another if the barrier between the objects is thin enough. The process is the same in principle as described for α decay. It is far more likely for a thin
barrier than a thick one. Scanning tunneling electron microscopes function on this principle. The current of electrons that travels between a probe and
a sample tunnels through a barrier and is very sensitive to its thickness, allowing detection of individual atoms as shown in Figure 31.33.
Figure 31.33 (a) A scanning tunneling electron microscope can detect extremely small variations in dimensions, such as individual atoms. Electrons tunnel quantum
mechanically between the probe and the sample. The probability of tunneling is extremely sensitive to barrier thickness, so that the electron current is a sensitive indicator of
surface features. (b) Head and mouthparts of Coleoptera Chrysomelidea as seen through an electron microscope (credit: Louisa Howard, Dartmouth College)
1138 CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS
PhET Explorations: Quantum Tunneling and Wave Packets
Watch quantum "particles" tunnel through barriers. Explore the properties of the wave functions that describe these particles.
Figure 31.34 Quantum Tunneling and Wave Packets (http://cnx.org/content/m42644/1.4/quantum-tunneling_en.jar)
Glossary
activity: the rate of decay for radioactive nuclides
alpha decay: type of radioactive decay in which an atomic nucleus emits an alpha particle
alpha rays: one of the types of rays emitted from the nucleus of an atom
antielectron: another term for positron
antimatter: composed of antiparticles
atomic mass: the total mass of the protons, neutrons, and electrons in a single atom
atomic number: number of protons in a nucleus
barrier penetration: quantum mechanical effect whereby a particle has a nonzero probability to cross through a potential energy barrier despite
not having sufficient energy to pass over the barrier; also called quantum mechanical tunneling
becquerel: SI unit for rate of decay of a radioactive material
beta decay: type of radioactive decay in which an atomic nucleus emits a beta particle
beta rays: one of the types of rays emitted from the nucleus of an atom
binding energy per nucleon: the binding energy calculated per nucleon; it reveals the details of the nuclear force—larger the BE / A , the more
stable the nucleus
binding energy: the energy needed to separate nucleus into individual protons and neutrons
carbon-14 dating: a radioactive dating technique based on the radioactivity of carbon-14
chart of the nuclides: a table comprising stable and unstable nuclei
curie: the activity of 1g of 226 Ra , equal to 3.70×1010 Bq
daughter: the nucleus obtained when parent nucleus decays and produces another nucleus following the rules and the conservation laws
decay constant: quantity that is inversely proportional to the half-life and that is used in equation for number of nuclei as a function of time
decay equation: the equation to find out how much of a radioactive material is left after a given period of time
decay series: process whereby subsequent nuclides decay until a stable nuclide is produced
decay: the process by which an atomic nucleus of an unstable atom loses mass and energy by emitting ionizing particles
electron capture equation: equation representing the electron capture
electron capture: the process in which a proton-rich nuclide absorbs an inner atomic electron and simultaneously emits a neutrino
electron’s antineutrino: antiparticle of electron’s neutrino
electron’s neutrino: a subatomic elementary particle which has no net electric charge
Geiger tube: a very common radiation detector that usually gives an audio output
gamma decay: type of radioactive decay in which an atomic nucleus emits a gamma particle
gamma rays: one of the types of rays emitted from the nucleus of an atom
half-life: the time in which there is a 50% chance that a nucleus will decay
ionizing radiation: radiation (whether nuclear in origin or not) that produces ionization whether nuclear in origin or not
CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS 1139
isotopes: nuclei having the same Z and different N s
magic numbers: a number that indicates a shell structure for the nucleus in which closed shells are more stable
mass number: number of nucleons in a nucleus
neutrino: an electrically neutral, weakly interacting elementary subatomic particle
neutron: a neutral particle that is found in a nucleus
nuclear radiation: rays that originate in the nuclei of atoms, the first examples of which were discovered by Becquerel
