Solution Manual Chapter 15, Nuclear Energy
Some useful conversions:
1.00 MeV is 1.60 × 10–13 joules.
1 fission reaction produces approximately 2.0 × 102 MeV.
Boltzmann’s constant, 8.617 × 10−5 eV/K
Avogadro’s number = 6.02 × 1023 entities per mol or 6.02 × 1026 entities per kmol.
____________________________________________________________________
15.1 Write down possible fission reactions (conserving charge and nucleons) for
XeandSrBaKr 140
54
92
38
142
56
92
36 ,,
(Krypton, barium, strontium and xenon respectively).
Need: Fission reactions producing isotopes of krypton, barium, strontium and xenon.
15.2 Find the error in this nuclear reaction: It describes a process for nuclear fusion.
(Fusion is the opposite of fission, because it’s the addition of a nuclear particle to a
nucleus to make a heavier element than the starting materials1.)
nHeHH 1
0
4
2
3
1
2
12
Why is tritium (see footnote) a particularly dangerous radioisotope?
Need: What’s wrong with the fusion reaction written above? Why is tritium
particularly dangerous?
1
H
2
1
is the stable hydrogen isotope called “heavy hydrogen” or “deuterium”, and its atom can be written
as D; its nucleus has the symbol d. Also
H
3
1
is a radioactive isotope of hydrogen with a 12.5 year half life
called “tritium” and can be written as T; its nucleus has the symbol t. Finally
He
4
2
is the nucleus of a
helium atom called an alpha particle, symbol . It’s the second element in the Periodic Table (having just
two protons and two neutrons in its nucleus). An alpha particle is a fairly common radioactive decay
product and possibly dangerous in its own right.
15.3. How much uranium-235 is used in grams in producing 1.0 MWD (i.e., a megawatt–
day) of energy given 2.0 × 102 MeV/fission?
Need: Amount of uranium in grams consumed to produce 1.0 MWD of energy.
Know: 1.0 MWD = 1.0 × 24 × 3600 = 8.6 × 104 MJ = 8.6 × 1010 J. Each nuclear
fission produces 2.0 × 102 MeV.
4
15.4. In the previous question approximately how much of this uranium has been
annihilated (answer in mg)?
Need: How much U-235 annihilated to produce 1.0 MWD?
15.5. Find the Error in This Solution: What is the average energy for an ideal gas of
neutrons in a graphite-moderated reactor 750C? An ideal gas’s average energy is
kT
with k = 8.617 × 10−5 eV/K.
Need: Average energy for an ideal gas of neutrons in a graphite–moderated reactor
750C.
15.6. Find the Error in This Solution: What’s the logarithmic energy decrement for a
neutron that thermalizes from 2. MeV to 0.1 eV?
Need: The logarithmic energy decrement for a neutron between 2. MeV and 0.1
eV
15.7. How many collisions does it take for neutrons in a graphite–moderated reactor2 to
slow to thermal energies at 20C and at 350C?
Need: # of collisions to thermalize a fast neutron given its initial energy is 2. MeV
Know: Use the logarithmic energy decrement method:
2/3 A
2
where
final
init E
E
n
p
.
At 20C a thermal neutron has energy of 0.0252eV and at 350C an energy of 0.0537
eV (see Example 15.4). A carbon nucleus has a mass of 12 so that = 2/(12.0 + 2/3)
= 0.157.
15.8. How many times can you use a charge of 235U/238U fissile fuel if you reprocess the
fuel when it is spent and recover all of the fissile Pu-239 there? Assume that 60% of the
original fissile charge of U-235 was indirectly converted to Pu-239 from U-238. (Hint:
It’s a geometric series if the Pu-239 converted from the original U-235 is reused.)
Need: Fuel value of initial charge of 235U
15.9. What is the ultimate fuel value of 235U in a light water reactor (x = 60%) and in a
graphite-moderated reactor (x = 95%)? (Hint: See Problem 15.8).
Need: Ultimate ideal value of initial charge of 235U in a light water and a graphite
moderated reactor.
15.10. How much heat in watts is generated by radioactive 90Sr in a nuclear core at
shutdown and at 193 years later? Assume that each radioactive decay of 90S produces
0.545 MeV/ disintegration and that the initial amount of 90Sr is 8. kg (see Example 15.7).
Does 90Sr meaningfully add to the decay heat in a nuclear meltdown?
Need: Heat produced by radioactive decay of 8. kg of 90Sr.
15.11. The total decay heat on shutdown is about 180 MW for a large power reactor.
What’s the average fission product half life on shutdown if there are 500. kg of fission
products and each radioactive decay releases 0.50 MeV? Assume the average molecular
mass of the fission products is 130. kg/kmol.
Need: Average half life by radioactive decay of 500. kg of short lived fission
products that produce 180 MW of heat.
Know: Initial fission products are 500. kg and the energy released per radioactive
decay is 0.50 MeV. Average molecular mass of the fission products is 130. kg/kmol.
Avogadro’s number is 6.02 × 1026 atoms/kmol.
15.12. A heterogeneous reactor, as the name suggests, has non-uniform properties, e.g., a
graphite moderator slab adjacent to a fissile
U
235
92
slab. Without doing the arithmetic can
you deduce arguments why this might increase the net thermal neutron flux? Hint:
Sketch the expected neutron distribution, both fast and thermal, under the sketch below.
What might this do to the resonance escape probability?
Need: Explanation of thermal neutron distribution in moderator and open
channels. Also will this increase or decrease p?
U
235
92
Graphite
Moderator
Graphite
Moderator
U235 fissile
fuel