College Physics: A Strategic Approach, 3e (Knight)
Chapter 30 Nuclear Physics
30.1 Conceptual Questions
1) Write the standard nuclear notation for the following nuclei: hydrogen-2, sulfur-33, and lead-
207.
2) Name the first three isotopes of hydrogen, write their symbols in standard notation, and
indicate which one is the most common and which one is the most unstable.
3) The primary reason that very large nuclei are unstable is due to
A) the cumulative repulsive force of the protons.
B) the cumulative attractive force between the protons and the orbiting electrons.
C) the repulsive force between the neutrons and the protons.
D) the extreme weakness of the gravitational attraction of the protons.
4) Atomic nuclei that are all isotopes of an element all have the same
A) number of nucleons.
B) mass.
C) number of protons.
D) number of neutrons.
5) All nuclei of a given element have the same number of
A) neutrons.
B) protons.
C) nucleons.
D) protons + neutrons.
6) An yttrium isotope has 39 protons and 50 neutrons in its nucleus. Which one of the following
symbols accurately represents this isotope?
A) Y
B) Y
C) Y
D) Y
E) Y
7) The atomic number of an atom is equal to the number of what particles in the nucleus?
A) protons
B) neutrons
C) nucleons
D) electrons
E) positrons.
8) The mass number of an atom is equal to the number of what particles in the nucleus?
A) protons
B) neutrons
C) nucleons
D) electrons
E) positrons.
9) The atomic number and mass number for calcium-39 are 20 and 39, respectively. How many
neutrons are in one atom?
A) 1
B) 19
C) 20
D) 39
E) 59
10) In a Nb nucleus, how many protons, neutrons, and electrons are found there?
A) 41, 52, 93.
B) 41, 52, 41.
C) 52, 41, 41.
D) 41, 52, 0.
E) 93, 41, 93.
11) The symbol for a certain isotope of polonium is Po. How many neutrons are there in the
nucleus of this isotope?
A) 84
B) 130
C) 214
D) 298
E) 314
12) The symbol for a certain isotope of radium is Ra. How many nucleons are there in the
nucleus of this isotope?
A) 88
B) 138
C) 214
D) 226
E) 314
13) The symbol for a certain isotope of strontium is Sr. What is the mass number of this
isotope?
A) 38
B) 52
C) 88
D) 90
E) 128
14) What is true of an element of atomic number 15 that has an isotope of mass number 32?
(There could be more than one correct choice.)
A) the number of protons in the nucleus is 15.
B) the number of neutrons in the nucleus is 15.
C) the number of protons in the nucleus is 32.
D) the number of nucleons in the nucleus is 47.
E) the number of neutrons in the nucleus is 17.
15) The atomic mass unit is defined as
A) the mass of a proton.
B) the mass of an electron.
C) the mass of a hydrogen-1 atom.
D) one twelfth the mass of a carbon-12 atom.
E) the mass of a carbon-12 nucleus.
16) A stable nucleus contains many protons very close to each other, all positively charged.
Why do the protons not fly apart due to mutual Coulomb repulsion?
A) An attractive nuclear force in the nucleus counteracts the effect of the Coulomb forces.
B) There are an equal number of electrons in the nucleus which neutralize the protons.
C) The neutrons in the nucleus shield the protons from each other.
D) The Coulomb force does not operate within nuclei.
E) The gravity of the protons and neutrons overcomes their repulsion at such close distances.
17) Which of the following statements is not true of the strong nuclear force?
A) The nuclear force has a short range, of the order of nuclear dimensions.
B) For two protons that are very close together, the nuclear force and the electric force have
about the same magnitudes.
C) The nuclear force does not depend on charge.
D) A nucleon in a large nucleus interacts via the nuclear force only with nearby nucleons, not
with ones far away in the nucleus.
E) The nuclear force affects both neutrons and protons.
18) The two strongest forces that act between protons in a nucleus are
A) the weak nuclear and electromagnetic forces.
B) the weak nuclear and the gravitational forces.
C) the electrostatic and the gravitational forces.
D) the strong nuclear and the electrostatic forces.
19) The main reason that there is a limit to the size of a stable nucleus is
A) the limited range of the gravitational force.
