Deck 30: Nuclear Physics

Question 1

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.

Answer 1

the electron masses do not cancel.

Question 2

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( ${ } _ { 1 } ^ { 2 } \mathrm { H }$ )= 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

Answer 2

2.6 * 10⁶ m/s

Question 3

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

Answer 3

0.14

Question 4

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 5

Two nuclei which share the same mass number A always are (Hint: Eliminate any wrong answers. )

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

Question 6

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 7

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 8

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 9

Two nuclei which share the same atomic number Z always are

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

Question 10

Calculate the binding energy per nucleon (MeV/nucleon)for tritium,( ${ } _ { 1 } ^ { 3 } \mathrm { H }$ )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 11

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 12

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 13

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 14

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 15

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 16

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

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

Question 17

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 18

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 19

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 20

Find the ratio of the binding energy per nucleon for helium ( ${ } _ { 2 } ^ { 4 } \mathrm { He }$ )to uranium-238 ( ${ } _ { 92 } ^ { 238 } \mathrm { U }$ ). 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 21

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 22

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 23

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 24

What value of Z (atomic number)and A (mass number)result in the following gamma decay? $${ } _ { 6 } ^ { 12 } \mathrm { C } \rightarrow { } _ { z } ^ { A } \mathrm { X } + \gamma$$

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 25

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

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

Question 26

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 27

How many radioactive atoms are present in a sample that has an activity of 0.5 $\mu$ Ci 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 28

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 29

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 30

The chart below shows part of the radioactive series beginning with the isotope ${ } _ { 92 } ^ { 235 } \mathrm { U }$ .The isotope marked with an X is

A) ${ } _ { 88 } ^ { 226 } \mathrm { Ra }$ .
B) ${ } _ { 88 } ^ { 227 } \mathrm { Ra }$ .
C) ${ } _ { 89 } ^ { 227 } \mathrm { Ac }$ .
D) ${ } _ { 90 } ^ { 231 } \mathrm { Th }$ .
E) ${ } _ { 91 } ^ { 231 } \mathrm {~Pa}$ .

Question 31

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 32

What value of Z (atomic number)and A (mass number)result in the following $\beta$ -decay? $${ } _ { 6 } ^ { 14 } \mathrm { C } \rightarrow { } _ { Z } ^ { A } \mathrm { X } + e ^ { - }$$

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

Question 33

What value of Z (atomic number)and A (mass number)result in the following $\beta$ -decay? $${ } _ { 7 } ^ { 12 } \mathrm {~N} \rightarrow { } _ { Z } ^ { A } \mathrm { X } + e ^ { + }$$

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

Question 34

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 35

The Q value for the following reaction, ${ } _ { 4 } ^ { 9 } \mathrm { Be } ( \alpha , \mathrm { n } ) { } _ { 6 } ^ { 12 } \mathrm { C }$ ,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 36

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

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

Question 37

What is the disintegration energy (in MeV)associated with this spontaneous decay? $${ } _ { 60 } ^ { 144 } \mathrm { Nd } \rightarrow { } _ { 58 } ^ { 140 } \mathrm { Ce } + { } _ { 2 } ^ { 4 } \mathrm { He }$$ 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 38

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 39

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 40

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 41

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 42

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 43

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 44

The chart below shows part of the radioactive series beginning with the isotope ${ } _ { 90 } ^ { 232 } \mathrm { Th }$ .The isotope marked with an X is

A) ${ } _ { 88 } ^ { 222 } \mathrm { Ra }$ .
B) ${ } _ { 88 } ^ { 224 } \mathrm { Ra }$ .
C) ${ } _ { 89 } ^ { 228 } \mathrm { Ac }$ .
D) $224 \mathrm { Th }$ .
E) ${ } _ { 90 } ^ { 228 } \mathrm { Th }$ .

Question 45

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) $- \frac { m _ { 1 } } { m _ { 2 } }$ .
B) $- \frac { m _ { 2 } } { m _ { 1 } }$ .
C)-1.
D) $+ \frac { m _ { 1 } } { m _ { 1 } + m _ { 2 } }$ .
E) $+ \frac { m _ { 2 } } { m _ { 1 } + m _ { 2 } }$ .

