Fission Reactions
Consider now a fission reaction for uranium-235 as shown in Fig. 1.2. From the reaction come approximately 200MeV of energy, two or three neutrons, two lighter nuclei (called fission fragments), and a number of gamma rays and neutrinos. The fission fragments undergo radioactive decay producing additional fission products. The energy produced from fission, the neutrons, and the fission products all play
critical roles in the physics of nuclear power reactors. We consider
each of them in turn.
Energy Release and Dissipation
The approximately 200MeV of energy released by a fission reaction
appears as kinetic energy of the fission fragments, neutrons, and
gamma rays, as well as that from the beta particles, gamma rays,
and neutrinos emitted as the fission products undergo radioactive
decay. This kinetic energy is dissipated to heat nearly instantaneously
as the reaction products interact with the surrounding
media. The forms that the interactions take, however, differ significantly
according to whether the particles are electrically charged or
neutral.
The fission fragments are highly charged, for the high speeds at
which they emerge from fission cause electrons to be ripped from
their shells as they encounter surrounding atoms. Charged particles
interact strongly with the surrounding atoms or molecules traveling
at high speed, causing them to ionize. Creation of ion pairs requires
energy, which is lost from the kinetic energy of the charged particle
causing it to decelerate and ultimately come to rest. The positive ions
and free electrons created by the passage of the charged particle will
subsequently reunite, liberating energy in the form of heat. The
distance required to bring the particle to rest is referred to as its
range. The range of fission fragments in solids amounts to only a
few microns, and thus most of the energy of fission is converted to
heat very close to the point of fission. Other charged particles, such
as the alpha and beta particles emitted in radioactive decay, behave
analogously, rapidly decelerating and coming to rest; for lighter
charged particles the ranges are somewhat longer.
Neutrons, gamma rays, and neutrinos are neutral and behave quite
differently. They are affected neither by the negative charge of electrons
surrounding a nucleus nor the electric field caused by a positively
charged nucleus. They thus travel in straight lines until making
a collision, at which point they scatter or are absorbed. If absorbed,
they cease to exist, with their energy dissipated by the collision. If they
scatter, they change direction and energy, and continue along another
straight line. The flight paths between collisions amount to very large
numbers of interatomic distances. With neutrinos these distances
are nearly infinite; for neutrons and gamma rays traveling in solids
they are typically measured in centimeters. Neutrons scatter only from
nuclei, whereas gamma rays are scattered by electrons as well. Except
at very low energies, a neutron will impart significant kinetic energy to
the nucleus, causing it to become striped of orbital electrons and therefore
charged. The electrons that gain kinetic energy from gamma ray
collisions, of course, are already charged. In either case the collision
partner will decelerate and come to rest in distances measured in
microns, dissipating its energy as heat very close to the collision site.
More than 80% of the energy released by fission appears as the
kinetic energy of the fission fragments. The neutrons, beta particles,
and gamma and neutrino radiation account for the remainder. The
energy of the neutrinos, however, is lost because they travel nearly
infinite distances without interacting with matter. The remainder of
the energy is recovered as heat within a reactor. This varies slightly
between fissionable isotopes; for uranium-235 it is approximately
193MeV or
The difference in energy dissipation mechanisms between
charged and neutral particles also causes them to create biological
hazards by quite different mechanisms. The alpha and beta radiation
emitted by fission products or other radioisotopes are charged particles.
They are referred to as non penetrating radiation since they
deposit their energy over a very short distance or range. Alpha or
beta radiation will not penetrate the skin and therefore is not a
significant hazard if the source is external to the body. They pose
more serious problems if radioisotopes emitting them are inhaled or
ingested. Then they can attack the lungs and digestive tract, and
other organs as well, depending on the biochemical properties of
the radioisotope. Radiostrontium, for example, collects in the bone
marrow and does its damage there, whereas for radioiodine the
thyroid gland is the critical organ. In contrast, since neutral particles
(neutrons and gamma rays) travel distances measured in centimeters
between collisions in tissue, they are primarily a hazard from
external sources. The damage neutral particles do is more uniformly
distributed over the whole body, resulting from the ionization of
water and other tissue molecules at the points where neutrons collide
with nuclei or gamma rays with electrons.
