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13. Nuclear Reactions (43.3-8) and Particle Physics (44)
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13. Nuclear Reactions (43.3-8) and Particle Physics (44)
Due: 11:59pm on Sunday, May 1, 2016
To understand how points are awarded, read the Grading Policy for this assignment.
Exercise 43.14
Description: ^238 U decays spontaneously by alpha emission to ^234 (Th). The atomic masses are 238.050788 u for ^238 U and 234.043601 u for ^234 (Th). (a)
Calculate the total energy released by this process. (b) Calculate the recoil velocity of the ^234...
decays spontaneously by
emission to
. The atomic masses are 238.050788
for
and 234.043601
for
.
Part A
Calculate the total energy released by this process.
Express your answer using four significant figures.
ANSWER:
= 4.270
Part B
Calculate the recoil velocity of the
nucleus.
Express your answer using four significant figures.
ANSWER:
= 2.432×105
Exercise 43.16
Description: (a) What particle is emitted in the following radioactive decay? ^27_14(Si) rightarrow^27_13(Al). (b) What particle is emitted in the following radioactive
decay? ^238_92U rightarrow^234_90(Th). (c) What particle is emitted in the following...
Part A
What particle is emitted in the following radioactive decay?
.
ANSWER:
particle
electron
positron
Part B
What particle is emitted in the following radioactive decay?
.
ANSWER:
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particle
electron
positron
Part C
What particle is emitted in the following radioactive decay?
.
ANSWER:
particle
electron
positron
Alternative Exercise 43.78
Description: Hydrogen atoms are placed in an external B-T magnetic field. (a) The protons can make transitions between states where the nuclear spin component is
parallel and antiparallel to the field by absorbing or emitting a photon. Which state has lower...
Hydrogen atoms are placed in an external 1.55-
magnetic field.
Part A
The protons can make transitions between states where the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. Which state
has lower energy: the state with the nuclear spin component parallel or antiparallel to the field?
ANSWER:
Parallel
Antiparallel
Part B
What is the frequency of the photon in part A?
ANSWER:
=
= 6.59×107
Part C
What is the wavelength of the photon in part A?
ANSWER:
=
= 4.55
Part D
In which region of the electromagnetic spectrum does it lie?
ANSWER:
radio wave
microwave
infrared
visible light
ultraviolet
X-Rays
Gamma Rays
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Part E
The electrons can make transitions between states where the electron spin component is parallel and antiparallel to the field by absorbing or emitting a photon. Which
state has lower energy: the state with the electron spin component parallel or antiparallel to the field?
ANSWER:
Parallel
Antiparallel
Part F
What is the frequency of the photon in part D?
ANSWER:
= 4.34×1010
=
Part G
What is the wavelength of the photon in part D?
ANSWER:
=
= 6.91×10−3
Part H
In which region of the electromagnetic spectrum does it lie?
ANSWER:
radio wavw
microwave
infrared
visible light
ultraviolet
X-Rays
Gamma Rays
Alternative Exercise 43.80
Description: (a) What is the maximum wavelength of a gamma ray that could break a deuteron into a proton and a neutron? (This process is called
photodisintegration.)...
Part A
What is the maximum wavelength of a
ray that could break a deuteron into a proton and a neutron? (This process is called photodisintegration.)
Express your answer using four significant figures.
ANSWER:
= 0.5575
Fusion and the Sun
Description: The energy from a single fusion reaction is found and then compared to the power output of the sun .
The sun, like all stars, releases energy through nuclear fusion. In this problem, you will find the total number of fusion reaction events that occur inside the sun every second.
You will be considering the proton-proton chain, in which four hydrogen nuclei are converted into a helium nucleus and two positrons. The net reaction for the proton-proton
chain is
.
To find the energy released by this reaction, you will need the following mass data:
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mass of
and
mass of
.
Using the masses of the neutral atoms in your calculation accounts for the energy released by the annihilation of the positrons with electrons, so you can work this problem
without reference to the positrons or their rest mass.
Part A
What is the total energy
released in a single fusion reaction event for the equation given in the problem introduction? Use
.
Express your answer in joules to two significant figures.
Hint 1. How to approach the question
Find the mass defect of the reaction (
); then use
.