B) the short range nature of the strong nuclear force.
C) the weakness of the gravitational force.
D) the weakness of the electrostatic force.
20) In massive stars, three helium nuclei fuse together, forming a carbon nucleus, and this
reaction heats the core of the star. The net mass of the three helium nuclei must therefore be
A) higher than that of the carbon nucleus.
B) less than that of the carbon nucleus.
C) the same as that of the carbon nucleus because mass is always conserved.
D) the same as that of the carbon nucleus because energy is always conserved.
21) A fusion reaction releases energy because the binding energy of the resulting nucleus
A) is greater than the binding energy of the original nuclei.
B) is equal to the binding energy of the original nuclei.
C) is less than the binding energy of the original nuclei.
D) is released in the process.
E) is absorbed in the process.
22) The binding energy per nucleon of a nucleus
A) increases steadily as we go to heavier elements.
B) decreases steadily as we go to heavier elements.
C) is approximately constant throughout the periodic table, except for very light nuclei.
D) has a maximum near iron in the periodic table and decreases after that for heavier elements.
E) has a minimum near iron in the periodic table and increases after that for heavier elements.
23) An α particle is also known as
A) an electron.
B) a positron.
C) a helium nucleus.
D) a high-energy photon.
24) A β– particle is also known as
A) an electron.
B) a positron.
C) a helium nucleus.
D) a high-energy photon.
25) A β+ particle is also known as
A) an electron.
B) a positron.
C) a helium nucleus.
D) a high-energy photon.
26) A gamma ray is also known as
A) an electron.
B) a positron.
C) a helium nucleus.
D) a high-energy photon.
27) What is the mass number of alpha particles?
A) 1
B) 2
C) 3
D) 4
E) 6
28) What are the mass number, the atomic number, and neutron number for each of the following
particles?
(a) proton
(b) neutron
(c) alpha particle
29) What are the mass number A and the charge (in units of e) for each of the following particles
or rays?
(a) beta-plus
(b) beta-minus
(c) gamma ray
30) The nuclei of He are also known as
A) α particles.
B) β particles.
C) γ rays.
D) x-rays.
E) positrons.
31) In beta-minus decay
A) a proton is emitted.
B) a neutron is emitted.
C) an electron is emitted.
D) an electron decays into another particle.
E) a proton is transformed into a neutron.
32) During β+ decay
A) a neutron is transformed to a proton.
B) a proton is transformed to a neutron.
C) a neutron is ejected from the nucleus.
D) a proton is ejected from the nucleus.
E) the number of nucleons decreases.
33) During β– decay
A) a neutron is transformed to a proton.
B) a proton is transformed to a neutron.
C) a neutron is ejected from the nucleus.
D) a proton is ejected from the nucleus.
E) the number of nucleons increases.
34) When a β+ particle is emitted from an unstable nucleus, the atomic number of the nucleus
A) increases by 1.
B) decreases by 1.
C) increases by 2.
D) decreases by 2.
E) does not change.
35) When a β– particle is emitted from an unstable nucleus, the atomic number of the nucleus
A) increases by 1.
B) decreases by 1.
C) increases by 2.
D) decreases by 2.
E) does not change.
36) When a β– particle is emitted from an unstable nucleus, the atomic mass number of the
nucleus
A) increases by 1.
B) decreases by 1.
C) increases by 2.
D) does not change.
37) In β– decay, the number of neutrons in the nucleus is
A) decreased by 1.
B) decreased by 2.
C) increased by 1.
D) increased by 2.
E) remains unchanged.
38) In β– decay, the number of protons in the nucleus is
A) decreased by 1.
B) decreased by 2.
C) increased by 1.
D) increased by 2.
E) remains unchanged.
39) In positron decay, the number of protons in the nucleus is
A) decreased by 1.
B) decreased by 2.
C) increased by 1.
D) increased by 2.
E) remains unchanged.
40) A radioactive isotope of atomic number Z emits an alpha particle, and the daughter nucleus
then emits a beta-minus particle. What is the atomic number of the resulting nucleus?
A) Z -1
B) Z + 1
C) Z – 2
D) Z – 3
41) A radioactive isotope of atomic number Z emits a beta-minus particle, and then the daughter
nucleus emits a gamma ray. What is the atomic number of the resulting nucleus after both
processes?