Neutron Multiplication
The two or three neutrons born with each fission undergo a number
of scattering collisions with nuclei before ending their lives in
absorption collisions, which in many cases cause the absorbing
nucleus to become radioactive. If the neutron is absorbed in a
fissionable material, frequently it will cause the nucleus to fission
and give birth to neutrons of the next generation. Since this process
may then be repeated to create successive generations of
neutrons, a neutron chain reaction is said to exist. We characterize
this process by defining the chain reaction’s multiplication, k, as
the ratio of fission neutrons born in one generation to those born
in the preceding generation. For purposes of analysis, we also
define a neutron lifetime in such a situation as beginning with
neutron emission from fission, progressing—or we might say
aging—though a succession of scattering collisions, and ending
with absorption
Suppose at some time, say t=0, we have no neutrons produced
by fission; we shall call these the zeroth generation. Then the first
generation will contain kno neutrons, the second generation
and so on: the ith generation will contain
On average, the time at which the ith generation is born will be t ¼ i.l, where l is the neutron lifetime. We can eliminate i between these expressions to estimate the number of neutrons present at time t:
Thus the neutron population will increase, decrease, or remain the same according to whether k is greater than, less than, or equal to one. The system is then said to be supercritical, subcritical, or critical, respectively.
following chapters deals with the determination of the multiplication, how it depends on the composition and size of a reactor, and how the time-dependent behavior of a chain reaction is affected by the presence of the small fraction of neutrons whose emission following fission is delayed. Subsequently we will examine changes in multiplication caused by changes in temperature, fuel depletion, and other factors central to the design and operation of power reactors.
Fission Products
Fission results in many different pairs of fission fragments. In most cases one has a substantially heavier mass than the other. For example, a typical fission reaction is
Fission fragments are unstable because they have neutron to proton ratios that are too large. Figure 1.4, which plots neutrons versus protons, indicates an upward curvature in the line of stable nuclei, indicating that the ratio of neutrons to protons increases above 1:1 as the atomic number becomes larger (e.g., the prominent isotopes of carbon and oxygen are caobon and oxygens
but for lead and thorium they are Pb and Th. As a nucleus fissions the ratio of neutrons to protons would stay the same in the fission fragments— as indicated by the dashed line in Fig. 1.4—were it not for the 2 to 3 neutrons given off promptly at the time of fission. Even then, the fission fragments lie above the curve of stable nuclei. Less than 1%
of these fragments decay by the delayed emission of neutrons. The
predominate decay mode is through beta emission, accompanied by
one or more gamma rays. Such decay moves the resulting nuclide
toward the line of stable nuclei as the arrows in Fig. 1.4 indicate.
However, more than one decay is most often required to arrive at
the range of stable nuclei. For the fission fragments in Eq. (1.24) we
have
Each of these decays has a characteristic half-life. With some notable
exceptions the half-lives earlier in the decay chain tend to be shorter
than those occurring later. The fission fragments taken together with
their decay products are classified as fission products.
Equation (1.24) shows only one example of the more than 40
different fragment pairs that result from fission. Fission fragments
have atomic mass numbers between 72 and 160. Figure 1.5 shows
the mass frequency distribution for uranium-235, which is typical
for other fissionable materials provided the neutrons causing fission
have energies of a few eV or less. Nearly all of the fission
products fall into two broad groups. The light group has mass
numbers between 80 and 110, whereas the heavy group has mass
numbers between 125 and 155. The probability of fissions yielding
products of equal mass increases with the energy of the incident
neutron, and the valley in the curve nearly disappears for fissions
caused by neutrons with energies in the tens of MeV. Because
virtually all of the 40 fission product pairs produce characteristic
chains of radioactive decay from successive beta emissions, more
than 200 different radioactive fission products are produced in a
nuclear reactor.