nuclear reaction energy: the energy created in a nuclear reaction
nucleons: the particles found inside nuclei
nucleus: a region consisting of protons and neutrons at the center of an atom
nuclide: a type of atom whose nucleus has specific numbers of protons and neutrons
parent: the original state of nucleus before decay
photomultiplier: a device that converts light into electrical signals
positron decay: type of beta decay in which a proton is converted to a neutron, releasing a positron and a neutrino
positron: the particle that results from positive beta decay; also known as an antielectron
protons: the positively charged nucleons found in a nucleus
quantum mechanical tunneling: quantum mechanical effect whereby a particle has a nonzero probability to cross through a potential energy
barrier despite not having sufficient energy to pass over the barrier; also called barrier penetration
radiation detector: a device that is used to detect and track the radiation from a radioactive reaction
radioactive dating: an application of radioactive decay in which the age of a material is determined by the amount of radioactivity of a particular
type that occurs
radioactive: a substance or object that emits nuclear radiation
radioactivity: the emission of rays from the nuclei of atoms
radius of a nucleus: the radius of a nucleus is r = r 0 A 1/3
range of radiation: the distance that the radiation can travel through a material
rate of decay: the number of radioactive events per unit time
scintillators: a radiation detection method that records light produced when radiation interacts with materials
solid-state radiation detectors: semiconductors fabricated to directly convert incident radiation into electrical current
tunneling: a quantum mechanical process of potential energy barrier penetration
Section Summary
• Some nuclei are radioactive—they spontaneously decay destroying some part of their mass and emitting energetic rays, a process called
nuclear radioactivity.
• Nuclear radiation, like x rays, is ionizing radiation, because energy sufficient to ionize matter is emitted in each decay.
• The range (or distance traveled in a material) of ionizing radiation is directly related to the charge of the emitted particle and its energy, with
greater-charge and lower-energy particles having the shortest ranges.
• Radiation detectors are based directly or indirectly upon the ionization created by radiation, as are the effects of radiation on living and inert
materials.
31.2 Radiation Detection and Detectors
• Radiation detectors are based directly or indirectly upon the ionization created by radiation, as are the effects of radiation on living and inert
materials.
31.3 Substructure of the Nucleus
• Two particles, both called nucleons, are found inside nuclei. The two types of nucleons are protons and neutrons; they are very similar, except
that the proton is positively charged while the neutron is neutral. Some of their characteristics are given in Table 31.2 and compared with those
of the electron. A mass unit convenient to atomic and nuclear processes is the unified atomic mass unit (u), defined to be
1 u = 1.6605×10−27 kg = 931.46 MeV / c 2.
1140 CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS
• A nuclide is a specific combination of protons and neutrons, denoted by
AZ X N or simply A X,
Z is the number of protons or atomic number, X is the symbol for the element, N is the number of neutrons, and A is the mass number or
the total number of protons and neutrons,
A = N + Z.
• Nuclides having the same Z but different N are isotopes of the same element.
• The radius of a nucleus, r , is approximately
r = r 0 A 1/3,
where r 0 = 1.2 fm . Nuclear volumes are proportional to A . There are two nuclear forces, the weak and the strong. Systematics in nuclear
stability seen on the chart of the nuclides indicate that there are shell closures in nuclei for values of Z and N equal to the magic numbers,
which correspond to highly stable nuclei.
31.4 Nuclear Decay and Conservation Laws
• When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear
decay, called alpha ( α) , beta ⎛⎝ β⎞⎠ , and gamma ( γ) . The α decay equation is
A
A − 4
4
Z X N → Z − 2 Y N − 2 + 2He2.
• Nuclear decay releases an amount of energy E related to the mass destroyed Δ m by
E = (Δ m) c 2.
• There are three forms of beta decay. The β− decay equation is
A
A
Z X N → Z + 1 Y N − 1 + β− + ν¯ e.
• The β+ decay equation is
A
A
Z X N → Z − 1 Y N + 1 + β+ + νe.