A) Z – 1
B) Z + 1
C) Z – 2
D) Z – 3
42) Polonium-216 decays to lead-212 by emitting what kind of nuclear radiation?
A) alpha
B) beta-minus
C) beta-plus
D) gamma
E) x-rays.
43) The atom Fr decays to Ra by emitting what kind of nuclear radiation?
A) alpha
B) beta-minus
C) beta-plus
D) gamma
E) x-rays.
44) A β– decay occurs in an unstable nucleus when
A) a proton is converted to an electron by the strong force.
B) a proton is converted to a neutron by the strong force.
C) a neutron is converted to a proton by the weak force.
D) a neutron is converted to an alpha particle by the weak force.
E) a neutron is converted to a positron by the weak force.
45) When an unstable nucleus decays by emitting an alpha particle, the atomic number Z of the
nucleus
A) increases by 4.
B) increases by 2.
C) decreases by 2.
D) decreases by 4.
E) remains unchanged.
46) When an unstable nucleus decays by emitting an alpha particle, the atomic mass number A of
the nucleus
A) increases by 4.
B) increases by 2.
C) decreases by 2.
D) decreases by 4.
E) remains unchanged.
47) The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is about 29 years. Suppose
you have samples of both isotopes, and that they initially contain equal numbers of atoms of
these isotopes. How will the activities (number of decays per second) of the samples compare?
A) The activity of the cobalt-60 sample will be greater.
B) The activities cannot be compared without more information.
C) The activities will be equal.
D) The activity of the strontium-90 sample will be greater.
48) The half-life of cobalt-60 is 5.3 years, while that of strontium-90 is about 29 years. Suppose
you have samples of both isotopes, and that they initially have the same activity (number of
decays per second). What must be true of the numbers of cobalt-60 and strontium-90 nuclei in
these samples?
A) There are more strontium-90 than cobalt-60 nuclei.
B) There are equal numbers of cobalt-60 and strontium-90 nuclei.
C) There are more cobalt-60 than strontium-90 nuclei.
D) It is not possible to compare numbers of nuclei without knowing the masses of the samples.
49) If the half-life of a material is 45 years, how much of it will be left after 100 years?
A) more than 1/2
B) less than 1/2 but more than 1/4
C) more than 1/4 but less than 1/2
D) less than 1/4 but more than 1/8
E) less than 1/8
50) What happens to the half-life of a radioactive substance as it decays?
A) It remains constant.
B) It increases.
C) It decreases at a constant rate.
D) It decreases at an exponential rate.
51) What happens to the half-life of a radioactive substance as we increase its temperature?
A) It does not change.
B) It increases.
C) It decreases at a constant rate.
D) It decreases at an exponential rate.
52) Two radioactive isotopes, X and Y, both decay to stable products. The half-life of X is about
a day, while that of Y is about a week. Suppose a radioactive sample consists of a mixture of
these two nuclides. If the mixture is such that the activities arising from X and Y are initially
equal, then a few days later the activity of the sample will be due
A) predominantly to Y.
B) predominantly to X.
C) entirely to Y.
D) to X and Y equally.
53) Suppose the half-life of an isotope is 2 days. You purchase 10 grams of the isotope, but it
was produced in a laboratory 4 days before it was delivered to you. How much of this isotope
will you have 3 days after it was delivered to you?
A) more than 2.5 grams but less than 5 grams
B) 2.5 grams
C) more than 1.25 grams but less than 2.5 grams
D) 1.25 grams
E) less than 1.25 grams
54) How many protons, neutrons, and nucleons are there in a carbon-14 nucleus?
55) Modern in-air nuclear bomb tests have created an extra high level of 14C in our atmosphere.
If future archaeologists date samples from this era, without knowing of this testing, will their
carbon-14 dates be too young, too old, or correct? If correct, why?
A) Too young.
B) Too old.
C) Correct, since 14C from bomb tests is different from that produced naturally.
D) Correct, because modern biological materials do not gather 14C from bomb tests.
56) Carbon-14 decays by β– emission. What nucleus is left after this decay?
