Deck 44: Nuclear Structure

Question 1

What value of Z (atomic number) and A (mass number) result in the following β-decay?

A) Z = 6; A = 12
B) Z = 5; A = 8
C) Z = 6; A = 11
D) Z = 8; A = 12
E) Z = 8; A = 11

Answer 1

Z = 6; A = 12

Question 2

The isotope, tritium, has a half-life of 12.3 years. Assume we have 10 kg of the substance. How much tritium will be left after 30 years?

A) 0.20 kg
B) 1.8 kg
C) 0.18 kg
D) 1.7 kg
E) 4.1 kg

Answer 2

1.8 kg

Question 3

What value of Z (atomic number) and A (mass number) result in the following β-decay?

A) Z = 5; A = 14
B) Z = 4; A = 10
C) Z = 6; A = 14
D) Z = 7; A = 14
E) Z = 7; A = 13

Answer 3

Z = 7; A = 14

Question 4

How many radioactive atoms are present in a sample that has an activity of 0.5 μCi and a half-life of 10 years? (1 curie = 3.7 × 10¹⁰ decays/s)

A) 9.5 × 10¹² atoms
B) 8.4 × 10¹² atoms
C) 7.3 × 10¹² atoms
D) 6.5 × 10¹² atoms
E) 2.7 × 10⁵ atoms

Question 5

The half-life of ¹³¹I is 8.04 days. Three days after it was prepared, its activity was 0.50 μCi. How many curies (in μCi) were initially prepared?

A) .60
B) .70
C) .65
D) .55
E) .39

Question 6

The isotope, tritium, has a half-life of 12.3 years. Assume we have 10 kg of the substance. What will be the initial decay rate, at t = 0 (in decays/s)?

A) 1.09 × 10¹⁴
B) 1.8 × 10−⁹
C) 5.6 × 10⁸
D) 3.6 × 10¹⁸
E) 3.6 × 10¹⁷

Question 7

Find the binding energy per nucleon (in MeV/nucleon) of carbon-12. Assume:
M_C = 12.000 000 u
M _p = 1.007 825 u
M _n = 1.008 665 u
U = 1.66 × 10−²⁷ kg

A) 1.2
B) 4.2 × 10−²
C) 7.4
D) 7.7
E) 5.6

Question 8

Naturally radioactive nuclei can decay spontaneously by emitting the following particles:

A) helium nuclei, electrons, photons
B) electrons, neutrons, protons
C) helium nuclei, electrons, protons
D) electrons, neutrons, photons
E) quarks and leptons

Question 9

Find the ratio of the binding energy per nucleon for helium ( ) to uranium-238 ( ). Assume:
M _p = 1.007 825 u
M _n = 1.008 665 u
M_He = 4.002 603 u
M_U = 238.050 786 u
U = 1.66 × 10−²⁷ kg

A) 1.07
B) 0.934
C) 63.7
D) 1.6 × 10−²
E) 3.24

Question 10

The radius of a nucleus of (in fm) is

A) 15.4
B) 5.5
C) 12.8
D) 6.6
E) 4.9

Question 11

44 g of petrified wood was found in a petrified forest. A sample showed a ¹⁴C activity of 100 decays/minute. How long has the tree been dead (in years)? (The half-life of carbon-14 is 5730 years and freshly cut wood contains 6.5 × 10¹⁰ atoms of ¹⁴C per gram.)

A) 12300
B) 15600
C) 8500
D) 4700
E) 2400

Question 12

The ratio of the radius of a classical electron (r_e = k_ee²/m_ec² = 2.8 × 10−¹⁵ m) to the radius of a ⁴He nucleus (r = r₀A^1/3) is

A) 2.0
B) 0.68
C) 1.5
D) 0.92
E) 2.4

Question 13

The isotope, tritium, has a half-life of 12.3 years. Assume we have 10 kg of the substance. What will be the disintegration constant (in s−¹)?

A) 5.6 × 10−²
B) 5.6 × 10⁸
C) 3.2 × 10⁷
D) 1.8 × 10−⁹
E) 1.6 × 10⁶

Question 14

An alpha particle is emitted from a radioactive source with an energy of 5 MeV. How fast is it moving (in m/s)? (m = 4.002 603 u, 1 u = 1.66 × 10−²⁷ kg.)