• The electron capture equation is
A
A
Z X N + e− → Z − 1 Y N + 1 + νe.
•
β− is an electron, β+ is an antielectron or positron, νe represents an electron’s neutrino, and ν¯ e is an electron’s antineutrino. In addition to all previously known conservation laws, two new ones arise— conservation of electron family number and conservation of the total number of
nucleons. The γ decay equation is
X N* → X N + γ 1 + γ 2 + ⋯
γ is a high-energy photon originating in a nucleus.
• Half-life t 1 / 2 is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei N as a function of time is
N = N 0 e− λt,
where N 0 is the number present at t = 0 , and λ is the decay constant, related to the half-life by
λ = 0.693
t
.
1 / 2
• One of the applications of radioactive decay is radioactive dating, in which the age of a material is determined by the amount of radioactive
decay that occurs. The rate of decay is called the activity R :
R = Δ N
Δ t .
• The SI unit for R is the becquerel (Bq), defined by
1 Bq = 1 decay/s.
•
R is also expressed in terms of curies (Ci), where
1 Ci = 3.70×1010 Bq.
• The activity R of a source is related to N and t 1 / 2 by
R = 0.693 N
t
.
1 / 2
• Since N has an exponential behavior as in the equation N = N 0 e− λt , the activity also has an exponential behavior, given by
R = R 0 e− λt,
where R 0 is the activity at t = 0 .
CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS 1141
• The binding energy (BE) of a nucleus is the energy needed to separate it into individual protons and neutrons. In terms of atomic masses,
BE = {[ Zm(1 H) + Nmn] − m( A X)} c 2,
where m⎛1
A
⎝ H⎞⎠ is the mass of a hydrogen atom, m⎛⎝ X⎞⎠ is the atomic mass of the nuclide, and mn is the mass of a neutron. Patterns in the
binding energy per nucleon, BE / A , reveal details of the nuclear force. The larger the BE / A , the more stable the nucleus.
• Tunneling is a quantum mechanical process of potential energy barrier penetration. The concept was first applied to explain α decay, but
tunneling is found to occur in other quantum mechanical systems.
Conceptual Questions
1. Suppose the range for 5.0 MeV α ray is known to be 2.0 mm in a certain material. Does this mean that every 5.0 MeV α a ray that strikes this
material travels 2.0 mm, or does the range have an average value with some statistical fluctuations in the distances traveled? Explain.
2. What is the difference between γ rays and characteristic x rays? Is either necessarily more energetic than the other? Which can be the most
energetic?
3. Ionizing radiation interacts with matter by scattering from electrons and nuclei in the substance. Based on the law of conservation of momentum
and energy, explain why electrons tend to absorb more energy than nuclei in these interactions.
4. What characteristics of radioactivity show it to be nuclear in origin and not atomic?
5. What is the source of the energy emitted in radioactive decay? Identify an earlier conservation law, and describe how it was modified to take such
processes into account.
instead of the south pole, in which directions will the α , β , and γ rays bend?
7. Explain how an α particle can have a larger range in air than a β particle with the same energy in lead.
8. Arrange the following according to their ability to act as radiation shields, with the best first and worst last. Explain your ordering in terms of how
radiation loses its energy in matter.
(a) A solid material with low density composed of low-mass atoms.
(b) A gas composed of high-mass atoms.
(c) A gas composed of low-mass atoms.
(d) A solid with high density composed of high-mass atoms.
9. Often, when people have to work around radioactive materials spills, we see them wearing white coveralls (usually a plastic material). What types
of radiation (if any) do you think these suits protect the worker from, and how?
31.2 Radiation Detection and Detectors
10. Is it possible for light emitted by a scintillator to be too low in frequency to be used in a photomultiplier tube? Explain.
