Deck 20: Nuclear Physics

Question 1

The superscript before the symbol for an element represents the number of

A) protons.
B) neutrons.
C) protons plus neutrons.
D) protons minus neutrons.
E) neutrons minus protons.

Answer 1

protons plus neutrons.

Question 2

The total binding energy of is approximately

A) 16.5 MeV
B) 40.0 MeV
C) 8.00 MeV
D) 26.0 MeV
E) 27.3 MeV

Answer 2

27.3 MeV

Question 3

Why is the ratio of neutrons to protons greater in the heavier elements?

A) The greater the number of protons, the weaker the proton-neutron strong nuclear force.
B) The greater the number of neutrons, the weaker the proton-neutron strong nuclear force.
C) The greater the number of protons, the greater the electrostatic force of repulsion.
D) The greater the number of neutrons, the greater the electrostatic force of repulsion.
E) There is actually a lesser ratio of neutrons to protons in the heavier elements.

Answer 3

The greater the number of protons, the greater the electrostatic force of repulsion.

Question 4

Which of the following is a negatively charged particle found in the nucleus of an atom?

A) proton
B) electron
C) neutron
D) nucleon
E) None of these is correct.

Question 5

The nuclear force is

A) short range and strongly dependent on the charge.
B) short range but proportional to the Coulomb force.
C) strongly dependent on the charge.
D) very strong (compared with Coulomb forces) and long range.
E) short range, charge independent, and very strong.

Question 6

The total binding energy of is approximately

A) 8.00 MeV
B) 56.0 MeV
C) 39.2 MeV
D) 37.6 MeV
E) 22.4 MeV

Question 7

One way to think about the low binding energy per nucleon for low A numbers is

A) that there are few protons, hence there is less electrostatic repulsion.
B) that there are few electrons to provide the electrostatic attraction.
C) at low A the number of nearest neighbors per nucleon is small compared to higher a
A numbers.
D) at low A, the nucleus is less spherical, hence there is less surface tension.
E) None of the above statements is correct.

Question 8

The subscript before the symbol for an element represents the number of

A) protons.
B) neutrons.
C) protons plus neutrons.
D) protons minus neutrons.
E) neutrons minus protons.

Question 9

The sodium atom has an atomic number of 11 and an atomic weight of 23. The neutral atom contains

A) 11 neutrons and 12 protons.
B) 11 protons and 12 neutrons.
C) 12 electrons and 11 neutrons.
D) 23 protons and 12 electrons.
E) 23 electrons and 12 neutrons.

Question 10

The graph that represents the interaction of the proton and neutron is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 11

The alpha particles from a naturally radioactive decay have a kinetic energy of
4)25 MeV. How close does an alpha particle come within a gold nucleus if the particle is heading directly towards the nucleus? Give your answer in terms of number of radii of the gold atom, r = 7.0 fm.

A) 2
B) 8
C) 12
D) 15
E) 19

Question 12

Rutherford's experiments, in which he bombarded a very thin gold foil with alpha particles, showed that

A) all of the $\alpha$ particles passed through the foil without significant deflection.
B) none of the $\alpha$ particles were able to penetrate the foil.
C) all of the $\alpha$ particles passed through the foil and were deflected through large angles.
D) most of the $\alpha$ particles passed through the foil with negligible deflection but some were deflected through large angles.
E) the $\alpha$ particles were linearly polarized after passing through the foil.

Question 13

The radius of the ⁶³Cu nucleus is approximately

A) 0.382 fm
B) 5.97 fm
C) 12.1 fm
D) 24.2 fm
E) 100 fm

Question 14

The radius of the ⁶⁴Ni nucleus is approximately

A) 1.4 fm
B) 2.8 fm
C) 6.0 fm
D) 11 fm
E) 90 fm

Question 15

Curve 2 is the binding energy per nucleon as a function of the mass number A. The other curves represent the contributions of various forms of energy that contribute to the binding energy. The curve that best represents the contribution of the Coulomb force is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 16

Estimate the mass density of the nucleus of an atom.

A) 10³ kg/m³
B) 10⁶ kg/m³
C) 10⁹ kg/m³
D) 10¹⁴ kg/m³
E) 10¹⁷ kg/m³

Question 17

The chemical characteristics of an atom (what element it is) are determined by

A) its atomic number.
B) its mass number.
C) its neutron number.
D) its nucleon number.
E) All of these are correct.

Question 18

For most nuclei, the total binding energy is proportional to the number of nucleons. This leads to the conclusion that nuclear forces show the property of

A) pairing
B) charge dependence
C) relativity
D) magnetism
E) None of these is correct.