ANSWER:
= 4.30×10−12
Part B
The power radiated by the sun is about
. Using this number, find the number of proton-proton chain fusion reactions that must go on inside the sun in one
second to release enough energy to balance the energy radiated away. (If this condition isn't met, the sun would cool off rapidly.)
Express your answer to two significant figures.
ANSWER:
reactions in one second = 9.30×1037
Also accepted: 9.24×1037
The proton-proton chain is not the only sequence of fusion reactions that occurs inside of the sun, but the others account for such a small amount of the sun's total
power output that we can ignore them in the rough calculations that we are doing.
Part C
What mass of hydrogen is converted into helium by the fusion reactions in one second? Use
for the mass of one hydrogen nucleus.
Express your answer in kilograms to two significant figures.
ANSWER:
hydrogen used up in one second = 6.20×1011
Part D
The heat of combustion of hydrogen (the energy released by burning hydrogen with oxygen) is
. What mass of hydrogen would have to be burned in
the sun in one second to release the same amount of energy (i.e., generate the same power) as is released by fusion?
Express your answer in kilograms to two significant figures.
Hint 1. Relating mass of burned hydrogen and power
Recall that one watt is equal to one joule per second. You are asked for the mass that must be burned in one second to generate the same energy as the sun
generates in one second. Thus, the question is really asking what mass of hydrogen must be burned to generate
.
The heat of combustion gives the number of joules generated by burning one kilogram of hydrogen. Use this to find the number of kilograms of hydrogen that must
be burned to generate
.
ANSWER:
mass of hydrogen = 2.80×1018
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At this rate, the sun would use up all of its hydrogen in only 17,000 years, instead of the roughly 5 billion years that solar physicists estimate for the sun's current fuel
supply. (Of course, this is just an abstraction since there is no supply of oxygen available for such "burning" to take place.)
Nineteenth-century physicists trying to determine the age of the sun based their calculations on how much energy the sun radiated. They immediately realized that
chemical reactions could not produce nearly enough energy to account for the sun being more than a few thousand years old, an age directly contradicted by
historical records. The largest energy source that they could imagine was the gravitational energy of all the matter that formed the sun. Even this source was far too
weak: Calculations based on gravitational energy only allowed the sun to be around 30 million years old, though it is, in fact, over 4.5 billion years old! No nineteenthcentury physicist could have envisioned the incredible amounts of energy released by nuclear reactions.
Antimatter
Description: Conceptual questions about the nature of antimatter, as well as creation and annihilation of pairs, followed by simple calculations of energy and momentum
in creation/annihilation processes.
The first antiparticle, the positron or antielectron, was discovered in 1932. It had been predicted by Paul Dirac in 1928, though the nature of the prediction was not fully
understood until the experimental discovery. Today, it is well accepted that all fundamental particles have antiparticles.
Part A
Which of the following are different for a particle and its antiparticle?
ANSWER:
charge only
mass only
spin only
charge and mass
charge and spin
mass and spin
charge and mass and spin
Part B
Which conservation law is violated by particle-antiparticle annihilation?
ANSWER:
conservation of energy
conservation of momentum
conservation of charge
conservation of lepton number
none of these
Part C
Suppose that an electron and a positron collide head-on. Both have kinetic energy of 4.00
and rest energy of 0.511
. They produce two photons, which by
conservation of momentum must have equal energy and move in opposite directions. What is the energy
of one of these photons?
Express your answer in
to three significant figures.
ANSWER:
=
= 4.51
Part D
Two protons, with equal kinetic energy, collide head-on. What is the minimum kinetic energy
energy of a pion is
.
Express your answer in
of one of these protons necessary to make a pion-antipion pair? The rest
to three significant figures
Hint 1. Connecting kinetic energy to mass
In a sufficiently violent particle collision, kinetic energy may be converted into the rest energy of new particles. All that is necessary is for the amount of kinetic
energy available to meet or exceed the rest energy of the pair that you wish to produce.
Hint 2. Available kinetic energy
Because the two protons collide head-on with equal kinetic energy, the net momentum before the collision is zero. Therefore, all of the kinetic energy could be
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turned into rest energy of a particle-antiparticle pair.