A) 2.4 × 10⁷
B) 1.6 × 10⁷
C) 3.7 × 10⁷
D) 4.6 × 10⁷
E) 2.1 × 10⁷

Question 15

The ratio of the density of a neutron (r = r₀A^1/3) to the density of a classical electron (r_e = ke²/m_ec² = 2.8 × 10−¹⁵ m) is

A) 4.3 × 10²
B) 2.3 × 10⁴
C) 1.4 × 10²
D) 6.9 × 10−³
E) 4.3 × 10³

Question 16

What value of Z (atomic number) and A (mass number) result in the following alpha decay?

A) Z = 92; A = 238
B) Z = 91; A = 238
C) Z = 90; A = 234
D) Z = 93; A = 238
E) Z = 88; A = 236

Question 17

For large mass number nuclei which are stable, the ratio of protons to neutrons is

A) equal to 1
B) greater than 1
C) less than 1
D) unrelated to the stability of nuclei
E) almost 2 to 1

Question 18

Two isotopes of uranium have the same

A) mass number
B) neutron number
C) atomic number
D) nucleon number
E) nucleon number and neutron number

Question 19

Calculate the binding energy per nucleon (MeV/nucleon) for tritium, ( ) a radioactive isotope of hydrogen. Assume:
M _p = 1.007 825 u
M _n = 1.008 665 u
M _t = 3.016 05 u
U = 1.66 × 10−²⁷ kg

A) 2.8
B) 3.1
C) 1.0
D) 8.5
E) 2.1

Question 20

Find the binding energy (in MeV) of carbon-12. Assume:
M_C = 12.000 000 u
M _p = 1.007 825 u
M _n = 1.008 665 u
U = 1.66 × 10−²⁷ kg

A) 14.8
B) 0.511
C) 9.11
D) 92.3
E) 46.2

Question 21

A glass container holds equal numbers of atoms of phosphorus 30 with a half-life of 2.5 minutes and of nitrogen 13 with a half-life of 10 minutes. After 20 minutes the ratio of the number of nitrogen atoms remaining to the number of phosphorus atoms remaining is

A)
.
B)
.
C)
.
D) 64.
E) 256.

Question 22

How can a nucleus be described by particular values of A, Z and N when the mass of the nucleus is not equal to Zm_p + Nm_n, where m_p and m_n are the masses of free protons and neutrons?

A) A, Z and N have no intrinsic meaning.
B) A, Z and N describe the number of particles of given types, but mass has no meaning when part of the mass is elsewhere in the universe.
C) A, Z and N describe the number of particles an ideal rather than a real nucleus would have.
D) A, Z and N describe the number of particles of given types in the nucleus, but not their masses in a bound state.
E) A, Z and N describe the number of particles of given types in the nucleus since the missing mass consists of electrons that are also present in the nucleus.

Question 23

Two nuclei may have equal Z, but different A, because they contain

A) equal numbers of protons and neutrons.
B) equal numbers of protons but different numbers of neutrons.
C) different numbers of protons but equal numbers of neutrons.
D) different numbers of protons and neutrons.
E) electrons as well as neutrons.

Question 24

In beta decays

A) a proton changes to a neutron.
B) a neutron changes to a proton.
C) an electron is present in the nucleus before the decay.
D) (a), (b) or (c) may occur.
E) only (a) or (b) may occur.

Question 25

When a neutron decays, a proton and an electron are observed. When the electrons emitted from a sample of neutrons are observed, they are found to have different kinetic energies. This was accounted for by

A) introducing a different particle, the neutrino.
B) introducing the effect of gravity on the particles.
C) including the kinetic energies of the neutron and proton.
D) modifying the laws of conservation of momentum and energy.
E) taking into account the uncertainties associated with Heisenberg's Uncertainty Principle.

