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Textbook Guide Physics: Electric Generator, The Chain Reaction, Uranium-236

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Fall 2016

Department
Physics
Course Code
PHY131H1

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Energy from the Nucleus
1 Nuclear Fission
One of the main goals of physics and engineering has
been extracting energy from natural sources.
There are two ways to do it:
Rearranging the outer electrons of atoms in more
stable configurations. This is the case of carbon-
based fuels.
Tinkering with the atom nucleus, and rearrang-
ing its nucleons. This is the case of uranium-
based nuclear reactors.
In this chapter we will study this second source of
energy.
In the Table 1 we compare the amount of energy that
its stored in 1 kg of six forms of fuels. The first three
have been implemented in practice, while the rest are
theoretical limits.
1.1 Basic Process
In the 1930’s Enrico Fermi proposed ways to use the
neutron as a projectile. In fact, he created new ele-
ments in his lab by bombarding different elements
with neutrons.
One particular class of neutron called thermal nu-
cleus - a neutron with low kinetic energy - was used
to produce barium from uranium.
The process was explained by Meiner and Frish: after
absorbing a thermal neutron, the uranium nucleus
could split into two approximately equal parts. One
of those is Barium, and the process received the name
fission.
The figure shows the distribution of mass numbers
from actual 235U fission events.
Note that there are two peaks with high probability
of occurrence (in the neighborhood of 7%):
Close to A= 95.
Close to A= 140.
Let’s see an example of a fission reaction:
Step 1. We start with 235U and we bombard it with
neutrons.
Step 2. The nucleus absorbs the neutron creating
236U. This is a highly excited state which un-
dergoes fission right away.
Step 3. The fragments emit two neutrons, and the re-
maining 140Xe and 94Sr.
The reaction is summarized in this equation
235U+n236U140Xe +94 Sr + 2n.(1)
The fission process conserves the total number of
protons and neutrons involved in the reaction.
Both elements are quite unstable, so after a few sec-
onds they start a process of particle emissions until
reaching a stable state.
For example, 140Xe turns into 140Ce in an average
time of 15 days. The same thing happen to 94Sr
(strontium) that turns into 94Zr (zirconium) in about
20 minutes.
Note that all these decays are produced because
when the original nucleus splits, the new nuclei have
a large neutron/proton ratio (1.6).
1
Form of Matter Process Time to power a 100 W lightbulb
Water A 50 [m] waterfall 5seconds
Coal Burning 8hours
Enriched UO2Fission in a reactor 690 years
235U Complete fission 3×104years
Hot deuterium gas Complete fusion 3×104years
Matter and antimatter Complete annihilation 3×107years
Table 1: Stored energy in fuels.
These are neutron rich atoms that need to eject a
few neutrons to become stable. The nucleus under-
goes a beta decay process until reaching a equilib-
rium point.
1.2 Energy Released During Fission
One way to estimate the total energy released during
nuclear fission is to compute the total binding energy
per nucleon Eben.
The energy Qreleased by fission is
Q=final
Eben  final number
of nucleons
initial
Eben  initial number
of nucleons (2)
1.3 A Model for Nuclear Fission
The process for nuclear fission was proposed by
Niels Bohr and John Wheeler and consists on the fol-
lowing steps.
Step 1. A high-mass nucleus absorbs a slow (ther-
mal) neutron.
Step 2. The neutron potential energy excites the nu-
cleus
Step 3. The excess energy makes the nucleus oscil-
lates.
This happens because there are two forces
counteracting:
Repulsion due to the Coulomb effect
over the protons in the nucleus.
Attraction, due to the strong force be-
tween protons and neutrons.
Step 4. At a certain point, the electric repulsion is
strong enough to break apart the nucleus
and fission occurs
Step 5. The fission decreases the mass energy, releas-
ing energy:
Step 6. The two fragments eject neutrons (beta de-
caying), reducing even more the mass energy.
2
We have said that fissionable elements have a high-
mass nucleus. But is this a sufficient condition as
well?
In nature, heavy elements such as 235U and 239Pu can
be fissioned by a thermal neutron, while others such
as 238U and 243Am are not. Why is that?
In the graph, we see that a nucleus must overcome a
potential maximum at about 5 [fm].
This potential barrier of height Ebmust be overcame
using an external source to produce nuclear fission.
The energy of the inbound neutron must be at least
as large as Ebto break the nucleus into two sections.