ANSWER:
= 140
The Cyclotron
Description: Several qualitative and quantitative questions: radius and frequency of revolution, energy of the particles. Focuses on classical model but last follow-up
statement makes reference to relativistic model.
Learning Goal:
To learn the basic physics and applications of cyclotrons.
Particle accelerators are used to create well-controlled beams of high-energy particles. Such beams have many uses, both in research and industry.
One common type of accelerator is the cyclotron, as shown in the figure. In a cyclotron, a magnetic field confines
charged particles to circular paths while an oscillating electric field accelerates them. It is useful to understand the
details of this process.
Consider a cyclotron in which a beam of particles of positive charge
restricted by the magnetic field
and mass
is moving along a circular path
(which is perpendicular to the velocity of the particles).
Part A
Before entering the cyclotron, the particles are accelerated by a potential difference
Express your answer in terms of
,
. Find the speed
with which the particles enter the cyclotron.
, and .
ANSWER:
=
Part B
Find the radius
of the circular path followed by the particles. The magnitude of the magnetic field is
Express your answer in terms of ,
,
.
, and .
Hint 1. Find the force
Find the magnitude of the force
acting on the particles.
Express your answer in terms of ,
,
, and . You may or may not use all these variables.
ANSWER:
=
Hint 2. Find the acceleration
Find the magnitude of the acceleration
Express your answer in terms of
of the particles.
and the radius of revolution .
ANSWER:
=
Hint 3. Solving for
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Use Newton's second law to construct an equation to be solved for .
ANSWER:
=
Part C
Find the period of revolution
for the particles.
Express your answer in terms of
Hint 1. Relationship between
,
, and .
and
The period is the amount of time it takes a particle to make one complete orbit. Since the speed of the particle is constant, the period will be equal to the distance
the particle travels in one orbit divided by the particle's speed:
.
ANSWER:
=
Note that the period does not depend on the particle's speed (nor, therefore, on its kinetic energy).
Part D
Find the angular frequency
of the particles.
Express your answer in terms of
,
Hint 1. Relationship between
, and .
and
Recall that the frequency of revolution is equal to
; it represents the number of revolutions a particle makes per second. The angular frequency
; it is the number of radians the particle traverses per second.
is equal to
ANSWER:
=
Part E
Your goal is to accelerate the particles to kinetic energy
Express your answer in terms of
Hint 1. Find
, ,
, and
. What minimum radius
of the cyclotron is required?
.
in terms of
Find an expression for the speed
Express your answer in terms of
of a particle in terms of its kinetic energy
and
.
.
ANSWER:
=
You can now substitute this value for
into your expression for
from Part B.
ANSWER:
=
Part F
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If you can build a cyclotron with twice the radius, by what factor would the allowed maximum particle energy increase? Assume that the magnetic field remains the same.
Hint 1. Find
in terms of
Using your result from Part E, solve for
Express your answer in terms of
,
in terms of
, , and
.
.
ANSWER:
=
In other words, the kinetic energy
is proportional to
.
ANSWER:
2
4
8
16
Part G
If you can build a cyclotron with twice the radius and with the magnetic field twice as strong, by what factor would the allowed maximum particle energy increase?
Hint 1. Find
in terms of
and
Using your result from Part E, solve for
Express your answer in terms of
,
in terms of
, , and
and
.
.
ANSWER:
=
It's now clear that the kinetic energy
is proportional to
.
ANSWER:
2
4
8
16
One limitation of the cyclotron has to do with the failure of the laws of classical mechanics to accurately predict the behavior of high-energy particles. When their
speeds become comparable to the speed of light , the angular frequency is no longer what you determined in Part D. Using special relativity, one can show that the
angular frequency is actually given by the formula
.
As you can see, the frequency drops as the energy (and speed) increases; the particles' motion falls out of phase with the pulsating voltage, restricting the cyclotron's
ability to accelerate the particles further
Designing a New Particle Accelerator
Description: Find the available energy for two related particle collisions.
A new particle accelerator facility is being built. The designers are considering two designs, one using stationary targets and the other using collisions of beams with the same
energy.
Part A
Consider a beam of protons with energy 204.0
. If these protons collide with stationary protons, what is the available energy
in a collision?
Express your answer in billions of electron volts to three significant figures.