A) carbon-13
B) carbon-14
C) carbon-15
D) nitrogen-14
E) nitrogen-15
57) A person receives an absorbed dose of protons of 20 millirads. The RBE of protons is 5.
What is this person’s equivalent dose in rem?
A) 4 millirem
B) 15 millirem
C) 20 millirem
D) 25 millirem
E) 100 millirem
58) The chief hazard of radiation damage to living cells is
A) due to heating.
B) due to ionization.
C) due to the creation of chemical impurities.
D) the creation of new isotopes within the body.
E) the creation of radioactive material within the body.
59) Inside the nucleus, the weakest of the four fundamental forces is
A) the weak nuclear force.
B) the electromagnetic force.
C) the gravitational force.
D) the strong nuclear force.
60) Inside the nucleus, the strongest of the four fundamental forces is
A) the weak nuclear force.
B) the electromagnetic force.
C) the gravitational force.
D) the strong nuclear force.
61) Leptons can interact by which of the following forces?
A) strong nuclear force, weak nuclear force, electromagnetic force, gravitation
B) strong nuclear force, weak nuclear force, electromagnetic force
C) weak nuclear force, electromagnetic force, gravitation
D) strong nuclear force, weak nuclear force
E) strong nuclear force, electromagnetic force, gravitation
62) Which of the following particles are leptons? (There may be more than one correct choice.)
A) protons
B) neutrons
C) electrons
D) photons
E) quarks
63) Elementary particles that experience the weak nuclear force but not the strong nuclear force
are called
A) leptons.
B) hadrons.
C) mesons.
D) bosons.
E) baryons.
64) What combination of quarks produces a proton and what are the electric charges on these
quarks, expressed in terms of e?
65) What combination of quarks produces a neutron and what are the electric charges on these
quarks, expressed in terms of e?
66) The proton is made up of which one of the following quark combinations (up, down, strange,
charm, top, bottom)?
A) uud
B) ddu
C) udd
D) ttb
E) bst
67) The neutron is made up of which one of the following quark combinations (up, down,
strange, charm, top, bottom)?
A) uud
B) ddu
C) udd
D) ttb
E) bst
68) Which of the following particles are not made up of quarks? (There could be more than one
correct choice.)
A) alpha particle
B) electron
C) proton
D) positron
E) neutron
69) Which of the following particles (or groups of particles) are made up of quarks?
A) protons, neutrons, and electrons
B) electrons and neutrinos
C) photons
D) protons and neutrons
E) All particles except for photons are made up of quarks.
70) What are the possible charges of a quark (not an antiquark)?
A) –e, 0, e
B) -2/3 e, -1/3 e, +1/3 e, +2/3 e
C) -2/3 e, +1/3 e
D) -1/3 e, +2/3 e
E) -1/3 e, +1/3 e
71) How many quarks are in a deuteron, H?
A) 2
B) 3
C) 4
D) 6
E) 9
72) How many quarks are in a tritium isotope, H?
A) 2
B) 3
C) 4
D) 6
E) 9
30.2 Problems
1) In a head-on collision, an alpha particle (Z = 2) of energy bounces straight back from
a nucleus of charge How close were the centers of the objects at closest approach? (1 eV =
1.60 × 10-19 J, e = 1.60 × 10-19 C, 1/4πε0 = 8.99 × 109 N ∙ m2/C2)
A) 2.81 × 10-14 m
B) 3.39 × 10-12 m
C) 6.56 × 10-15 m
D) 2.17 × 10-14 m
2) In the first nuclear reaction observed, physicists saw an alpha particle (Z = 2) interact with a
nitrogen nucleus in air (Z = 7) to produce a proton. The energy of the alpha particle was
enough to enable the nuclei to touch in spite of the Coulomb repulsion. What distance (in fm)
between the centers of the alpha particle and the nitrogen was reached? This determines a limit
on the radius of the nitrogen nucleus. (1 eV = 1.60 × 10-19 J, e = 1.60 × 10-19 C, 1/4πε0 = 8.99
× 109 N ∙ m2/C2)
A) 0 fm
B) 0 fm
C) 0 fm
D) 0 fm
3) The diameter of an atom is 1.4 × 10-10 m and the diameter of its nucleus is 1.0 × 10-14 m.