Question 46

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 47

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 48

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 49

The nuclear reaction(s)that is(are)most likely to be employed in fusion reactors on Earth is(are)

A) ${ } _ { 1 } ^ { 2 } \mathrm { H } + { } _ { 1 } ^ { 2 } \mathrm { H } \rightarrow { } _ { 2 } ^ { 3 } \mathrm { He } + { } _ { 0 } ^ { 1 } \mathrm { n }$ .
B) ${ } _ { 1 } ^ { 2 } \mathrm { H } + { } _ { 1 } ^ { 2 } \mathrm { H } \rightarrow { } _ { 1 } ^ { 3 } \mathrm { H } + { } _ { 1 } ^ { 1 } \mathrm { H }$ .
C) ${ } _ { 1 } ^ { 2 } \mathrm { H } + { } _ { 1 } ^ { 3 } \mathrm { H } \rightarrow { } _ { 2 } ^ { 4 } \mathrm { He } + { } _ { 0 } ^ { 1 } \mathrm { n }$ .
D)all of the above.
E)only (a)and (b)above.

Question 50

Find the unknown atomic number and mass number respectively,for the following reaction $$\mathrm { n } + { } _ { 92 } ^ { 235 } \mathrm { U } \rightarrow { } _ { Z } ^ { A } \mathrm { X } + { } _ { 38 } ^ { 94 } \mathrm { Sr } + 2 \mathrm { n }$$

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

Question 51

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 52

One of the naturally occurring radioactive series begins with ${ } _ { 92 } ^ { 238 } \mathrm { U }$ .Which of the following isotopes is the stable isotope at the end of this series?

A) ${ } _ { 82 } ^ { 206 } \mathrm {~Pb}$
B) ${ } _ { 82 } ^ { 207 } \mathrm {~Pb}$
C) ${ } _ { 82 } ^ { 208 } \mathrm {~Pb}$
D) ${ } _ { 83 } ^ { 209 } \mathrm { Bi }$
E)None of the above choices can be correct.

Question 53

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

A) $\alpha$
B) $\beta ^ { + }$
C) $\beta ^ { - }$
D) $\gamma$
E)Answers (a),(b),and (c)are correct.

Question 54

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 55

How much energy (in MeV)is released when a ${ } _ { 92 } ^ { 235 } \mathrm { U }$ fissions to ${ } _ { 56 } ^ { 141 } \mathrm { Ba }$ and $_{36}^{92} \mathrm{Kr}$ in the reaction $\mathrm { n } + { } _ { 92 } ^ { 235 } \mathrm { U } \rightarrow { } _ { 56 } ^ { 141 } \mathrm { Ba } + { } _ { 36 } ^ { 92 } \mathrm { Kr } + 3 \mathrm { n }$ 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 56

How much kinetic energy must a deuterium ion (charge 1.6 * 10 ^{- 19} C)have to approach to within 10 ^{- 14} m of another deuterium ion? (1 MeV = 1.6*10 ^{- 13} J)

Question 57

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 58

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) $- \frac { m _ { 1 } } { m _ { 1 } + m _ { 2 } }$ .
B) $- \frac { m _ { 2 } } { m _ { 1 } + m _ { 2 } }$ .
C)-1.
D) $+ \frac { m _ { 1 } + m _ { 2 } } { m _ { 1 } }$ .
E) $+ \frac { m _ { 1 } + m _ { 2 } } { m _ { 2 } }$ .

Question 59

The reaction ${ } _ { 1 } ^ { 0 } \mathrm { n } + { } _ { Z } ^ { A } \mathrm { X } \rightarrow { } _ { Z } ^ { A + 1 } \mathrm { X } ^ { + }$ is known as a ____ reaction.

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

Question 60

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 $\mathrm { n } + { } _ { 92 } ^ { 235 } \mathrm { U } \rightarrow { } _ { 56 } ^ { 141 } \mathrm { Ba } + { } _ { 36 } ^ { 92 } \mathrm { Kr } + 3 \mathrm { n }$ . 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 61

How many grams of deuterium (atomic mass = 2.014 1 u)must be fused to helium (atomic mass 4.002 6 u)in one second to produce 3 000 MJ of energy? [1 u = 1.66 *10 ^{- 27} kg]

Question 62

How many grams of U-235 must be fissioned every day to produce 1 000 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]