SOLUTIONS MANUAL FOR
NUCLEAR
ENGINEERING
FUNDAMENTALS
A Practical Perspective
by
Robert Masterson
** Immediate Download
** Swift Response
** All Chapters included
, Nuclear Engineering and Its Applications
Question Manual
Answers to Questions in Chapters 1 to 33
Chapter 1
Questions for Chapter 1
The following questions cover the material presented in this chapter, and in some cases, previous chapters as well. They are designed to
test how well the student has acquired a working knowledge of the subject matter.
1. What percentage of the internal volume V of an atom is completely empty space ? Ans: Approximately 99.999 %
2. Suppose that an element has eleven protons in the nucleus. What element is it and what is its chemical symbol? How many
electrons does it have orbiting the nucleus ? Ans: The element is sodium, which has the chemical symbol Na. It has 11 electrons
orbiting the nucleus.
3. Suppose that two of the electrons are stripped off of the nucleus. What is the atom of the element called in this case? Ans: A
sodium ion
4. How many particles are there in a gluon, and what is its purpose ? Ans: Part 1: Two - a quark and an anti-quark pair. Part 2: The
purpose of the gluon is to hold the quarks in the protons and neutrons together and also to bind together the protons and the
neutrons into the nucleus as a whole
5. What quarks can be found in a proton and what quarks can be found in a neutron? Ans: Part 1: In a proton, there are two up quarks
and a down quark. Part 2: In a neutron, there are two down quarks and an up quark.
6. What causes the nuclei of some atoms to decay, and what causes the nuclei of other atoms to be stable ? Ans: The ratio of the
number of neutrons to the number of protons.
7. How long do protons live before they decay ? Ans: As far as we know protons never delay. If they do decay, their half life is at
least 20 billion years.
8. How long does a neutron live outside of the nucleus of an atom before it decays ? Ans: On average, about 15 minutes
9. Why does it not decay sooner when it is inside of the nucleus ? Ans: Inside of the nucleus, it is exposed to additional gluons.
Somehow these gluons prevent one of the down quarks from decaying into an up quark.
10. What does a neutron typically decay into ? Ans: When a neutron decays, it usually decays into a proton and an electron
11. What is the heaviest element in the Periodic Table, and what is the lightest ? Ans: Uranium and hydrogen
12. Who invented the Heisenberg Uncertainty Principle, and write down an equation that describes it mathematically ? Ans: Part 1:
Werner Heisenberg Part 2: E*t h or p*x h
13. What does the term “mass-energy” refer to ? Ans: The fact that mass and energy are related by Einstein’s famous equation E =
mc2.
14. What is the “expectation value” of a nuclear reaction ? Ans: The expected outcome of the reaction, when averaged over billions of
individual reactions
15. What kind of equation do neutrons follow when they travel through space in large numbers ? Ans: A neutron diffusion equation
16. What property of the neutron can we use to control the rate at which it interacts with other materials ? Ans: Its nuclear cross
section
17. Who is Richard Feynman, and what did he do? Ans: A Nobel Prize winning physicist who helped to perfect the nuclear theory of
electricity and magnetism. His biography can be found at the following URL: www.feynman.com
18. What “spin” do force particles like the photon and the gluon have, and what nuclear spin does a matter particle like the neutron
have ? Ans: Force particles have a spin of 0 or 1 and matter particles have a spin of ½.
19. Name four conservation laws that all nuclear particles must obey, Ans: The conservation of mass, momentum, energy, and spin
20. Suppose that a force particle has a rest mass mo and travels at 50% of the speed of light. What is the effective range of the force
that this force particle can transmit ? Ans: According to the Uncertainty Principle, its range is limited by t = h/E or t = h/ mo c2.
Since it travels at 50% of the speed of light c, the maximum distance it can travel to transmit the force is x = vt = (c/2) h/ moc2
= h/2 moc.
21. How big is a proton or a neutron ? Ans: About 10-16 cm in diameter
22. Name two types of Baryons that nuclear engineers need to be aware of when designing a reactor core. Ans: protons and neutrons
,23. All nuclear reactions must conserve a fundamental nuclear property known as the spin S. If two particles go into a reaction, and
three particles come out of it, write an expression showing how the spin of the particles in the reaction must be conserved. Ans: S1
IN + S 2IN = S 3 OUT + S 4OUT + S 5 OUT.
24. What is the definition of a Hadron ? Ans: A Hadron is a very heavy composite particle that is made out of two or three quarks in a
bound state.
25. According to the Standard Model of Particle Physics, is an electron heavier than or lighter than a neutron ? Ans: It is much lighter
than the neutron – by a factor of about 2000.
