Energy and Human Ambitions on a Finite Planet, 2021a

15 Nuclear <strong>Energy</strong> 271
decay, β − decay, β + decay, <strong>and</strong> spontaneous fission?
14. In a year, an average American uses about 3 × 10 11 J of energy.
How much mass does this translate to via E mc 2 ? Rock has a
density approximately 3 times that of water, translating to about
3 mg per cubic millimeter. So roughly how big would a chunk of
rock material be to provide a year’s worth of energy if converted
to pure energy? Is it more like dust, a grain of s<strong>and</strong>, a pebble, a
rock, a boulder, a hill, a mountain?
15. The world uses energy at a rate of 18 TW, amounting to almost
6 × 10 20 J per year. What is the mass-equivalent 83 83: i This is how much mass would have
of this amount to “disappear” each year to satisfy current
of annual energy? What context can you provide for this amount human dem<strong>and</strong>.
of mass?
16. How much mass does a nuclear plant convert into energy if
running uninterrupted for a year at 2.5 GW (thermal)?
17. A large boulder whose mass is 1,000 kg having a specific heat
capacity of 1,000 J/kg/ ◦ C is heated from 0 ◦ C to a glowing 1,800 ◦ C.
How much more massive is it, assuming no atoms have been
added or subtracted?
4
18. Replicate the computations in Table 15.5 for He, paralleling the
56Fe
case in Example 15.3.2. Along the way, report the Δm in kg
<strong>and</strong> the corresponding ΔE in Joules, which are not in the table.
19. To illustrate the principle, let’s say we start with a nucleus whose
mass is 200.000 a.m.u. <strong>and</strong> inject 1,600 MeV of energy to completely
dismantle the nucleus into its constituent parts. How much mass
would the final collection of parts have?
a) the exact same: 200.000 a.m.u.
b) less than 200.000 a.m.u.
c) more than 200.000 a.m.u.
20. Using the setup from Problem 19, compute the mass of the final
configuration in a.m.u., after adding energy to disassemble the
nucleus.
21. Referring to Figure 15.10, what is the total binding energy (in MeV)
of a nucleus whose mass number is A 180?
Hint: convert MeV to Joules, then kg, then
a.m.u.
Hint: Fig. 15.10 is binding energy per nucleon.
22. Explain in some detail what happens if control rods are too effective
at absorbing neutrons so that each fission event produces too few
unabsorbed neutrons.
235
23. Which of the following is true about the fragments from a U
fission event?
a) any number of fragments (2 through 235) can be produced
b) a small number of fragments will emerge (2 to 5)
c) two nearly identical fragments will emerge
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Freely available at: https://escholarship.org/uc/energy_ambitions.