31.3 Substructure of the Nucleus
11. The weak and strong nuclear forces are basic to the structure of matter. Why we do not experience them directly?
12. Define and make clear distinctions between the terms neutron, nucleon, nucleus, nuclide, and neutrino.
13. What are isotopes? Why do different isotopes of the same element have similar chemistries?
31.4 Nuclear Decay and Conservation Laws
14. Star Trek fans have often heard the term “antimatter drive.” Describe how you could use a magnetic field to trap antimatter, such as produced by
nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the
fraction of matter converted into energy.
15. What conservation law requires an electron’s neutrino to be produced in electron capture? Note that the electron no longer exists after it is
captured by the nucleus.
16. Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same
time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the
Southern Hemisphere and some 100,000 light-years away from Earth, neutrinos from the explosion were observed at about the same time as the
light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?
17. What do the three types of beta decay have in common that is distinctly different from alpha decay?
1142 CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS
18. In a 3×109 -year-old rock that originally contained some 238 U , which has a half-life of 4.5×109 years, we expect to find some 238 U
remaining in it. Why are 226 Ra , 222 Rn , and 210 Po also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8
days, and 138 days, respectively)?
19. Does the number of radioactive nuclei in a sample decrease to exactly half its original value in one half-life? Explain in terms of the statistical
nature of radioactive decay.
20. Radioactivity depends on the nucleus and not the atom or its chemical state. Why, then, is one kilogram of uranium more radioactive than one
kilogram of uranium hexafluoride?
21. Explain how a bound system can have less mass than its components. Why is this not observed classically, say for a building made of bricks?
22. Spontaneous radioactive decay occurs only when the decay products have less mass than the parent, and it tends to produce a daughter that is
more stable than the parent. Explain how this is related to the fact that more tightly bound nuclei are more stable. (Consider the binding energy per
nucleon.)
23. To obtain the most precise value of BE from the equation BE=⎡
1
⎤
A
⎣ ZM⎛⎝ H⎞⎠ + Nmn⎦ c 2 − m⎛⎝ X⎞⎠ c 2 , we should take into account the binding
energy of the electrons in the neutral atoms. Will doing this produce a larger or smaller value for BE? Why is this effect usually negligible?
24. How does the finite range of the nuclear force relate to the fact that BE / A is greatest for A near 60?
25. Why is the number of neutrons greater than the number of protons in stable nuclei having A greater than about 40, and why is this effect more
pronounced for the heaviest nuclei?
26. A physics student caught breaking conservation laws is imprisoned. She leans against the cell wall hoping to tunnel out quantum mechanically.
Explain why her chances are negligible. (This is so in any classical situation.)
27. When a nucleus α decays, does the α particle move continuously from inside the nucleus to outside? That is, does it travel each point along an
imaginary line from inside to out? Explain.
CHAPTER 31 | RADIOACTIVITY AND NUCLEAR PHYSICS 1143
Problems & Exercises
14. (a) Show that if you assume the average nucleus is spherical with a
radius r = r 0 A 1 / 3 , and with a mass of A u, then its density is
31.2 Radiation Detection and Detectors
independent of A .
1. The energy of 30.0 eV is required to ionize a molecule of the gas
(b) Calculate that density in u/fm3 and kg/m3 , and compare your
inside a Geiger tube, thereby producing an ion pair. Suppose a particle of
ionizing radiation deposits 0.500 MeV of energy in this Geiger tube. What
results with those found in Example 31.1 for 56 Fe .
maximum number of ion pairs can it create?
2. A particle of ionizing radiation creates 4000 ion pairs in the gas inside
15. What is the ratio of the velocity of a 5.00-MeV β ray to that of an α
a Geiger tube as it passes through. What minimum energy was
particle with the same kinetic energy? This should confirm that β s travel
deposited, if 30.0 eV is required to create each ion pair?
much faster than α s even when relativity is taken into consideration.
3. (a) Repeat Exercise 31.2, and convert the energy to joules or calories.
(See also Exercise 31.11.)
(b) If all of this energy is converted to thermal energy in the gas, what is
16. (a) What is the kinetic energy in MeV of a β ray that is traveling at
its temperature increase, assuming 50.0 cm3 of ideal g