Question 19

The total binding energy per nucleon of is approximately

A) 0.04215 MeV
B) 0.00602 MeV
C) 5.606 MeV
D) 6.593 MeV
E) 0.00590 MeV

Question 20

The fact that the binding energy per nucleon is roughly a constant over most of the range of stable nuclei indicates that the nuclear force is

A) short range.
B) long range.
C) weak.
D) strong.
E) repulsive.

Question 21

The pair of nuclides that represents isotopes is

A)
B)
C)
D)
E)

Question 22

A certain radioactive element has a half-life of 20 d. The time it will take for 7/8 of the atoms originally present to disintegrate is

A) 20 d
B) 40 d
C) 60 d
D) 80 d
E) 100 d

Question 23

How many times larger is the volume of the nucleus 208Pb (Z=82) compared to the nucleus 40Ca (Z=20)?

A) 0.58
B) 1.7
C) 5.2
D) 4.1
E) 2.3

Question 24

Which of the following common isotopes has the highest binding energy per nucleon, ⁴He, ¹²C, ¹⁶O, or ²⁴Mg?

A) ⁴He
B) ¹²C
C) ¹⁶O
D) ²⁴Mg
E) They are all the same.

Question 25

Atoms of an element that have different atomic masses are called

A) ions
B) isobars
C) isotopes
D) metastable
E) dielectrics

Question 26

When an alpha particle (⁴He) with a kinetic energy of 6.54 MeV strikes a ²⁷Al nucleus, a ³⁰P nucleus is created and a neutron is ejected. Assume that the ³⁰P nucleus has no final kinetic energy. Given the following masses for the various particles, what is the kinetic energy of the ejected neutron?

A) 3.71 MeV
B) 2.83 MeV
C) 6.54 MeV
D) 9.37 MeV
E) 0.45 MeV

Question 27

The word isotopes describes elements that have

A) the same atomic number but different atomic mass.
B) the same atomic mass but different atomic number.
C) the same atomic mass and the same atomic number but different chemical properties.
D) similar chemical properties, though they differ in both atomic mass and atomic number.
E) the same number of valence electrons.

Question 28

The half-life of phosphorus-32 is 14.3 d. If you have 1.00 g of phosphorous-32 today, the amount remaining in 10 d will be approximately

A) 700 mg
B) 650 mg
C) 616 mg
D) 384 mg
E) 350 mg

Question 29

The half-life of radium is about 1600 y. If you have 1.00 g of radium today, the amount remaining in 1000 y will be approximately

A) 625 mg
B) 958 mg
C) 707 mg
D) 841 mg
E) 649 mg

Question 30

The strong nuclear force acts between which of the following?

A) pairs of protons in the nucleus
B) pairs of neutrons in the nucleus
C) members of proton-neutron pairs in the nucleus
D) the nucleus and the electrons
E) Answers a, b, and c are correct.

Question 31

The volume of a nucleus is directly proportional to the number of _______ it contains.

A) electrons
B) protons
C) neutrons
D) isotopes
E) nucleons

Question 32

A sample of (which decays by $\beta$ -emission) has an activity of 14.7 mCi. After
26)1 d it has an activity of 4.25 mCi. The half-life of ³²P is approximately

A) 3.03 d
B) 7.30 d
C) 12.1 d
D) 14.6 d
E) 24.2 d

Question 33

In this problem, Z is the atomic number, N is the neutron number, and A is the mass number. For stable isotopes with A greater than 44, as A increases, the ratio Z/N

A) remains the same.
B) decreases.
C) equals A - N.
D) increases.
E) None of these is correct.

Question 34

Radon (Rn) is a gas. Its nucleus decays with the emission of an alpha particle to form an isotope of polonium (Po):
The masses of the particles are: The rest energy of a unified mass unit is 931.5 MeV. The kinetic energy of the ejected particles is

A) 6.26 MeV
B) 6.16 MeV
C) 6.04 MeV
D) 6.61 * 10^-3 MeV
E) 5.73 MeV

Question 35

The nuclear radius of is approximately

A) 1.05 fm
B) 4.50 fm
C) 0.350 fm
D) 11.2 fm
E) 1.85 fm

Question 36

How many times larger is the radius of the nucleus ²⁰⁸Pb (Z=82) compared to the nucleus ⁴⁰Ca (Z=20)?

A) 0.58
B) 1.7
C) 5.2
D) 4.1
E) 2.3

Question 37

Two nuclides that are isotopes could lie on curve

A) 1
B) 2
C) 3
D) 4
E) 5

Question 38

The activity of a radioactive sample is defined as the number of decays per second. For a sample with N particles and a decay constant $\lambda$ , the activity is

A) proportional to $\lambda$ and inversely proportional to N.
B) proportional to $\lambda$ but independent of N.
C) directly proportional to both $\lambda$ and N.
D) independent of $\lambda$ but proportional to N.
E) inversely proportional to both $\lambda$ and N.

