Deck 27: Nuclear Physics

Question 1

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 toward 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

Answer 1

8

Question 2

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.

Answer 2

None of these is correct.

Question 3

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 3

protons plus neutrons.

Question 4

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 5

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 6

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 7

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.

Question 8

Atoms of an element that have different atomic masses are called

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

Question 9

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 10

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 11

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 12

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 13

The pair of nuclides that represents isotopes is

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

Question 14

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 15

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 16

Two nuclides that are isotopes could lie on curve

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

Question 17

The nuclear radius of is approximately

A) 1.05 fm.
B) 3.60 fm.
C) 0.350 fm.
D) 11.2 fm.
E) 1.85 fm.

Question 18

The radius of the ⁶⁴Ni nucleus is approximately

A) 1.2 fm.
B) 2.4 fm.
C) 4.8 fm.
D) 16 fm.
E) 64 fm.

Question 19

The radius of the ⁶³Cu nucleus is approximately

A) 0.382 fm.
B) 4.78 fm.
C) 12.1 fm.
D) 24.2 fm.
E) 100 fm.

Question 20

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 21

The element that is commonly used as a control rod in a nuclear reactor is

A) "¹H."
B) "²⁵Mg."
C) "⁴¹K."
D) "¹⁰⁰Ru."
E) "¹¹³Cd."

Question 22

The nuclear reaction process in which a heavy nucleus splits into two roughly equal parts is known as

A) fission.
B) fusion.
C) spallation.
D) isomerism.
E) internal conversion.

Question 23

The control rods in a nuclear reactor are used to

A) produce neutrons.
B) add fuel to the reactor.
C) fragment elements by fission.
D) absorb γ rays.
E) absorb neutrons.

Question 24

About 200 MeV of energy is released in the average fission reaction of a uranium nucleus. Most of this energy is in the form of

A) kinetic energy of fission neutrons.
B) kinetic energy of fission fragments.
C) emitted β- and γ rays.
D) energy of a particles and γ rays.
E) electromagnetic radiation in the visible portion of the spectrum.

Question 25

Assuming that 200 MeV of energy is released per fission, the mass of ²³⁵U that undergoes fission to operate a 250-MW reactor for 1 y is approximately

A) 100 kg.
B) 200 kg.
C) 400 kg.
D) 500 kg.
E) 1 Mg.

Question 26

Neutrons produced in the fission of uranium are rapidly moving projectiles and must be slowed before they can produce more fission. If the neutrons collide elastically, hydrogen is effective in slowing them down because

A) hydrogen atoms repel neutrons.
B) a hydrogen atom is much more massive than a neutron.
C) a hydrogen atom and a neutron have about the same mass.
D) a neutron is much more massive than a hydrogen atom.
E) hydrogen atoms attract neutrons.

Question 27

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 28

Fission occurs because the average binding energy per nucleon for the fission fragments is higher than that for the original nucleus. The change in binding energy per nucleon is approximately

A) 0.50 MeV.
B) 1.0 MeV.
C) 7.0 MeV.
D) 28 MeV.
E) 0.20 keV.

Question 29

The graph that represents the interaction energy U) of the proton and neutron as a function of distance r is

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

Question 30

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 31

The graph that represents the Coulomb interaction energy U) between two protons as a function of distance r is

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

Question 32

One way to think about the low binding energy E_b) 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 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 33

The main purpose of a moderator in a nuclear reactor is to

A) absorb the neutrons and thereby decrease the reaction rate.
B) absorb the neutrons and thereby increase the reaction rate.
C) slow the neutrons and thereby decrease the reaction rate.
D) slow the neutrons and thereby increase the reaction rate.
E) cool the reactor chamber.

Question 34

A moderator is used to slow

A) protons.
B) alpha particles.
C) neutrons.
D) beta particles.
E) photons.

Question 35

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 36

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 37

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 38

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 39

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 40

The total binding energy of is approximately

A) 16.5 MeV.
B) 40.0 MeV.
C) 8.00 MeV.
D) 26.0 MeV.
E) 27.4 MeV.

Question 41

The following fusion reaction occurs in the Sun: The masses of the nuclei are ³He = 3.016 049 u
⁴He = 4.002 604 u
⁷Be = 7.016 930 u
The energy released or absorbed by the reaction is

A) 920 MeV, absorbed.
B) 1.60 MeV, absorbed.
C) 920 MeV, released.
D) 1.60 MeV, released.
E) 270 MeV, released.

Question 42

1 d it has a decay rate 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 43

06 d it has a decay rate 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 44

After a star fuses most its hydrogen into helium, it begins to fuse the helium into carbon. The energy released in fusing helium nuclei α particles) into carbon is approximately

A) 0.730 MeV.
B) 1.46 MeV.
C) 7.30 MeV.
D) 14.6 MeV.
E) 73.0 MeV.

Question 45

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 46

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 47

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 48

What are the numbers of protons Z and neutrons N in the missing fragment of the following fission reaction?

A) Z = 55 and N = 37
B) Z = 37 and N = 55
C) Z = 92 and N = 37
D) Z = 37 and N = 92
E) Z = 37 and N = 58

Question 49

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 50

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 51

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 52

The decay rate 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 decay rate 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 53

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 54

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 55

Nuclear fusion takes place when

A) a large nucleus splits into two fragments with the release of a few neutrons.
B) an α particle is ejected from the nucleus.
C) a positive β particle is ejected from the nucleus.
D) small nuclei combine to form a larger one.
E) heavy hydrogen is accelerated.

Question 56

A fusion reaction that is highly probable is The amount of fusion energy released in this reaction is approximately

A) 1.0 MeV.
B) 2.0 MeV.
C) 3.0 MeV.
D) 4.0 MeV.
E) 5.0 MeV.

Question 57

If, on the average, each fission reaction of ²³⁵U releases 200 MeV of energy, how many nuclei of ²³⁵U fission every second in a 200-MW reactor?

A) 6.3 × 10¹⁷.
B) 6.0 × 10²³.
C) 1.0 × 10¹⁹.
D) 1.6 × 10¹⁹.
E) 2.7 × 10¹⁸.

Question 58

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) 648 mg.

Question 59

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 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) "3ln 2)/ $\lambda$ ."
E) " $\lambda$ /3."

Question 61

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 decay rate 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 62

3 g/cm³ and its molar mass is 207 g.

A) 3.5 × 10^-22 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 63

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 64

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 65

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 66

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 67

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 68

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 69

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 70

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 a Tuesday. The half-life of this isotope is 13.2 h. What is the decay rate 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 71

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 72

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 73

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 74

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 75

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 76

A β 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.

Question 77

Uranium decomposes radioactively to form thorium atomic number 90) by emitting an α particle from its nucleus. The force of repulsion between the thorium nucleus and the α 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 78

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 79

When a gamma ray passes through a material,

A) the gamma ray can cause photoelectric effect.
B) the gamma ray can cause the nucleus to disintegrate.
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 80

At a particular time, a radioactive source A has a decay rate of 1.60 × 10¹¹ Bq and a half-life of 15.0 d, and a second source B has a decay rate of 8.50 × 10¹¹ Bq. Sources A and B have the same decay rate 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.