Deck 21: Nuclei and Radioactivity

Question 1

What value of Z (atomic number) and A (mass number) result in the following alpha decay? ${ }_{92}^{238} \mathrm{U} \rightarrow{ }_{Z}^{A} \mathrm{X}+\alpha$

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

Answer 1

C

Question 2

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.

Answer 2

only (a) or (b) may occur.

Question 3

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 neighbours.
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 $\approx$ Z.

Answer 3

The quantum number effect: all nucleons in the nucleus have the same set of quantum numbers.

Question 4

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 5

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 6

An alpha particle is emitted from a radioactive source with an energy of 5 MeV.How fast is it moving (in m/s)? (m = 4.002603 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 7

What is the disintegration energy (in MeV) associated with this spontaneous decay? ${ }_{60}^{144} \mathrm{Nd} \rightarrow{ }_{58}^{140} \mathrm{Ce}+{ }_{2}^{4} \mathrm{He}$ mNd = 143.910083 u mCe = 139.905434 u
MHe = 4.002603 u
1 u = 1.66 * 10-27 kg

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

Question 8

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 9

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 10

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 11

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

Question 12

The Q value for the following reaction, , is (in MeV): m(alpha) = 4.002603 u m(Be) = 9.012182 u
M(n) = 1.008665 u
M(C) = 12.00000 u
1 u = 1.66 *10-27 kg

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

Question 13

The radius of a nucleus of (in fm) is: ${ }_{67}^{165} \mathrm{Ho}$

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

Question 14

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 15

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 16

The ratio of the radius of a classical electron (re = kee2/mec2 = 2.8 * 10-15 m) to the radius of a 4He nucleus (r = r0A1/3) is:

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

Question 17

Find the binding energy (in MeV) of carbon-12.Assume: mC = 12.000000 u
M p = 1.007825 u
M n = 1.008665 u
U = 1.66 *10-27 kg

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

Question 18

How can a nucleus be described by particular values of A, Z and N when the mass of the nucleus is not equal to Zmp + Nmn, where mp and mn 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 19

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 20

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 21

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 22

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.

Question 23

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 24

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 25

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 26

Approximately how much uranium (in kg) must undergo fission per day to provide 1000 MW of power? (Assume an efficiency of 30%).The nuclear reaction is: . 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)1.0
B)3.5
C)2.3
D)4.6
E)0.1

Question 27

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 28

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 29

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 $\Delta$ T.
D)convection losses associated with $\Delta$ T.
E)neutron collisions with atoms of moderator.

Question 30

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 1% 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 31

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 32

A neutron is known to undergo beta decay (n $\rightarrow$ 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 33

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 34

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 35

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 36

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 37

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 38

The reaction is known as a ____ reaction.

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

Question 39

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 40

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 41

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% of the 14C content of an equal carbon sample from a present-day tree, what is the age of the ancient site?

Question 42

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 43

The mass of is 55.9349 u and the mass of is 55.9399 u.Which isobar decays into the other, and by what 2 possible processes?

Question 44

The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars.These stars eventually explode, releasing these elements into space.If we assume that at the time of the explosion there were equal amount of U-235 and U-238, how long ago did the star(s) explode that released the elements that formed our Earth? The present U-235/U-238 ratio is 0.007 0.[The half-lives of U-235 and U-238 are 0.7 * 109 yr and 4.47 * 109 yr.]

Question 45

A beam of high-energy $\alpha$ -particles is incident upon a person and deposits 0.35 J of energy in 0.80 kg of tissue.What dose in rads and what equivalent dose in rems does the individual receive? [RBE $\alpha$ = 20]

Question 46

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 47

How many grams of deuterium (atomic mass = 2.0141 u) must be fused to helium (atomic mass 4.0026 u) in one second to produce 3000 MJ of energy? [1 u = 1.66 *10^-27 kg]

Question 48

How many grams of U-235 must be fissioned every day to produce 1000 MW of electricity in a nuclear power plant that is 1/3 efficient? [Assume 208 MeV/fission and 1 MeV = 1.6 * 10^-13 J]