PROBLEM SOLUTION MANUAL FOR
Fundamentals of Nuclear
Science and Engineering
Third Edition
by
J. Kenneth Shultis
and
Richard E. Faw
Dept. of Mechanical and Nuclear Engineering
Kansas State University
Manhattan, KS 66506
email:
Revised June 2016
(c) Copyright 2007-2016
All Rights Reserved
This typescript is the property of the authors. It may not be copied in part or in
total without permission of the authors.
, Notice
This collection contains solutions to most of the problems in our book Funda-
mentals of Nuclear Science and Engineering, 3/e (Taylor & Francis, Boca Raton,
Florida, 2007. We do not warrant that all the solutions are correct or that other
approaches could give equally valid results. This collection is provided to you solely
as an aid in your teaching, and we ask that you do not copy this set for others
without our permission. If, in your teaching, you develop better solutions than are
presented here or find corrections are needed, we would appreciate receiving copies
so that, over time, this collection will be improved.
A sporadically updated errata for the book can be found on the world wide web
at http://www.mne.ksu.edu/~jks/books.htm
,Chapter 1
Fundamental Concepts
PROBLEMS
1. Both the hertz and the curie have dimensions of s−1. Explain the difference
between these two units.
Solution:
The hertz is used for periodic phenomena and equals the number of “cycles
per second.” The curie is used for the random or stochastic rate at which a
radioactive source decays, specifically, 1 Ci = 3.7 × 1010 decays/second.
2. Advantages of SI units are apparent when one is presented with units of barrels,
ounces, tons, and many others.
(a) Compare the British and U.S. units for the gallon and barrel (liquid and
dry measure) in SI units of liters (L).
(b) Compare the long ton, short ton, and metric ton in SI units of kg.
Solution:
Unit conversions are taken from the handbook Conversion Factors and Tables,
3d ed., by O.T. Zimmerman and I. Lavine, published by Industrial Research
Service, Inc., 1961.
(a) In both British and U.S. units, the gallon is equivalent to 4 quarts, eight
pints, etc. However, the quart and pint units differ in the two systems. The
U.S. gallon measures 3.7853 L, while the British measures 4.546 L. Note
that the gallon is sometimes used for dry measure, 4.405 L U.S. measure.
The barrel in British units is the same for liquid and dry measure, namely,
163.65 L. The U.S. barrel (dry) is exactly 7056 in 3, 115.62 L. The U.S.
barrel (liq) is 42 gallons (158.98 L) for petroleum measure, but otherwise
(usually) is 31.5 gallons (119.24 L).
(b) The common U.S. unit is the short ton of 2000 lb, 907.185 kg, 20 short
hundredweight (cwt). The metric ton is exactly 1000 kg, and the long ton
is 20 long cwt, 22.4 short cwt, 2240 lb, or 1016 kg.
1-1
, 1-2 Fundamental Concepts Chap. 1
3. Compare the U.S. and British units of ounce (fluid), (apoth), (troy), and
(avdp).
Solution:
The U.S. and British fluid ounces are, respectively, 1/32 U.S. quarts (0.02957
L) and 1/40 British quarts (0.02841 L). The oz (avdp.) is exactly 1/16 lb
(avdp), i.e., 0.02834 kg. Avdp., abbreviation for avoirdupois refers to a system
of weights with 16 oz to the pound. The apoth. apothecary or troy ounce is
exactly 480 grains, 0.03110 kg.
4. Explain the SI errors (if any) in and give the correct equivalent units for the
following units: (a) mgrams/kiloL, (b) megaohms/nm, (c) N· m/s/s, (d) gram
cm/(s−1/mL), and (e) Bq/milli-Curie.
Solution:
(a) Don’t mix unit abbreviations and names; SI prefixes only in numerator:
correct form is µg/L.
(b) Don’t mix names and abbreviations and don’t use SI prefixes in denomi-
nator: correct form nohm/m.
(c) Don’t use hyphen and don’t use multiple solidi: correct form N m s−2.
(d) Don’t mix names and abbreviations, don’t use multiple solidi, and don’t
use parentheses: correct form g cm s mL or better 10 µg m s L.
(e) Don’t mix names with abbreviations, and SI prefix should be in numerator:
correct form kBq/Ci.
5. Consider H2, D2, and H2O, treated as ideal gases at pressures of 1 atm and
temperatures of 293.2◦K . What are the molecular and mass densities of each.
Solution:
According to the ideal gas law, molar densities are identical for ideal gases
under the same conditions, i.e., ρm = p/RT . From Table 1.5, R = 8.314472
Pa m3/K. For p = 0.101325 MPa= 1 atm., and T = 293.2◦K , ρm = 41.56
mol/m3. Multiplication by molecular weights yield, respectively, 83.78 , 167.4,
and 749.0 g/m3 for the three gases.
6. In vacuum, how far does light move in 1 ns?
Solution:
∆x = c∆t = (3 × 108 m/s) × (10−9 s) = 3 × 10−4 m = 30 cm.