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Hint 1. Formula for available energy
Recall that the formula for available energy
target particle, and
is
, where
is the total energy of the moving particle. For cases where
.
is the mass of the moving particle,
is the mass of the
, such as this problem, the formula reduces to
ANSWER:
= 19.6
=
Part B
Now, consider two beams of protons, moving in opposite directions, each with energy 102
. What is the available energy
when these beams collide?
Express your answer in billions of electron volts to three significant figures.
Hint 1. Considering the momentum
In all particle collisions, momentum must be conserved. This is the reason that the available energy in collisions with a stationary target is less than the total energy
of the collision: some of the energy must go into kinetic energy for the product to conserve momentum. If two beams of identical protons collide head-on, what is
the total momentum of a pair of protons just before the collision? What is the minimum amount of energy that must go into kinetic energy to have the same total
momentum after the collision?
ANSWER:
=
= 204
Part C
If the accelerator is intended to be a source of W bosons (mass of W boson = 80.4
), which design should be chosen?
ANSWER:
Only the design from Part A can be chosen, because the W bosons will have low energy and will thus be easier to work with.
Only the design from Part B can be chosen, because it is the only one with enough energy to make W bosons.
Either design can be chosen, because the energy of the W bosons is not a concern.
Neither design can be chosen, because neither has sufficient energy to make W bosons.
Combining Quarks
Description: In this problem the student determines the quark content of particles with specific charge, baryon number, and strangeness.
Assume that each particle contains only combinations of the quarks , , and
and the antiquarks , , and .
Part A
Deduce the quark content of a particle with charge +e, baryon number 0, and strangeness +1.
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Hint 1. Charges of quarks
The electric charges of the three quarks , , and
are, respectively,
,
where
is the magnitude of the electron charge. Note that the antiquarks will have the same charge magnitude, just with opposite sign to its corresponding quark.
Hint 2. Baryons versus mesons
Recall that hadrons are a general classification of particles that consist of quarks. They are divided into two subclasses: baryons, which consist of three quarks and
have baryon number
(as well as antibaryons with three antiquarks and baryon number
), and mesons, which consist of a quark-antiquark pair
and have baryon number
. Since
in this problem, you are looking for a quark-antiquark pair.
Hint 3. Definition of strangeness
Strangeness is a quantum number that is used to track the number of strange particles in a hadron (both mesons and baryons). If a particle has a strange quark (
), then it has strangeness
. If the particle has an antistrange quark ( ), then it has strangeness
. These numbers are additive; two strange
quarks in combination means a strangeness of
.
ANSWER:
Part B
Deduce the quark content of a particle with charge +e, baryon number
1, and strangeness +1.
Hint 1. Charges of quarks
The electric charges of the three quarks , , and
are, respectively,
,
where
is the magnitude of the electron charge. Note that the antiquarks will have the same charge magnitude, just with opposite sign to its corresponding quark.
Hint 2. Baryons versus mesons
Recall that hadrons are a general classification of particles that consist of quarks. They are divided into two subclasses: baryons, which consist of three quarks and
have baryon number
(as well as antibaryons with three antiquarks and baryon number
), and mesons, which consist of a quark-antiquark pair
and have baryon number
.
Hint 3. Definition of strangeness
Strangeness is a quantum number that is used to track the number of strange particles in a hadron (both mesons and baryons). If a particle has a strange quark (
), then it has strangeness
. If the particle has an antistrange quark ( ), then it has strangeness
. These numbers are additive; two strange
quarks in combination means a strangeness of
.
ANSWER:
Part C
Deduce the quark content of a particle with charge 0, baryon number +1, and strangeness
2.
Hint 1. Charges of quarks
The electric charges of the three quarks , , and
are, respectively,
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,
where
is the magnitude of the electron charge. Note that the antiquarks will have the same charge magnitude, just with opposite sign to its corresponding quark.
Hint 2. Baryons versus mesons
Recall that hadrons are a general classification of particles that consist of quarks. They are divided into two subclasses: baryons, which consist of three quarks and
have baryon number
(as well as antibaryons with three antiquarks and baryon number
), and mesons, which consist of a quark-antiquark pair
and have baryon number
.