Question 26

The Q value for the following reaction, , is (in MeV) m(alpha) = 4.002 603 u
M(Be) = 9.012 182 u
M(n) = 1.008 665 u
M(C) = 12.000 00 u
1 u = 1.66 × 10−²⁷ kg

A) 8.4
B) 6.2
C) 7.3
D) 5.7
E) 3.5

Question 27

Heavy nuclei are unstable because

A) each nucleon is a separate particle that is not acted on by the nuclear force.
B) there are not enough protons present relative to the number of neutrons for the electrical force to be strong enough.
C) the nuclear force dominates the Coulomb repulsive force at distances less than 2 fm, but falls off rapidly at greater distances.
D) nuclei are stable only when the number of neutrons equals the number of protons.
E) nuclei are stable only when the number of protons exceeds the number of neutrons.

Question 28

Which of the effects listed below is not a major effect influencing the binding energy of the nucleus in the liquid-drop model?

A) The volume effect: the binding energy per nucleon is approximately constant when A > 50.
B) The surface effect: nucleons in the surface have fewer neighbors.
C) The quantum number effect: all nucleons in the nucleus have the same set of quantum numbers.
D) The Coulomb repulsion effect: protons repel protons.
E) The symmetry effect: stable nuclei tend to have N ≈ Z.

Question 29

What value of Z (atomic number) and A (mass number) result in the following gamma decay?

A) Z = 5; A = 12
B) Z = 4; A = 8
C) Z = 7; A = 12
D) Z = 6; A = 12
E) Z = 6; A = 11

Question 30

In nuclear magnetic resonance, nuclei absorb energy when flipping between nuclear

A) mass states.
B) spin states.
C) charge states.
D) decay states.
E) isotope states.

Question 31

The chart below shows part of the radioactive series beginning with the isotope . The isotope marked with an X is

A)
.
B)
.
C)
.
D)
.
E)
.

Question 32

What is the disintegration energy (in MeV) associated with this spontaneous decay? m_Nd = 143.910 083 u m_Ce = 139.905 434 u
M_He = 4.002 603 u
1 u = 1.66 × 10−²⁷ kg

A) 1.54
B) 2.37
C) 1.90
D) 4.13
E) 8.21

Question 33

Because we know that the half-lives of many radioactive isotopes are millions of years, we can deduce that

A) the longer it exists the more radioactive nuclei Earth produces.
B) the sun is the source of all the radioactive nuclei on Earth.
C) there must have been many more radioactive nuclei on Earth when life began.
D) there must have been far fewer radioactive nuclei on Earth before life began.
E) the natural radioactivity of minerals on the Earth was created by the Earth's internal temperature.

Question 34

Two nuclei which share the same atomic number Z always are

A) stable.
B) unstable.
C) isotopes.
D) isobars.
E) radioactive.

Question 35

The radius of an approximately spherical nucleus is given by r =

A) r₀Z³.
B) r₀Z^1/3.
C) r₀A³.
D) r₀A^1/3.
E) r₀(A − Z)^1/3.

Question 36

It is often possible to use atomic masses when calculating the binding energy of a nucleus. This is not true for calculating the Q value for the e⁺ decay process since

A) the electron masses do not cancel.
B) a positron is an antiparticle.
C) the electron masses cancel.
D) the mass of a positron cannot be neglected when compared to the mass of a nucleus.
E) none of the above.

Question 37

According to the shell model, binding energy per nucleon is greater when N or Z is equal to one of the numbers below except for

A) 2.
B) 8.
C) 13.
D) 20.
E) 28.

Question 38

The reaction energy associated with a nuclear reaction is

A) the total change in rest energy as a result of the reaction.
B) equivalent to the disintegration energy.
C) the minimum energy necessary for such a reaction to occur.
D) called the threshold energy.
E) the binding energy of the nucleons.

Question 39

Rutherford's experiment, in which he fired alpha particles of 7.7 MeV kinetic energy at a thin gold foil, showed that nuclei were very much smaller than the size of an atom because

A) some alpha particles passed through the foil undeflected.
B) some alpha particles were deflected backwards.
C) some alpha particles were captured by the gold nuclei.
D) the alpha particles could not get closer than 10−¹⁰ m to the gold nuclei.
E) the alpha particles split into deuterium nuclei when they encountered the gold nuclei.