Roughly 8% of the 200MeV of energy produced from fission is
attributable to the beta decay of fission products and the gamma rays
associated with it. Thus even following shutdown of a chain reaction,
radioactive decay will continue to produce significant amounts of
heat. Figure 1.6 shows the decay heat for a reactor that has operated at
a power P for a long time. The heat is approximated by the Wigner-
Way formula as
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critical roles in the physics of nuclear power reactors. We consider
each of them in turn.
Energy Release and Dissipation
The approximately 200MeV of energy released by a fission reaction
appears as kinetic energy of the fission fragments, neutrons, and
gamma rays, as well as that from the beta particles, gamma rays,
and neutrinos emitted as the fission products undergo radioactive
decay. This kinetic energy is dissipated to heat nearly instantaneously
as the reaction products interact with the surrounding
media. The forms that the interactions take, however, differ significantly
according to whether the particles are electrically charged or
neutral.
The fission fragments are highly charged, for the high speeds at
which they emerge from fission cause electrons to be ripped from
their shells as they encounter surrounding atoms. Charged particles
interact strongly with the surrounding atoms or molecules traveling
at high speed, causing them to ionize. Creation of ion pairs requires
energy, which is lost from the kinetic energy of the charged particle
causing it to decelerate and ultimately come to rest. The positive ions
and free electrons created by the passage of the charged particle will
subsequently reunite, liberating energy in the form of heat. The
distance required to bring the particle to rest is referred to as its
range. The range of fission fragments in solids amounts to only a
few microns, and thus most of the energy of fission is converted to
heat very close to the point of fission. Other charged particles, such
as the alpha and beta particles emitted in radioactive decay, behave
analogously, rapidly decelerating and coming to rest; for lighter
charged particles the ranges are somewhat longer.
Neutrons, gamma rays, and neutrinos are neutral and behave quite
differently. They are affected neither by the negative charge of electrons
surrounding a nucleus nor the electric field caused by a positively
charged nucleus. They thus travel in straight lines until making
a collision, at which point they scatter or are absorbed. If absorbed,
they cease to exist, with their energy dissipated by the collision. If they
scatter, they change direction and energy, and continue along another
straight line. The flight paths between collisions amount to very large
numbers of interatomic distances. With neutrinos these distances
are nearly infinite; for neutrons and gamma rays traveling in solids
they are typically measured in centimeters. Neutrons scatter only from
nuclei, whereas gamma rays are scattered by electrons as well. Except
at very low energies, a neutron will impart significant kinetic energy to
the nucleus, causing it to become striped of orbital electrons and therefore
charged. The electrons that gain kinetic energy from gamma ray
collisions, of course, are already charged. In either case the collision
partner will decelerate and come to rest in distances measured in
microns, dissipating its energy as heat very close to the collision site.
More than 80% of the energy released by fission appears as the
kinetic energy of the fission fragments. The neutrons, beta particles,
and gamma and neutrino radiation account for the remainder. The
energy of the neutrinos, however, is lost because they travel nearly
infinite distances without interacting with matter. The remainder of
the energy is recovered as heat within a reactor. This varies slightly
between fissionable isotopes; for uranium-235 it is approximately
193MeV or
The difference in energy dissipation mechanisms between
charged and neutral particles also causes them to create biological
hazards by quite different mechanisms. The alpha and beta radiation
emitted by fission products or other radioisotopes are charged particles.
They are referred to as non penetrating radiation since they
deposit their energy over a very short distance or range. Alpha or
beta radiation will not penetrate the skin and therefore is not a
significant hazard if the source is external to the body. They pose
more serious problems if radioisotopes emitting them are inhaled or
ingested. Then they can attack the lungs and digestive tract, and
other organs as well, depending on the biochemical properties of
the radioisotope. Radiostrontium, for example, collects in the bone
marrow and does its damage there, whereas for radioiodine the
thyroid gland is the critical organ. In contrast, since neutral particles
(neutrons and gamma rays) travel distances measured in centimeters
between collisions in tissue, they are primarily a hazard from
external sources. The damage neutral particles do is more uniformly
distributed over the whole body, resulting from the ionization of
water and other tissue molecules at the points where neutrons collide
with nuclei or gamma rays with electrons.