Hint 3. Definition of strangeness
Strangeness is a quantum number that is used to track the number of strange particles in a hadron (both mesons and baryons). If a particle has a strange quark (
), then it has strangeness
. If the particle has an antistrange quark ( ), then it has strangeness
. These numbers are additive; two strange
quarks in combination means a strangeness of
.
ANSWER:
Exercise 43.44
Description: The United States uses 1.4*10^19 J of electrical energy per year. Assume, that all this energy came from the fission of ^235U, which releases 200 MeV per
fission event. Assume that all fission energy is converted into electrical energy. (a) How ...
The United States uses 1.4 10
of electrical energy per year. Assume, that all this energy came from the fission of
Assume that all fission energy is converted into electrical energy.
, which releases 200
per fission event.
Part A
How many kilograms of
would be used per year?
Express your answer to two significant figures and include the appropriate units.
ANSWER:
5
= 1.7×10
Also accepted: 1.71×105
, 1.7×105
Part B
How many kilograms of uranium would have to be mined per year to provide that much
? (Recall that only 0.70
of naturally occurring uranium is
.)
Express your answer to two significant figures and include the appropriate units.
ANSWER:
7
= 2.4×10
Also accepted: 2.4×107
, 2.44×107
, 2.43×107
, 2.4×107
, 2.4×107
A Decay Chain
Description: Find the daughter nucleus of, energy released by, and number of beta and alpha decays involved in the Th-232 decay chain.
When the daughter nucleus produced in a radioactive decay is itself unstable, it will eventually decay and form its own daughter nucleus. If the newly formed daughter nucleus
is also unstable, another decay will occur, and the process will continue until a nonradioactive nucleus is formed. Such a series of radioactive decays is called a decay chain.
A good example of a decay chain is provided by
, a naturally occurring isotope of thorium.
Part A
The first step in the decay chain of
is an alpha decay. What is the daughter nucleus formed by this first decay?
Hint 1. Alpha decay
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In alpha-particle decay, a helium nucleus (consisting of two protons and two neutrons) is emitted from the parent atom, leaving it with four fewer nucleons and an
atomic number reduced by two.
Hint 2. Find the numbers of protons and neutrons in the daughter nucleus
Recall that in radioactive decays the atomic number and mass number are conserved. How many protons and neutrons are there in the daughter nucleus when
undergoes an alpha decay?
ANSWER:
232 neutrons and 88 protons
88 neutrons and 232 protons
88 neutrons and 140 protons
140 neutrons and 88 protons
ANSWER:
Part B
What is the energy
228.0301069 .
released in the first step of the thorium-232 decay chain? The atomic mass of
is 232.038054
and the atomic mass of
is
Express your answer numerically in megaelectron volts.
Hint 1. How to approach the problem
The energy
released in a decay depends on the difference in mass,
, of the system before and after the decay. It can be calculated using the relation
. You need to take into account the mass of the particle emitted in the decay when calculating the mass of the system after the decay. Also, note that
the number of electrons in the parent nucleus is the same as the number of electrons in the daughter nucleus plus the number of electrons in the alpha particle, so
the electrons do not contribute to the total mass difference.
Hint 2. Find the mass difference
What is the difference in mass,
, of the system before and after the alpha decay?
Express your answer numerically in atomic mass units to four significant digits.
Hint 1. Atomic mass of an alpha particle
The atomic mass of an alpha particle is 4.002603 .
ANSWER:
= 0.005343
Now use the relation
and remember to convert atomic mass units to electron volts.
ANSWER:
= 4.98
Part C
then decays through a series of beta-minus decays; eventually, another isotope of thorium,
chain process?
, is formed. How many beta-minus decays will occur during this
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Hint 1. Beta decay
In a beta-minus decay, an electron (as well as an antineutrino with negligible mass) is emitted as a neutron is converted into a proton. Such a decay increases the
atomic number by one without changing the number of nucleons.
ANSWER:
1
2
4
6
Part D
then decays by emitting alpha particles until
is formed. How many alpha decays will occur during this chain process?
Hint 1. Alpha decay
In alpha-particle decay, a helium nucleus (consisting of two protons and two neutrons) is emitted from the parent atom, leaving it with four fewer nucleons and an
atomic number reduced by two.