Question 40

It is often possible to use the atomic masses when calculating the binding energy of a nucleus. The reason for this is

A) the electron masses do not cancel.
B) the electron masses cancel.
C) tables of nuclear masses are usually not available.
D) the mass of the electron can usually be neglected when compared to the mass of the neutron.
E) the atomic masses are the same as the nuclear masses.

Question 41

Approximately how much uranium (in kg) must undergo fission per day to provide 1 000 MW of power? (Assume an efficiency of 30%). The nuclear reaction is . m(n) = 1.008 665 u
M(U) = 235.043 915 u
M(Ba) = 140.913 9 u
M(Kr) = 91.897 3 u
U = 1.66 × 10−²⁷ kg

A) 1.0
B) 3.5
C) 2.3
D) 4.6
E) 0.1

Question 42

In which of the following decays does the atomic mass number of the daughter nucleus differ from that of the parent nucleus?

A)

B)

C)

D)

E) Answers (a), (b), and (c) are correct.

Question 43

The chart below shows part of the radioactive series beginning with the isotope . The isotope marked with an X is

A)
.
B)
.
C)
.
D)
.
E)
.

Question 44

What is the average kinetic energy (in keV) of an ion that has a temperature of 10⁸ K?

A) 8.2
B) 13
C) 4.3
D) 16
E) 21

Question 45

The radiocarbon content of ¹⁴C decreases after the death of a living system with a half-life of 5730 y. If an archaeologist working a dig finds an ancient firepit containing some partially consumed firewood and the wood contains only 12.5 percent of the ¹⁴C content of an equal carbon sample from a present-day tree, what is the age of the ancient site?

Question 46

A neutron is characterized by the term "thermal neutron" when

A) its energy is of the order kT, where T is on the order of 0°C.
B) its energy is of the order kT, where T is on the order of 0 K.
C) its energy is of the order kT, where T is on the order of 273°C.
D) its energy is of the order kT, where T is on the order of 100°C.
E) its energy is of the order kT, where T is on the order of 0°R.

Question 47

A self-sustained chain reaction occurs when the reproduction constant, K, is equal to

A) 3.0
B) 2.0
C) 2.5
D) 1.0
E) 0.5

Question 48

One of the naturally occurring radioactive series begins with . Which of the following isotopes is the stable isotope at the end of this series?

A)

B)

C)

D)

E) None of the above choices can be correct.

Question 49

Find the unknown atomic number and mass number respectively, for the following reaction

A) 141, 53
B) 140, 54
C) 53, 41
D) 54, 140
E) 54, 141

Question 50

A pure sample of ²²⁶Ra contains 2.0 × 10¹⁴ atoms of the isotope. If the half-life of ²²⁶Ra = 1.6 × 10³ years, what is the decay rate of this sample? (1 Ci = 3.7 × 10¹⁰ decays/s)

Question 51

Find the number of nuclei per unit volume (n = nuclei/cm³) for lead. atomic weight = 202.7
Density = 11.5 g/cm³
Avogadro's number = 6.02 × 10²³

A) 2.51 × 10²²
B) 3.42 × 10²²
C) 2.93 × 10²²
D) 2.94 × 10²³
E) 2.05 × 10²¹

Question 52

A beam of 1-MeV gamma rays incident on a piece of 0.50-cm thick lead is reduced by 50% of its initial value. How thick must the lead be to reduce the beam to one percent of its initial value?

A) 1.1 cm
B) 2.2 cm
C) 3.3 cm
D) 4.4 cm
E) 8.4 cm

Question 53

Linus claims that the added gravitational force of neutrons holds the particles in a nucleus together. Linnea says that they stick together because they lose their electric charge when they form a nucleus. Which one, if either, is correct, and why?

A) Linus, because more particles exert gravitational forces on one another than exert electromagnetic forces.
B) Linus, because the numerical magnitude of G/k_e is 7.42 × 10−²¹.
C) Linnea, because the numerical magnitude of G/k_e is 7.42 × 10−²¹.
D) Both, because electric charge is lost and then gravity holds the nucleus together.
E) Neither, because gravity is not lost, and the numerical magnitude of k_e/G is 1.35 × 10²⁰.

