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

9 pages65 viewsFall 2016

Department
Physics
Course Code
PHY131H1
Professor
all

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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).
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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.
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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.
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