ANSWER:
2
4
6
8
The chain continues with two more intermediate states until the stable isotope of lead
is formed, after a total of 10 decays.
± Half-Life and Radioactive Dating
Description: ± Includes Math Remediation. The equations for decay and half-life are derived, and then a simple problem in carbon-14 dating is solved.
Learning Goal:
To understand decay in terms of half-life and to solve radioactive dating problems.
Particles in a nucleus are bound by the strong force. A reasonable model of this binding would be a barrier potential of finite energy. Quantum mechanics allows a small,
nonzero probability for a particle to "tunnel" through a potential barrier. Working with this rough model, we can say that, for a given unstable nucleus, there is a constant
probability of some particle, say an alpha particle, tunneling through the barrier and being emitted as radiation. Since this probability is constant, depending only on the
particular nuclide involved, you would expect the number of decays per second to be proportional to the number of nuclei present. Since the number of decays is the same as
the amount by which the total number of nuclei (of the particular type being considered) is reduced, you can construct the relationship
,
where
is the number of nuclei at a time . The constant of proportionality
is called the decay constant.
Part A
If
, where
is some constant, what is
Express your answer in terms of
?
, , and .
ANSWER:
=
Notice that this expression is equal to
. Thus,
is the general solution to the differential equation for radioactive decay.
Part B
Given that at time
there is a quantity of nuclei present
Express your answer in terms of
(in other words,
), find the value of the constant
in the equation
.
and .
Hint 1. Find
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Since
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, simply plug zero into your equation
Express your answer in terms of
to find
.
and .
ANSWER:
=
ANSWER:
=
Part C
Combining your answers from Parts A and B gives the equation
Express your answer in terms of
. Find the time
at which half of the original number of nuclei will remain.
and .
Hint 1. What values to use
Which of the following correctly pairs the value of
and the value of
that should be entered into
to find the value of
?
ANSWER:
0 and
and
and
and
and
ANSWER:
=
Part D
How many nuclei are left after a time
Express your answer in terms of
?
and
.
ANSWER:
=
This is half the number of nuclei that were present at time
, which was itself half the number present at time zero. The number
is called the half-life of the
nucleus. Frequently, the half-life is given instead of the decay constant when discussing the decay of radioactive nuclei. If you measure the number of nuclei at any
time and then wait one half-life,
of the nuclei will remain. If you wait two half-lives then
will remain. If you wait three half-lives,
will remain, and so on.
The decay of radioactive nuclei can be used to measure the age of artifacts, fossils, and rocks.
Dating an organic artifact entails looking at its carbon content. Carbon exists in three isotopic forms:
,
, and
. Both
and
are stable whereas
is
radioactive. To find the age of an organic artifact, first, you measure how much
is found within the artifact. Then, you estimate how much would have been in it when it
was first made. You then plug these two values into the decay equation to find how old the artifact is.
The quantity of
originally in the artifact may be estimated fairly accurately because the percent of atmospheric carbon in the form of the isotope
stays relatively
constant with time. Since plants constantly take in new carbon from atmospheric carbon dioxide, the percent of
in a plant should be the same as the percent in the
atmosphere, until the plant dies and stops taking in new carbon. Therefore, you can use this percent and the present quantity of total carbon in the artifact to find how much
was in it when it died.
The half-life of
is 5730 years.
Part E
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If a sample shows only one-fourth of its estimated original quantity of
need to plug into it at all for this problem.)
, how old is it? Think about half-lives; don't try to just plug into the decay equation. (You shouldn't
Express your answer in years to three significant figures.
Hint 1. Find the number of half-lives
If the quantity is 1/4 of the original, how many half-lives must have passed?
Express your answer as an integer.
ANSWER:
2 half-lives
Since you know that a half-life for
is 5730 years, you can use the number of half-lives to find the total age of the sample.
ANSWER:
age = 1.15×104 years
Part F
The previous part could be done without using the decay equation, because the ratio of original
to present
so simple. To solve more general carbon dating problems, you must first find the value of the decay constant for
Using the given half-life, 5730 years, find the value of the decay constant for
.
was an integer power of 1/2. Most problems are not
, so that you can easily use the decay equation.
Express your answer in inverse years to three significant figures.