Fundamentals of Nuclear
Science and Engineering
Third Edition
by
J. Kenneth Shultis
and
Richard E. Faw
Dept. of Mechanical and Nuclear Engineering
Kansas State University
Manhattan, KS 66506
email:
Revised June 2016
(c) Copyright 2007-2016
All Rights Reserved
This typescript is the property of the authors. It may not be copied in part or in
total without permission of the authors.
, Notice
This collection contains solutions to most of the problems in our book Funda-
mentals of Nuclear Science and Engineering, 3/e (Taylor & Francis, Boca Raton,
Florida, 2007. We do not warrant that all the solutions are correct or that other
approaches could give equally valid results. This collection is provided to you solely
as an aid in your teaching, and we ask that you do not copy this set for others
without our permission. If, in your teaching, you develop better solutions than are
presented here or find corrections are needed, we would appreciate receiving copies
so that, over time, this collection will be improved.
A sporadically updated errata for the book can be found on the world wide web
at http://www.mne.ksu.edu/~jks/books.htm
,Chapter 1
Fundamental Concepts
PROBLEMS
1. Both the hertz and the curie have dimensions of s−1. Explain the difference
between these two units.
Solution:
The hertz is used for periodic phenomena and equals the number of “cycles
per second.” The curie is used for the random or stochastic rate at which a
radioactive source decays, specifically, 1 Ci = 3.7 × 1010 decays/second.
2. Advantages of SI units are apparent when one is presented with units of barrels,
ounces, tons, and many others.
(a) Compare the British and U.S. units for the gallon and barrel (liquid and
dry measure) in SI units of liters (L).
(b) Compare the long ton, short ton, and metric ton in SI units of kg.
Solution:
Unit conversions are taken from the handbook Conversion Factors and Tables,
3d ed., by O.T. Zimmerman and I. Lavine, published by Industrial Research
Service, Inc., 1961.
(a) In both British and U.S. units, the gallon is equivalent to 4 quarts, eight
pints, etc. However, the quart and pint units differ in the two systems. The
U.S. gallon measures 3.7853 L, while the British measures 4.546 L. Note
that the gallon is sometimes used for dry measure, 4.405 L U.S. measure.
The barrel in British units is the same for liquid and dry measure, namely,
163.65 L. The U.S. barrel (dry) is exactly 7056 in 3, 115.62 L. The U.S.
barrel (liq) is 42 gallons (158.98 L) for petroleum measure, but otherwise
(usually) is 31.5 gallons (119.24 L).
(b) The common U.S. unit is the short ton of 2000 lb, 907.185 kg, 20 short
hundredweight (cwt). The metric ton is exactly 1000 kg, and the long ton
is 20 long cwt, 22.4 short cwt, 2240 lb, or 1016 kg.
1-1
, 1-2 Fundamental Concepts Chap. 1
3. Compare the U.S. and British units of ounce (fluid), (apoth), (troy), and
(avdp).
Solution:
The U.S. and British fluid ounces are, respectively, 1/32 U.S. quarts (0.02957
L) and 1/40 British quarts (0.02841 L). The oz (avdp.) is exactly 1/16 lb
(avdp), i.e., 0.02834 kg. Avdp., abbreviation for avoirdupois refers to a system
of weights with 16 oz to the pound. The apoth. apothecary or troy ounce is
exactly 480 grains, 0.03110 kg.
4. Explain the SI errors (if any) in and give the correct equivalent units for the
following units: (a) mgrams/kiloL, (b) megaohms/nm, (c) N· m/s/s, (d) gram
cm/(s−1/mL), and (e) Bq/milli-Curie.
Solution:
(a) Don’t mix unit abbreviations and names; SI prefixes only in numerator:
correct form is µg/L.
(b) Don’t mix names and abbreviations and don’t use SI prefixes in denomi-
nator: correct form nohm/m.
(c) Don’t use hyphen and don’t use multiple solidi: correct form N m s−2.
(d) Don’t mix names and abbreviations, don’t use multiple solidi, and don’t
use parentheses: correct form g cm s mL or better 10 µg m s L.
(e) Don’t mix names with abbreviations, and SI prefix should be in numerator:
correct form kBq/Ci.
5. Consider H2, D2, and H2O, treated as ideal gases at pressures of 1 atm and
temperatures of 293.2◦K . What are the molecular and mass densities of each.
Solution:
According to the ideal gas law, molar densities are identical for ideal gases
under the same conditions, i.e., ρm = p/RT . From Table 1.5, R = 8.314472
Pa m3/K. For p = 0.101325 MPa= 1 atm., and T = 293.2◦K , ρm = 41.56
mol/m3. Multiplication by molecular weights yield, respectively, 83.78 , 167.4,
and 749.0 g/m3 for the three gases.
6. In vacuum, how far does light move in 1 ns?
Solution:
∆x = c∆t = (3 × 108 m/s) × (10−9 s) = 3 × 10−4 m = 30 cm.