In other words, fission will occur if the absorbed neu-
tron provides an excitation energy Enat least as large
as Eb.
This condition explains why certain materials are
more susceptible to fission than others.
But the fact that thermal fission will not occur does
not mean that you cannot start the process by another
mean.
In fact, the process can be started using a fast neu-
tron, which creates fast fission.
This is the principle behind a nuclear reaction, where
the process is started by fast neutron emitter, that cre-
ate a first wave of fission, that in turn ejects thermal
neutrons that hit other heavy nuclei. This chain reac-
tion continues until all the “fuel” is depleted.
2 Nuclear Reactor
A nuclear reactor is system where a fission chain re-
action occurs in a controlled manner.
2.1 Preparing the Fissionable Material
Most nuclear reactors use 235U as effective agent
(fuel).
In nature, uranium contains
0.7% of 235U
99.3% of 238U, which is not fissionable by ther-
mal neutrons.
The first task to prepare the reactor is to enrich the
uranium, a process where one increases the propor-
tion of 235U to 3% by artificially separating the iso-
tope.
2.2 Desirable Characteristics of a Working
Reactor
When designing a working reactor, one needs to take
into account three potential problems:
1. Neutron Leakage. Not all neutrons involved on
the chain reaction will impact 235U atoms.
Leakage can be controlled by using a reactor core
large enough, reducing the surface-to-volume ra-
tio.
2. Neutron High Energy. The most effective form
of fission is produced by thermal neutrons. How-
ever, the neutrons ejected after fission are highly
energetic, with a kinetic energy on the order of 2
MeV.
What we need is to slow down these neutrons so
they can become thermal neutrons (on the order
of 0.04 eV).
The solution comes from mixing the effective
agent with another substance, called moderator
that must:
slow down neutrons via elastic collisions.
not remove neutrons from the core by ab-
sorbing them.
In North America most nuclear reactor use water
as moderator.
3. Neutron Nonfission Capture. When neutrons are
being slowed down, they can be captured by 238U
when their kinetic energy is in the 1-100 eV range.
This process, called resonance capture removes
neutrons from the chain reaction as well.
3

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Description
Energy from the Nucleus 1 Nuclear Fission One of the main goals of physics and engineering has been extracting energy from natural sources. There are two ways to do it: ▯ Rearranging the outer electrons of atoms in more stable configurations. This is the case of carbon- based fuels. ▯ Tinkering with the atom nucleus, and rearrang- ing its nucleons. This is the case of uranium- based nuclear reactors. Note that there are two peaks with high probability In this chapter we will study this second source of of occurrence (in the neighborhood of 7%): energy. ▯ Close to A = 95. ▯ Close to A = 140. Let’s see an example of a fission reaction: 235 Step 1. We start with U and we bombard it with neutrons. Step 2. The nucleus absorbs the neutron creating In the Table 1 we compare the amount of energy that 236 its stored in 1 kg of six forms of fuels. The first three U. This is a highly excited state which un- dergoes fission right away. have been implemented in practice, while the rest are theoretical limits. Step 3. The fragments emit two neutrons, and the re- 140 94 maining Xe and Sr. 1.1 Basic Process The reaction is summarized in this equation In the 1930’s Enrico Fermi proposed ways to use the 235U + n ! 236U ! 140Xe + 94Sr + 2n: (1) neutron as a projectile. In fact, he created new ele- ments in his lab by bombarding different elements The fission process conserves the total number of with neutrons. protons and neutrons involved in the reaction. One particular class of neutron called thermal nu- Both elements are quite unstable, so after a few sec- cleus - a neutron with low kinetic energy - was used onds they start a process of particle emissions until to produce barium from uranium. reaching a stable state. 140 140 The process was explained by Meiner and Frish: after For example, Xe turns into Ce in an average absorbing a thermal neutron, the uranium nucleus time of 15 days. The same thing happen to 94Sr 94 could split into two approximately equal parts. One (strontium) that turns into Zr (zirconium) in about of those is Barium, and the process received the name 20 minutes. fission. Note that all these decays are produced because The figure shows the distribution of mass numbers when the original nucleus splits, the new nuclei have 235 from actual U fission events. a large neutron/proton ratio (▯ 1:6). 