Hint 1. Relating
and
Recall that in Part C you found the relation
.
ANSWER:
= 1.210×10−4
Part G
Suppose that an Egyptian farmer claims to have discovered a linen burial cloth used during Egypt's Middle Kingdom some 4000 years ago. Careful analysis shows that
the cloth contains 80% of the
that it is estimated to have originally contained. How old is the cloth?
Express your answer in years to two significant figures.
ANSWER:
age = 1800 years
Although the cloth does seem to be rather old, it isn't close to 4000 years old. Radioactive dating is an important technique used by archaeologists to find the age of
newly discovered items and to determine the authenticity of supposed artifacts.
Exercise 43.35
Description: Food is often irradiated with either x rays or electron beams to help prevent spoilage. A low dose of 5-75 kilorads (krad) helps to reduce and kill inactive
parasites, a medium dose of 100-400 krad kills microorganisms and pathogens such as...
Food is often irradiated with either x rays or electron beams to help prevent spoilage. A low dose of 5-75 kilorads (
dose of 100-400
kills microorganisms and pathogens such as salmonella, and a high dose of 2300-5700
refrigeration.
) helps to reduce and kill inactive parasites, a medium
sterilizes food so that it can be stored without
Part A
A dose of 175
kills spoilage microorganisms in fish. If x rays are used, what would be the dose in
?
ANSWER:
=
= 1750
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Part B
What would be the dose in
?
ANSWER:
= 1750
=
Part C
What would be the dose in
?
ANSWER:
=
= 1.75×105
Part D
How much energy would a 160- portion of fish absorb?
ANSWER:
=
= 280
Part E
If electrons of RBE 1.50 are used instead of x rays, what would be the dose in
?
ANSWER:
=
= 1750
Part F
What would be the dose in
?
ANSWER:
=
= 2630
Part G
What would be the dose in
?
ANSWER:
=
= 2.63×105
Part H
How much energy would a 160- portion of fish absorb?
ANSWER:
=
= 280
Alternative Exercise 43.81
Description: The isotope ^226(Ra) undergoes alpha decay with a half-life of 1620 years. (a) What is the activity of 1.00 g of ^226(Ra) in Bq? (b) What is the activity of
1.00 g of ^226(Ra) in Ci?
The isotope
undergoes
decay with a half-life of 1620
.
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Part A
What is the activity of 1.00
of
in
?
of
in
?
ANSWER:
= 3.61×1010
Part B
What is the activity of 1.00
ANSWER:
= 0.977
Alternative Exercise 43.88
Description: The isotope ^90(Sr) undergoes beta^- decay with a half-life of 28 years. (a) What nucleus is produced by this decay? (b) If a nuclear power plant is
contaminated with ^90Sr, how long will it take for the radiation level to decrease to 1.0% of its...
The isotope
undergoes
decay with a half-life of 28 years.
Part A
What nucleus is produced by this decay?
ANSWER:
Part B
If a nuclear power plant is contaminated with
Sr, how long will it take for the radiation level to decrease to 1.0% of its initial value?
Express your answer using two significant figures.
ANSWER:
= 190
Exercise 43.20
Description: Radioactive isotopes used in cancer therapy have a "shelf-life," just like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a
nuclear reactor, the activity of a sample of ^60(Co) is 5000 Ci. When its activity falls below...
Radioactive isotopes used in cancer therapy have a "shelf-life," just like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the
activity of a sample of
is 5000
. When its activity falls below 3500
, it is considered to be too weak a source to use in treatment. You work in the radiology
department of a large hospital. One of these
sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014.
Part A
Is the source still usable? The half-life of
is 5.271
.
ANSWER:
yes
no
Exercise 43.36
Description: It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans), using x rays, just to see if they detect
anything suspicious. A number of medical people have recently questioned the advisability of such...
It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans), using x rays, just to see if they detect anything suspicious. A
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number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of 12
applied to the whole body. By contrast, a chest x ray typically administers 0.20
to only 5.0
of tissue.
,
Part A
How many chest x rays would deliver the same total amount of energy to the body of a 75
person as one whole-body scan?
Express your answer using two significant figures.
ANSWER:
= 900
± Nuclear Power
Description: ± Includes Math Remediation. The energy per reaction is calculated for fission of uranium-235. This is compared to the energy usage of the US in a year.