Neutron Multiplication
The two or three neutrons born with each fission undergo a number
of scattering collisions with nuclei before ending their lives in
absorption collisions, which in many cases cause the absorbing
nucleus to become radioactive. If the neutron is absorbed in a
fissionable material, frequently it will cause the nucleus to fission
and give birth to neutrons of the next generation. Since this process
may then be repeated to create successive generations of
neutrons, a neutron chain reaction is said to exist. We characterize
this process by defining the chain reaction’s multiplication, k, as
the ratio of fission neutrons born in one generation to those born
in the preceding generation. For purposes of analysis, we also
define a neutron lifetime in such a situation as beginning with
neutron emission from fission, progressing—or we might say
aging—though a succession of scattering collisions, and ending
with absorption
Suppose at some time, say t=0, we have no neutrons produced
by fission; we shall call these the zeroth generation. Then the first
generation will contain kno neutrons, the second generation
and so on: the ith generation will contain
On average, the time at which the ith generation is born will be t ¼ i.l, where l is the neutron lifetime. We can eliminate i between these expressions to estimate the number of neutrons present at time t:
Thus the neutron population will increase, decrease, or remain the same according to whether k is greater than, less than, or equal to one. The system is then said to be supercritical, subcritical, or critical, respectively.
following chapters deals with the determination of the multiplication, how it depends on the composition and size of a reactor, and how the time-dependent behavior of a chain reaction is affected by the presence of the small fraction of neutrons whose emission following fission is delayed. Subsequently we will examine changes in multiplication caused by changes in temperature, fuel depletion, and other factors central to the design and operation of power reactors.
Fission Products
Fission results in many different pairs of fission fragments. In most cases one has a substantially heavier mass than the other. For example, a typical fission reaction is
Fission fragments are unstable because they have neutron to proton ratios that are too large. Figure 1.4, which plots neutrons versus protons, indicates an upward curvature in the line of stable nuclei, indicating that the ratio of neutrons to protons increases above 1:1 as the atomic number becomes larger (e.g., the prominent isotopes of carbon and oxygen are caobon and oxygens
but for lead and thorium they are Pb and Th. As a nucleus fissions the ratio of neutrons to protons would stay the same in the fission fragments— as indicated by the dashed line in Fig. 1.4—were it not for the 2 to 3 neutrons given off promptly at the time of fission. Even then, the fission fragments lie above the curve of stable nuclei. Less than 1%
of these fragments decay by the delayed emission of neutrons. The
predominate decay mode is through beta emission, accompanied by
one or more gamma rays. Such decay moves the resulting nuclide
toward the line of stable nuclei as the arrows in Fig. 1.4 indicate.
However, more than one decay is most often required to arrive at
the range of stable nuclei. For the fission fragments in Eq. (1.24) we
have
Each of these decays has a characteristic half-life. With some notable
exceptions the half-lives earlier in the decay chain tend to be shorter
than those occurring later. The fission fragments taken together with
their decay products are classified as fission products.
Equation (1.24) shows only one example of the more than 40
different fragment pairs that result from fission. Fission fragments
have atomic mass numbers between 72 and 160. Figure 1.5 shows
the mass frequency distribution for uranium-235, which is typical
for other fissionable materials provided the neutrons causing fission
have energies of a few eV or less. Nearly all of the fission
products fall into two broad groups. The light group has mass
numbers between 80 and 110, whereas the heavy group has mass
numbers between 125 and 155. The probability of fissions yielding
products of equal mass increases with the energy of the incident
neutron, and the valley in the curve nearly disappears for fissions
caused by neutrons with energies in the tens of MeV. Because
virtually all of the 40 fission product pairs produce characteristic
chains of radioactive decay from successive beta emissions, more
than 200 different radioactive fission products are produced in a
nuclear reactor.
Roughly 8% of the 200MeV of energy produced from fission is
attributable to the beta decay of fission products and the gamma rays
associated with it. Thus even following shutdown of a chain reaction,
radioactive decay will continue to produce significant amounts of
heat. Figure 1.6 shows the decay heat for a reactor that has operated at
a power P for a long time. The heat is approximated by the Wigner-
Way formula as
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