What fraction of the atom’s volume is occupied by its nucleus?
A) 3.6 × 10-13
B) 7.1 × 10-5
C) 5.1 × 10-9
D) 2.6 × 10-17
4) The radius R of a nucleus of mass number A is given by R = R0 A1/3, where R0 = 1.2 × 10-15
m, calculate the density of a nucleus that has contains 57 protons and 82 neutrons. The mass of a
nucleon (proton or neutron) is 1.67 × 10-27 kg.
5) How much energy is released when 0.60 μg of 3H have decayed to 3He? The mass of 3He is
3.0160293 u, the mass of 3H is 3.0160492 u, 1 u = 931.5 MeV/c2, 1 eV = 1.60 × 10-19 J, and
NA = 6.022 × 1023 molecules/mol.
6) A summary of the nuclear reactions that power our sun is 4p → 4He + 2e–, with masses of
938.272 MeV/c2 for a proton, 3727.38 MeV/c2 for the helium nucleus, and 0.511 MeV/c2 for
each electron. How much energy is released by each of these reactions?
A) 24.69 MeV
B) 28.3 MeV
C) 2790.13 MeV
D) 279.01 MeV
7) A beryllium-8 nucleus at rest undergoes double alpha decay as follows:
Be → He + He
The known atomic masses are:
He: 4.002603 u
Be: 8.005305 u
What is the kinetic energy of each departing alpha particle? (1 u = 931.5 MeV/c2)
A) 46 keV
B) 65 keV
C) 92 keV
D) 130 keV
E) 180 keV
8) One of the fusion reactions that occurs in the sun is:
He + He → He + H + H
The following atomic masses are known:
H: 1.007825 u
He: 3.016029 u
He: 4.002603 u
What is the reaction energy released in this fusion reaction? (1 u = 931.5 MeV/c2)
A) 11 MeV
B) 13 MeV
C) 15 MeV
D) 17 MeV
E) 19 MeV
9) The following masses are known:
n 1.008665 u
H 1.007825 u
Ra 226.025403 u
What is the binding energy of Ra? (1 u = 931.5 MeV/c2)
A) 1700 MeV
B) 1900 MeV
C) 2100 MeV
D) 2300 MeV
E) 2500 MeV
10) The stability of C with respect to alpha, beta-plus and beta-minus decay is to be
determined. The following atomic masses are known:
He: 4.002603 u
Be: 7.016928 u
B: 11.009305 u
C: 11.011433 u
N: 11.026742 u
The C nucleus is
A) not subject to alpha, beta-plus or beta-minus decay.
B) subject to alpha decay only.
C) subject to beta-plus decay only.
D) subject to beta-minus decay only.
E) subject to beta-plus or beta-minus decay, but not to alpha decay.
11) The stability of Cl with respect to alpha, beta-plus and beta-minus decay is to be
determined. The following atomic masses are known:
He: 4.002603 u
P: 31.973907 u
S: 35.967081 u
Cl: 35.968307 u
Ar: 35.967546 u
The Cl nucleus is
A) not subject to alpha, beta-plus or beta-minus decay.
B) subject to alpha decay only.
C) subject to beta-plus decay only.
D) subject to beta-minus decay only.
E) subject to beta-plus or beta-minus decay, but not to alpha decay.
12) Bismuth Bi is known to be radioactive. The stability of Bi with respect to alpha, beta-
plus and beta-minus decay is to be determined. The following atomic masses are known:
He: 4.002603 u
Tl: 207.981998 u
Pb: 211.991871 u
Bi: 211.991255 u
Po: 211.988842 u
The Bi nucleus is
A) subject to alpha decay only.
B) subject to beta-plus decay only.
C) subject to beta-minus decay only.
D) subject to alpha or beta-plus decay, but not beta-minus decay.
E) subject to alpha or beta-minus decay, but not beta-plus decay.
13) Uranium-238 decays into thorium-234 plus an alpha particle. The known masses are
He: 4.002603 u
Th: 234.043583 u
U: 238.050786 u
How much energy is released in this process? (1 u = 931.5 MeV/c2)
A) 4.28 MeV
B) 3.76 MeV
C) 3.18 MeV
D) 2.89 MeV
E) 5.05 MeV