26. A Plutonium-239 nucleus has 94 protons. How many neutrons does it contain ? Ans: It contains 239 – 94 = 145 neutrons
27. What is the density of a typical atomic nucleus ? Ans: About 1.8 x 1017 kg/m3
28. Which particle is heavier - an up quark or a down quark ? Ans: A down quark
29. What is the approximate rest mass of the photon, which is a particle that can be produced in a nuclear reactor core in great
numbers ? Ans: Its rest mass is zero, which means that we can never find a photon sitting still
30. Suppose that a uranium-235 nucleus splits apart, and that it transforms itself into two fission products that have an average binding
energy of 8 MeV per nucleon. Approximately how much mass per nucleon is converted into energy in the process ? Ans: Uranium
has an average binding energy of about 7.6 MeV per nucleon, so approximately 0.4 MeV of energy is released per nucleon in the
process. The mass converted into energy in the process is therefore m = E/c2 = 0.4 MeV/c2 per nucleon
31. What is the difference between a Baryon and a Meson ? Ans: Baryons are made up of three quarks and Mesons are made up of
two
32. What are the three fundamental differences between the nuclear force, which is carried by the gluons, and the electrical force,
which is carried by the photons ? Ans: The nuclear force is much stronger than the electrical force; the energy levels of the protons
and the neutrons in the nucleus are not quantized to the same extent that the energy levels of the electrons are, and the nuclear
forces have a much shorter range than the electrical ones. For example, they have a range of about 10 –12 cm vs. an essentially
infinite one when photons (the carriers of the electromagnetic force) are involved.
33. What is the diameter of an atom and what is the diameter of the nucleus ? Ans: The average atom is about 0.25 x 10-8 cm across
and the average nucleus is about 1 x 10-12 cm across
34. What is the electrical charge of a Quark ? Ans: +1/3,-1/3, +2/3 or -2/3
35. What is a Fermion ? Ans: Fermions are matter particles that have a fractional spin of ½ or – ½.
36. What force particle is responsible for all of the chemical reactions that occur in a nuclear power plant ? Ans: The photon, which is
the carrier of the electromagnetic force field
37. Suppose you are a reactor operator who wants to make sure that neutrons do not decay into protons and electrons while you are
operating the reactor. Is this a common problem that you need to be concerned about ? No, because the half life of a neutron
outside of an atomic nucleus is about 15 minutes.
38. What is an example of a common Fermion ? Ans: The electron
39. Write a simple equation for the diameter of the atomic nucleus. Ans: D = 2.5 A 1/3 x 10-13 cm
40. A student who is studying nuclear physics decides to become a nuclear engineer. He is put in charge of discovering where all of
the decay heat in a reactor core comes from. What physical process is responsible for generating most of this decay heat ? Ans:
The process of radioactive beta decay, and to be specific, the process of - decay
41. What sort of quantum statistics do all Fermions behave ? Ans: Fermi-Dirac statistics
42. What is the name of the theory invented by Richard Feynman to describe the electromagnetic field, and which led to the discovery
of the Feynman Diagram? Ans; Quantum Electrodynamics (Q.E.D).
43. How many times stronger is the nuclear force (between two protons) than the electrical force ? Ans: About 140 (The exact
number is 137)
44. Complete the following sentence with the appropriate word or phrase: __________ particles are virtual particles that have an
integer spin. Ans: Force particles
45. How many different types of quarks are relevant to the field of nuclear power as a whole ? Ans: Two – the up quark and the down
quark
46. Where does the energy in a nuclear reactor come from ? Ans: From converting a small amount of mass m inside of the nucleus of
an atom into a large amount of energy E. The relationship between the two is given by Einstein’s famous equation E = mc2,
where c is the speed of light
47. What is the approximate size of a quark ? About 10-18 cm.
48. When an atom is NOT electrically neutral, what is it called ? Ans: An ion
49. What is the ratio of the radius of a neutron to the radius of a quark ? Ans: About 100
50. Who first proposed the existence of quarks within the nucleus of an atom ? Ans: Murray Gell-Man and Martin Zweig
51. Name a common type of ion with a charge of +2 that is produced in a commercial nuclear reactor core. Ans: A helium ion – i.e.,
an alpha particle
52. According to conventional wisdom, is a neutron larger than or smaller than a quark ? Ans: It is larger because it is composed of
two down quarks and an up quark
53. What is a Boson ? Ans: Bosons are force particles that have an integer spin (0, 1, or -1)
54. The energies of most nuclear particles are measured in electron volts (or eV). Approximately how many joules are there in an
electron volt ? Ans: 1 eV = 1.6×10−19 joules
55. What is an example of a common Boson that has a very long range ? Ans: The photon
, 56. Suppose that 60 neutrons and 40 protons go into a nuclear reaction, and 59 neutrons and 41 protons come out of it. Is the Baryon
number B conserved in this case ? Ans: Yes, since B = N + Z
57. What sort of quantum statistics do all Bosons behave ? Ans: Bose-Einstein statistics
58. What is the First Law of Thermodynamics ? Ans: The law of the conservation of energy (E IN = E OUT) or (Q IN = Q OUT), where in
this case, the symbol Q refers to heat
59. From a practical point of view, name two geometrical shapes that can be used to describe an atomic nucleus. Ans: An ellipse and a
sphere; however, when doing a parametric analysis, the spherical shape is more commonly used.