Question 54

How much energy (in MeV) is released when a fissions to and in the reaction m(n) = 1.008665 u m(U) = 235.043915 u
M(Ba) = 140.9139 u
M(Kr) = 91.8973 u
U = 1.66 × 10−²⁷ kg

A) 100
B) 50
C) 200
D) 150
E) 250

Question 55

A neutron is known to undergo beta decay (n → p + e− + ). A reasonable mean lifetime for free neutrons is

A) 10 years
B) 10 hours
C) 10 days
D) 10 minutes
E) 10−²³ s

Question 56

A thermal neutron has an energy (in eV) on the order of

A) 40
B) 0.4
C) 4
D) 0.04
E) 400

Question 57

The mass of is 55.9349 u and the mass of is 55.939 9 u. Which isobar decays into the other, and by what 2 possible processes?

Question 58

Homer says that we can safely use nuclear power because all radioactive nuclei are gone after two half-lives. Marge says that only the decay rate is zero after two half-lives. Which one, if either, is correct, and why?

A) Homer, because half of the nuclei disintegrate in each half-life.
B) Marge, because the number of decays per unit time is halved in each half-life.
C) Homer, because it's safe to handle radioactive substances after two half-lives.
D) Both, because when all nuclei disintegrate the decay rate is also zero.
E) Neither, because one quarter of the nuclei are left after two half-lives.

Question 59

The half-life of ¹³¹I is 8 days. On a certain day, the activity of an ¹³¹I sample is 6.4 mCi. What is its activity 40 days later?

Question 60

The nuclear probability of interacting with neutrons depends most strongly on the neutron's

A) mass
B) area
C) volume
D) speed
E) charge

Question 61

The reaction is known as a ____ reaction.

A) beta capture
B) beta emission
C) neutron capture
D) neutron emission
E) photon emission

Question 62

Radioactive technetium, a gamma emitter, is taken up by the heart muscle in a medical test. The detector for the radiation emitted from the heart could be a

A) Tokamak.
B) quarter-wavelength antenna.
C) Geiger counter.
D) photoelectric tube.
E) diffraction grating.

Question 63

How fast must two deuterium atoms be moving so they can overcome the Coulomb force of repulsion, and attain the necessary 10−¹⁴ m for fusion? (m( ) = 2.014 1 u)

A) 3.9 × 10⁶ m/s
B) 1.3 × 10⁶ m/s
C) 2.6 × 10⁶ m/s
D) 5.2 × 10⁶ m/s
E) 3.7 × 10⁶ m/s

Question 64

When a fast neutron collides with a hydrogen or deuterium nucleus, the most likely result is that

A) the neutron has an appreciable gain in kinetic energy, the gain being greatest for head-on collisions.
B) the neutron has an appreciable gain in kinetic energy, the gain being greatest for oblique collisions.
C) the neutron has an appreciable loss in kinetic energy, the loss being greatest for head-on collisions.
D) the neutron has an appreciable loss in kinetic energy, the loss being greatest for oblique collisions.
E) the neutron is absorbed by the hydrogen or deuterium nucleus.

Question 65

Which of the following is not a radiation detector?

A) cloud chamber
B) Geiger counter
C) scintillation counter
D) neutron activation
E) spark chamber

Question 66

When a nucleus at rest spontaneously splits into fragments of mass m₁ and m₂, the ratio of the momentum of m₁ to the momentum of m₂ is

A)
.
B)
.
C) −1.
D)
.
E)
.

Question 67

Background radiation from cosmic rays and radioactive nuclei in our surroundings is about 0.13 rem/year. Suppose we assume this all comes from cosmic rays which have an RBE factor of 1.0. The RBE factor for the most dangerous types of radiation is 20. How many rads of the most dangerous radiation could a 100-year-old person have been exposed to in her lifetime without having gone over the recommended limit of 0.5 rem/year?

A) 0.37
B) 0.50
C) 1.85
D) 13
E) 37

Question 68

Calculate the half-value thickness (in mm) of lead if it reduces the intensity of a beam of x-rays whose wavelength is 10 pm by a factor of two. (Assume the linear absorption coefficient of lead is 43 cm−¹ for x-rays of wavelength 10 × 10−¹² m.)