Nuclear reactors generate power by harnessing the energy from nuclear fission. In a fission reaction, uranium-235 absorbs a neutron, bringing it into a highly unstable state as
uranium-236. This state almost immediately breaks apart into two smaller fragments, releasing energy. One typical reaction is
,
where
indicates a neutron. In this problem, assume that all fission reactions are of this kind. In fact, many different fission reactions go on inside a reactor, but all have
similar reaction energies, so it is reasonable to calculate with just one. The products of this reaction are unstable and decay shortly after fission, releasing more energy. In this
problem, you will ignore the extra energy contributed by these secondary decays.
You will need the following mass data:
mass of
,
mass of
,
mass of
mass of
, and
.
Part A
What is the reaction energy
of this reaction? Use
.
Express your answer in millions of electron volts to three significant figures.
Hint 1. Formula for reaction energy
.
ANSWER:
= 185
Part B
Using fission, what mass
of uranium-235 would be necessary to supply all of the energy that the United States uses in a year, roughly
?
Express your answer in kilograms to two significant figures.
Hint 1. Relating MeV and joules
and
.
Hint 2. Find the mass of one uranium atom
Find the mass of one atom of uranium-235. Recall that the mass in atomic mass units is equal to the mass in grams of one mole of atoms. Avagadro's number,
, gives the number of atoms in one mole.
Give your answer in kilograms to three significant figures.
ANSWER:
mass of one atom of
= 3.900×10−25
Divide the mass per atom by the energy released per atom to get the mass of uranium used up per unit of energy released.
ANSWER:
= 1.30×105
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As a comparison, a coal-burning plant would have to burn many times more coal than this to provide the energy needs of even one large city for just one day. It
should be noted that nuclear power plants do not pose a substantial risk to surrounding communities, though this is a common misconception.
Exercise 44.4
Description: A proton and an antiproton annihilate, producing two photons. (a) Find the energy of each photon if the p and bar p are initially at rest. Determine the values
in the center-of-momentum reference frame. (b) Find the frequency of each photon if the...
A proton and an antiproton annihilate, producing two photons.
Part A
Find the energy of each photon if the
and
are initially at rest. Determine the values in the center-of-momentum reference frame.
Express your answers using three significant figures separated by a comma.
ANSWER:
,
,
=
= 938, 938
Part B
Find the frequency of each photon if the
and
are initially at rest. Determine the values in the center-of-momentum reference frame.
Express your answers using three significant figures separated by a comma.
ANSWER:
,
= 2.27×1023, 2.27×1023
,
=
Part C
Find the wavelength of each photon if the
and
are initially at rest. Determine the values in the center-of-momentum reference frame.
Express your answers using three significant figures separated by a comma.
ANSWER:
,
=
= 1.32×10−15, 1.32×10−15
,
Part D
Find the energy of each photon if the
reference frame.
and
collide head-on, each with an initial kinetic energy of 670
. Determine the values in the center-of-momentum
Express your answers using three significant figures separated by a comma.
ANSWER:
,
= 1.61×103, 1.61×103
,
=
Part E
Find the frequency of each photon if the
reference frame.
and
collide head-on, each with an initial kinetic energy of 670
. Determine the values in the center-of-momentum
Express your answers using three significant figures separated by a comma.
ANSWER:
,
=
,
= 3.89×1023, 3.89×1023
Part F
Find the wavelength of each photon if the
and
collide head-on, each with an initial kinetic energy of 670
. Determine the values in the center-of-momentum
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reference frame.
Express your answers using three significant figures separated by a comma.
ANSWER:
,
=
,
= 7.71×10−16, 7.71×10−16
Exercise 44.24
Description: Which of the following reactions obey the conservation of baryon number? (a) p + p to p + e^+... (b) p + n to (2 e)^+ + e^-... (c) p to n + e^- ( + )bar nu_e...
(d) p + (bar p) to2 gamma...
Which of the following reactions obey the conservation of baryon number?
Part A
ANSWER:
obeys
does not obey
Part B
ANSWER:
obeys
does not obey
Part C
ANSWER:
obeys
does not obey
Part D
ANSWER:
obeys
does not obey
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