60. What quantity does the Second Law of Thermodynamics attempt to conserve ? Ans: The entropy S
61. If an atom has 92 protons and 146 neutrons, what type of atom is it ? Ans: Uranium-238
62. How is the Baryon number defined, and what is the Baryon number for this particular atom ? Ans: The Baryon number is defined
as the number of protons Z plus the number of neutrons N, so for this particular atom, the answer is 238.
63. If an atom were as big as our entire planet, then how large would the nucleus of the atom be ? Ans: About the size of a soccer
field or an NFL football field
64. Is the element Plutonium a naturally occurring element or is it a man-made one ? Ans: Plutonium can occur in nature, but it decays
too quickly to be found in large quantities over geological periods of time. For this reason, the plutonium we have in the world
today is classified as a man-made element
65. At the next level of nuclear structure, what is the difference between a proton and a neutron ? Ans: A proton is a composite
particle that consists of two up quarks and a down quark and a neutron is a composite particle that consists of two down quarks
and an up quark.
66. Suppose that masses of the proton and the neutron are given by the symbol m, and that the radius R of a nucleus is also known.
Write an expression for the average density of the nucleus. Ans: = 3m/R3
67. According to a table presented earlier in the chapter, which element has the largest electron cloud, and which one has the smallest
? Ans: The element Cesium has the largest electron cloud and the element hydrogen has the smallest
68. When the mass of a nuclear particle is converted entirely into energy, in what form does this energy tend to manifest itself within a
reactor core ? Ans: In the form of Heat
69. For most elements in the Periodic Table, what is the average binding energy per nucleon ? Ans: About 8 MeV per nucleon
70. Who is Hideki Yukawa and what did he do ? Ans: He proposed a model for the nuclear force field that showed that it has a very
short range. The range of the nuclear force could then be found by taking the derivative of the Yukawa potential
71. Name an additional conservation law that the neutrons and protons inside of the nucleus must obey. Ans: The conservation of the
Baryon number
72. Does the nucleus of an atom have a rigid boundary ? Ans: No – it has an indefinite or oscillatory one
73. Suppose that you discover a nuclear particle travelling through a reactor core that has a spin of zero. Is this particle more likely to
be a matter particle or a force particle ? Ans: It is more likely to be a force particle.
74. Approximately how many times smaller is the nucleus of an atom than the size of the electron cloud that surrounds it ? Ans:
About a factor of 10,000
75. According to the Standard Model of Particle Physics, how many “force particles” are there in the universe ? What are the names of
these particles ? Ans: There are currently only four force particles in the universe – the photon, the gluon, the W boson, and the Z
boson. A fifth particle called the graviton has been proposed to explain the force of gravity, but so far it has not been discovered
experimentally
76. What particle has been proposed to give other particles in a reactor a measureable rest mass, and what is its mass and its spin ?
Ans: The Higgs Boson, which has a rest mass of 128 Gev/c2 and a spin of 0.
77. At what fraction of the speed of light does an electron orbit an atomic nucleus? Ans: About 1 % of the speed of light
78. Approximately what is the ratio of the volume of the largest electron cloud surrounding an atom to the smallest ? Ans: About a
factor of 500
79. What is another name for the Theory of Everything, which attempts to explain the existence of all of the particles in the universe ?
Ans: The Theory of Strings or the TOE
80. What particle has been proposed to be the carrier of the gravitational force field ? Ans: The graviton
81. How many types of neutrinos can be found in a nuclear reactor ? Ans: Up to this time, 3 – the electron neutrino, the muon
neutrino, and the tau neutrino; however, the electron neutrino is by far the most common
82. Does the neutrino have a measureable rest mass ? Ans: yes – but it is very small (on the order of about 250,000 times smaller than
the rest mass of the electron)
83. What is the Higgs field and what is its purpose ? Ans: The Higgs field is a theoretical field that permeates all of space and time,
and gives mass to all elementary subatomic particles that it contains
84. The nuclear power business owes its existence to the fact that heavy elements like uranium have a lower average binding energy
per nucleon than lighter elements like iron do. Approximately how much smaller is the average binding energy per nucleon for
uranium than it is for iron ? Ans: According to Table 1.1, Iron has an average binding energy of about 8.8 MeV per nucleon, and
uranium has an average binding energy of about 7.6 MeV per nucleon. The difference in binding energy is therefore equal to 8.8
MeV – 7.6 MeV = 1.2 MeV (approximately equal to 15 %).
85. What elegant mathematical model can be used to predict the properties of all of the particles that can be found in a nuclear reactor
today ? Ans: The Standard Model of Particle Physics
86. For heavy elements, what neutron to proton ratio results in the most stable isotopes and nuclear fuels ? Ans: A neutron to proton
ratio between 1.6 and 1.5.