Question 39

A sample of (which decays by $\beta$ -emission) has an activity of 10.0 mCi. After
6)06 d it has an activity of 7.5 mCi. The half-life of ³²P is approximately

A) 3.03 d
B) 7.30 d
C) 12.1 d
D) 14.6 d
E) 24.2 d

Question 40

If the radioactivity of thorium C decreases to one-half in 1 h, in another 60 min its activity, compared with that at the beginning of the first hour, will be

A) 1/4
B) zero
C) 1/8
D) 1/16
E) 1/120

Question 41

A radioactive substance in the laboratory has a half-life of 8 h. At noon today, a Geiger counter reads 480 counts/min above background. At noon tomorrow, the counter should read about

A) 480 counts/min
B) 240 counts/min
C) 120 counts/min
D) 60 counts/min
E) 30 counts/min

Question 42

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 0?

A) 1.04 * 10⁶
B) 1.67* 10⁶
C) 2.08 * 10⁶
D) 3.41 * 10⁶
E) 3.79 * 10⁶

Question 43

When a gamma ray passes through a material,

A) the gamma ray can cause photoelectric effect.
B) the gamma ray can cause Compton scattering.
C) the gamma ray can cause pair production.
D) the gamma ray can pass right through the material unchanged.
E) All the above processes can take place.

Question 44

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. If the detection efficiency is 25%, how many radioactive nuclei are there at time t = 2 min?

A) 1.04 * 10⁶
B) 1.67 * 10⁶
C) 2.08 *10⁶
D) 3.41 * 10⁶
E) 3.79 * 10⁶

Question 45

The graph shows the number of undecayed atoms as a function of time. The half-life of this radioactive element is approximately

A) 1 s
B) 2 s
C) 10 s
D) 4 s
E) 5 s

Question 46

In what type of radioactive decay are the mass numbers of the parent and daughter nuclei different?

A) alpha
B) beta
C) gamma
D) both alpha and beta
E) both beta and gamma

Question 47

The half-life of a radioactive substance is 5 min. Which of the following statements is true of the decay of this substance?

A) After 10 min, one-fourth of the original substance remains.
B) The amount of the substance remaining after a given time is proportional to the number of minutes.
C) The amount of the substance remaining after a given time is inversely proportional to the number of minutes.
D) After 10 min, none of the original substance remains unchanged.
E) None of these is correct.

Question 48

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 4 min will be

A) 1500 counts/s
B) 750 counts/s
C) 375 counts/s
D) 188 counts/s
E) 94 counts/s

Question 49

The intensity of gamma rays passing through a material as a function of thickness, x is given by where n is the number of atoms per cm³ and $\sigma$ is the absorption cross section. It is observed that the intensity of gamma rays of a particular energy is reduced by half when they passed through 1 cm of lead. What is the thickness of lead needed to reduce the intensity to a quarter?

A) 1.0 cm
B) 1.5 cm
C) 2.0 cm
D) 3.0 cm
E) 4.0 cm

Question 50

The Federal Aviation Administration limits the number of hours flight crews can be at high altitudes, $\backsim$ 10,000 m. One of the reasons is because

A) the crews can suffer from altitude sickness.
B) at high altitudes there are more gamma rays that can damage human tissues.
C) at high altitudes the air is thinner so there is less oxygen.
D) they do not want the crews to accrue too many frequent flyer miles.
E) None of the above statements is correct.

Question 51

The graph shows the number of nuclei N remaining as a function of time. The point on the graph that corresponds to the number of nuclei remaining after two half-lives have elapsed is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 52

A radioactive nucleus with Z = 92 and A = 235 decays through a series of alpha, beta, and gamma emissions to a stable nucleus with Z = 82 and A = 207. The number of alpha particles and the number of beta particles emitted during the entire process are

A) 8 alpha particles and 6 beta particles.
B) 7 alpha particles and 4 beta particles.
C) 7 alpha particles and 10 beta particles.
D) 14 alpha particles and 7 beta particles.
E) None of these is correct.

Question 53

The graph shows the activity as a function of time for a radioisotope. The half-life of this particular radioisotope is approximately

A) 5 h
B) 4 h
C) 8 h
D) 20 h
E) 10 h

Question 54

The intensity of gamma rays passing through a material as a function of thickness, x is given by where n is the number of atoms per cm³ and $\sigma$ is the absorption cross section. If the intensity of gamma rays of a particular energy is reduced by half when they passed through 1 cm of lead, what is the absorption cross section for the gamma rays? The density of lead is 11.3 g/cm³ and its molar mass is 207 g.