1 Form of Matter Process Time to power a 100 W lightbulb Water A 50 [m] waterfall 5 seconds Coal Burning 8 hours Enriched UO 2 Fission in a reactor 690 years 235U Complete fission 3 ▯ 10 years 4 Hot deuterium gas Complete fusion 3 ▯ 10 years Matter and antimatter Complete annihilation 3 ▯ 10 years Table 1: Stored energy in fuels. These are neutron rich atoms that need to eject a few neutrons to become stable. The nucleus under- goes a beta decay process until reaching a equilib- rium point. 1.2 Energy Released During Fission This happens because there are two forces counteracting: One way to estimate the total energy released during nuclear fission is to compute the total binding energy per nucleon ▯E . ▯ Repulsion due to the Coulomb effect ben over the protons in the nucleus. The energy Q released by fission is ▯ Attraction, due to the strong force be- ▯ ▯▯ ▯ tween protons and neutrons. Q = final final number ▯ ▯E ben of nucleons Step 4. At a certain point, the electric repulsion is ▯ ▯▯ ▯ initial initial number (2) strong enough to break apart the nucleus ▯E ben of nucleons 1.3 A Model for Nuclear Fission The process for nuclear fission was proposed by Niels Bohr and John Wheeler and consists on the fol- and fission occurs lowing steps. Step 1. A high-mass nucleus absorbs a slow (ther- mal) neutron. Step 5. The fission decreases the mass energy, releas- ing energy: Step 2. The neutron potential energy excites the nu- cleus Step 6. The two fragments eject neutrons (beta de- caying), reducing even more the mass energy. Step 3. The excess energy makes the nucleus oscil- lates. 2 We have said that fissionable elements have a high- 2.1 Preparing the Fissionable Material mass nucleus. But is this a sufficient condition as Most nuclear reactors use 235U as effective agent well? In nature, heavy elements such as 235U and 23Pu can (fuel). be fissioned by a thermal neutron, while others such In nature, uranium contains as 23U and 243Am are not. Why is that? ▯ ▯ 0:7% of 235U 238 ▯ ▯ 99:3% of U, which is not fissionable by ther- mal neutrons. The first task to prepare the reactor is to enrich the uranium, a process where one increases the propor- tion of 23U to 3% by artificially separating the iso- tope. 2.2 Desirable Characteristics of a Working Reactor When designing a working reactor, one needs to take into account three potential problems: In the graph, we see that a nucleus must overcome a 1. Neutron Leakage. Not all neutrons involved on potential maximum at about 5 [fm]. 235 the chain reaction will impact U atoms. This potential barrier of height b must be overcame using an external source to produce nuclear fission. Leakage can be controlled by using a reactor core large enough, reducing the surface-to-volume ra- The energy of the inbound neutron must be at least tio. as large as E to break the nucleus into two sections. b In other words, fission will occur if the absorbed neu- 2. Neutron High Energy. The most effective form of fission is produced by thermal neutrons. How- tron provides an excitation energy Enat least as large ever, the neutrons ejected after fission are highly as Eb. energetic, with a kinetic energy on the order of 2 This condition explains why certain materials are MeV. more susceptible to fission than others. What we need is to slow down these neutrons so But the fact that thermal fission will not occur does they can become thermal neutrons (on the order not mean that you cannot start the process by another of 0.04 eV). mean. The solution comes from mixing the effective In fact, the process can be started using a fast neu- agent with another substance, called moderator tron, which creates fast fission. that must: This is the principle behind a nuclear reaction, where ▯ slow down neutrons via elastic collisions. the process is started by fast neutron emitter, that cre- ▯ not remove neutrons from the core by ab- ate a first wave of fission, that in turn ejects thermal neutrons that hit other heavy nuclei. This chain reac- sorbing them. tion continues until all the “fuel” is depleted. In North America most nuclear reactor use water as moderator. 3. Neutron Nonfission Capture. When neutrons are 238 2 Nuclear Reactor being slowed down, they can be captured by U when their kinetic energy is in the 1-100 eV range. A nuclear reactor is system where a fission chain re- This process, called resonance capture removes action occurs in a controlled manner. neutrons from the chain reaction as well. 3 The way to address this problem is by use a non- The process losses 370 neutrons and generates 1000 homogeneous mix of the effective agent and the thermal neutrons to start the next cycle. moderator. One reactor parameter that is quite important is For example, the uranium is usually packed in called multiplication factor k. fuel rods that form the reactor core that are im- # neutrons at cycle beginning mersed in a water pool. k = (3) # neutrons at the cycle
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