A) 0.24
B) 0.20
C) 0.12
D) 0.16
E) 0.18

Question 69

When a beam of nuclear radiation of initial intensity I₀ passes through a thickness x of material, the intensity of the beam exiting the material is I =

A) I₀e−μx.
B) I₀eμx.
C) I₀(e−μx − 1).
D) I₀(eμx − 1).
E) I₀(1 − e−μx).

Question 70

In order to control a nuclear reactor, control rods can be pulled out of or pushed into the reactor core by remote control. These rods control the reactor by

A) slowing down the fast neutrons so the neutrons can be absorbed by ²³⁸U.
B) speeding up slow neutrons so the neutrons can be absorbed by ²³⁸U.
C) slowing down fast neutrons so they cannot initiate further fusion reactions in ²³⁵U.
D) speeding up fast neutrons so they cannot initiate further fusion reactions in ²³⁵U.
E) capturing thermal neutrons so they cannot initiate further fission reactions in ²³⁵U.

Question 71

A radioactive sample with decay rate R and decay energy Q has power output

A)
.
B) RQ.
C) Q²R.
D) equal to any of the above.
E) equal to (a) or (c) above.

Question 72

In neutron capture by an atomic nucleus, the atomic number changes by

A) −2.
B) −1.
C) 0.
D) +1.
E) +2.

Question 73

One rad is

A) the amount of radiation that deposits 10−² J of energy into 1 kg of absorbing material.
B) the amount of ionizing radiation that will produce 1/3 × 10−⁹ C of electric charge in 1 cm³ of air under standard conditions.
C) the amount of radiation needed for ionization of an atom.
D) the amount of radiation needed for dissociation of a molecule.
E) the amount of radiation that deposits one erg of energy in 1g of material.

Question 74

A principal mechanism for energy loss during nuclear fusion is bremsstrahlung. This loss is associated with

A) x-rays emitted due to electron-ion collisions.
B) radiation losses due to T⁴ losses.
C) conduction losses associated with ΔT.
D) convection losses associated with ΔT.
E) neutron collisions with atoms of moderator.

Question 75

Approximately how fast is an ion of helium moving if it is in a plasma with a temperature of 10⁸ K? m(He) = 4.002 603 u and u = 1.66 × 10−²⁷ kg.

A) 10⁶ m/s
B) 10⁴ m/s
C) 10² m/s
D) 10 m/s
E) 1 m/s

Question 76

When a nucleus at rest spontaneously splits into fragments of mass m₁ and m₂, the ratio of the velocity of m₁ to the velocity of m₂ is

A)
.
B)
.
C) −1.
D)
.
E)
.

Question 77

Radiant energy reaching the Earth from the sun is not sufficient to keep the Earth's surface temperature comfortable for life. Of the following, the most likely source of the additional thermal energy is from

A) fusion of hydrogen nuclei in the Earth's core.
B) fusion of high Z nuclei in the Earth's core.
C) fission of radioactive nuclei inside the Earth.
D) fission of radioactive nuclei in cosmic rays.
E) deflection of radioactive nuclei in cosmic rays.

Question 78

One roentgen is defined as

A) the amount of ionizing radiation that will produce 1/3 × 10−⁹ C of electric charge in 1 cm³ of air under standard conditions.
B) the amount of radiation that deposits 10−² J of energy into 1 kg of absorbing material.
C) the amount of radiation needed for ionization of an atom.
D) the amount of radiation needed for dissociation of a molecule.
E) the amount of radiation that deposits 1 erg of energy in 1 g of air.

Question 79

What energy is needed (in MeV) so two deuterium atoms moving together will reach the necessary 10−¹⁴ m for fusion?

A) 0.511
B) 0.14
C) 2.5
D) 4.3
E) 1.0

Question 80

A rem (roentgen equivalent in man) is defined as (the product of)

A) the dose in RBE.
B) the dose in roentgen and the RBE factor.
C) the dose in rad times the dose in roentgen.
D) the dose in rad and the RBE factor.
E) the dose in rad and energy of radiation.