A) 3.5 * 10<sup>-

22</sup> cm²
B) 6.8 * 10
²² cm²
C) 4.6 * 10
²³ cm²
D) 2.1 * 10
²³ cm²
E) 8.4 * 10
²⁴ cm²

Question 55

A radioactive source has a half-life of 2 min. At time t = 0 it is placed near a detector and the counting rate is observed to be 3000 counts/s. The counting rate at t = 10 min will be

A) 1500 counts/s
B) 750 counts/s
C) 375 counts/s
D) 188 counts/s
E) 94 counts/s

Question 56

The graph shows the number of radioactive nuclei N remaining as a function of time. The point on the graph that corresponds to the half-life of the decay process is

A) 1
B) 2
C) 3
D) 4
E) 5

Question 57

In what type of radioactive decay are the mass numbers of the parent and daughter nuclei the same?

A) alpha
B) beta
C) gamma
D) both alpha and beta
E) both beta and gamma

Question 58

Which of the following radioactive decay products has the largest electric charge?

A) alpha particles
B) beta particles
C) gamma rays
D) neutrons
E) All of these have the same charge.

Question 59

The graph shows the decay curves of four radioactive elements. The half-life is the same for elements

A) 1 and 2
B) 3 and 4
C) 1 and 4
D) 2 and 3
E) 1 and 3

Question 60

The "third-life," the time it takes nuclei to decay until one-third of the original amount remains, expressed in terms of the decay constant $\lambda$ , is

A) (ln 2)/3 $\lambda$
B) (ln 3)/ $\lambda$
C) (ln 0.333)/ $\lambda$
D) 3(ln 2)/ $\lambda$
E) $\lambda$ /3

Question 61

Uranium decomposes radioactively to form thorium (atomic number 90) by emitting an $\alpha$ particle from its nucleus. The force of repulsion between the thorium nucleus and the $\alpha$ particle when the distance between them is 9.0 fm is approximately

A) 7.2 fN
B) 57 nN
C) 4.6 pN
D) 1.02 kN
E) 0.51 kN

Question 62

A radiologist uses a radioactive isotope of iodine, ¹²³I, for thyroid scans. She receives a shipment of 15 mCi of this isotope at noon on Tuesday. The half-life of this isotope is 13.2 h. How much activity remains at noon on Thursday of the same week?

A) 12 mCi
B) 1.2 mCi
C) 2.4 mCi
D) 4.2 mCi
E) 24 mCi

Question 63

A radioactive sample is detected to produce 2500 decays per minute at 6:00 p.m. and 150 decays per minute at 11:00 p.m. the same day. What is the half-life of the sample?

A) 2.81 hrs
B) 0.56 hrs
C) 1.23 hrs
D) 1.77 hrs
E) 0.89 hrs

Question 64

The energy at which the endothermic reaction takes place is

A) 1.19 MeV
B) 0.925 MeV
C) 1.52 MeV
D) 1.28 MeV
E) 9.25 MeV

Question 65

At a particular time, a radioactive source A has a strength of 1.60 * 10¹¹ Bq and a half-life of 15.0 d, and a second source B has a strength of 8.50 * 10¹¹ Bq. Sources A and B have the same strength 45.0 d later. The half-life of B is

A) 0.19 d
B) 8.3 d
C) 2.8 d
D) 5.4 d
E) 28 d

Question 66

Initially a mixture of two radioactive sources contains the same number of nuclei of source A and source B. The half-life of A is 2 hours, and the half-life of B is 3 hours. What will be the ratio of remaining nuclei of A divided by remaining nuclei B after 12 hours? (Assume A does not decay into B or vice-versa.)

A) 0.250
B) 0.125
C) 0.5
D) 0.0625
E) None of these is correct.

Question 67

The graph shows the activity as a function of time for a radioactive sample. The decay constant for this sample is approximately

A) 0.11 d^-1
B) 0.69 d^-1
C) 0.090 d^-1
D) 6.0 d^-1
E) 1.8 d^-1

Question 68

A barn is a unit of

A) momentum
B) energy
C) range
D) cross section
E) impact parameter

Question 69

In Positron Emission Tomography (or PET) scans, a very small amount of a radioactive drug is given to a patient. Fluorine-18 doped or labeled fluorodeoxyglucose, also called FDG, is a radioactive version of the sugar glucose with a half-life of 110 minutes. Once injected into the body, it will go to places where glucose is used for energy. For example, FDG will go to the brain, and, in particular, to those parts of the brain that are actively burning glucose for energy. A variety of different images are observed depending on the parts of the brain being used in certain tasks, such as reading or listening. If the patient came back at the same time the next day after their initial injection for a further scan, how much of the original Fluorine-18 activity would remain?

