to contain 10 B, which has
a high neutron absorption cross section. 81 What happens to this
nucleus when it absorbs a neutron, <strong>and</strong> is the result stable? If not,
track the decay chain until it l<strong>and</strong>s on a stable nucleus.
80: ...afactorof6different
81: ...asindicated by the orange lower-half
of the corresponding box in Figure 15.4
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11. If someone managed to create a B nucleus, what would its fate
be? Track the decay chain on Figure 15.4—indicating the type of
decay at each step—until it reaches stability, <strong>and</strong> indicate how
long each step is likely to take.
12. A particular nuclide is found to have lost 3 neutrons <strong>and</strong> 1 proton
after a decay chain. What combination of α <strong>and</strong> β decays could
account for this result?
13. How would you qualitatively describe the overall sense from
Figure 15.8 in terms of where 82 on the chart one is likely to see α
82: Region descriptions can include references
to the mass range (e.g., low mass
or high mass), above or below the stable
elements (proton-rich or neutron-rich).
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.