A) zero
B) 1.15 * 10^-2 %
C) 3.53 * 10^-2 %
D) 5.41 * 10^-2 %
E) 5.41 * 10^-4 %

Question 70

An old piece of dead wood contains 38% of the ¹⁴C abundance of a living sample. How old is it? (The half-life of ¹⁴C is 5730 years.)

A) 3.95 * 10³ years
B) 8.78 * 10³ years
C) 8.00 * 10³ years
D) 7.66 * 10³ years
E) 3.47 * 10³ years

Question 71

A nuclear explosion produces (among a lot of other things) 7.9 * 10²³ Bq of iodine-131, which has a half-life of 8.05 d, and 5.7 * 10²¹ Bq of barium-140, which has a half-life of 12.8 d. The total activity that remains after 145 d is

A) 3.5 * 10¹⁸ Bq
B) 1.16 * 10²⁰ Bq
C) 2.2* 10¹⁸ Bq
D) 5.2 * 10¹⁸ Bq
E) 7.3 * 10¹⁸ Bq

Question 72

Many famous artifacts have been dated using ¹⁴C dating techniques. One of these were the Dead Sea Scrolls or manuscripts. An activity level of 0.20 Bq per gram of carbon was measured. If the half-life of ¹⁴C is 5730 years and there are about 15 decays per minute per gram of carbon in a living organism, then calculate the age of the famous manuscripts.

A) 2.7 * 10³ years
B) 1.9 * 10³ years
C) 1.3 * 10³ years
D) 3.7 * 10⁴ years
E) None of these is correct.

Question 73

A particle is incident on a nucleus. The particle

A) can be scattered elastically by the nucleus.
B) can be scattered inelastically by the nucleus with the nucleus in an excited state.
C) can be absorbed by the nucleus completely.
D) can be absorbed by the nucleus and other particle(s) emitted.
E) All of the above are possible.

Question 74

A 2000-year-old piece of dead wood gives 1400 counts per week in our detector system. How many counts per week would our system detect if the wood were living? (The half-life of ¹⁴C is 5730 years.)

A) 1520 counts per week
B) 3200 counts per week
C) 1270 counts per week
D) 1780 counts per week
E) 2130 counts per week

Question 75

In gamma-decay a nucleus in an excited state decays to a lower energy state by the emission of a high energy photon called a gamma-ray.

A) Gamma-decay is always slow (greater than a ns).
B) Gamma-decay is always fast (less than a ns).
C) Gamma-decay is usually fast but can in special cases be slow.
D) Gamma-decay is always accompanied by the emission of a neutrino.
E) Gamma-decay is always accompanied by the emission of a $\beta$ -particle.

Question 76

Oxygen-15 is a $\beta$ + emitter that is often used in PET scans. It has a half-life of 122 seconds. Calculate how long it takes for the patient's initial activity to be reduced by a factor of 100.

A) 203 mins
B) 1.22 *10⁴ mins
C) 13.5 mins
D) 8.13 mins
E) None of these is correct.

Question 77

Radon ²²²Rn is a radioactive gas produced as part of the natural decay chain of uranium. Because it is a gas, it can pose a health problem through inhalation, especially when high concentrations accumulate in homes. Suppose 5 *10⁸ radon atoms are present in a basement at some time. If the basement is sealed and left, then how many radon atoms remain after a month (31 days)? (The half-life of ²²²Rn is 3.82 days.)

A) 1.81* 10⁶
B) 1.49 * 10⁵
C) 1.23 *10⁶
D) 6.16 * 10⁷
E) None of these is correct.

Question 78

Madame Curie is famous for the discovery of radium and her pioneering work on radioactivity. The half-life of radium (molar weight = 226g) is 1600 years. What is the activity (in Curie's) of 5.0g of radium?

A) 4.94 Ci
B) 1.83 *10¹¹ Ci
C) 0.512 Ci
D) 52.3 Ci
E) 3.59* 10¹¹ Ci

Question 79

Cesium-137 has a half-life of 31.0 y. The time required for the cesium-137 now present to decrease to 1/30 its present value is

A) 930 y
B) 30 y
C) 465 y
D) 152 y
E) 1.6 y

Question 80

A $\beta$ particle is an energetic

A) photon emitted by a nucleus.
B) electron or positron.
C) proton emitted by a nucleus.
D) neutron emitted by a nucleus.
E) None of these is correct.