Chapter 1
Learning Objectives
• Historical Recap
• Understand the different length scales of
nuclear physics
• Know the nomenclature for isotopes and
nuclear reactions
• Know the different types of neutron
nuclear collisions and their relationship to
each other
• Basic principles of nuclear reactor
Learning Objectives
•
•
•
•
•
•
•
•
•
Neutron Sources
Basic Principles of Nuclear Reactor
Binding
g energy
gy curve
Liquid drop model
Fission Reaction
ODE Review
Radioactive Decay
Decay Chains
Chart of Nuclides
Historical Recap
• Driscoll handout
• New programs
– GNEP/AFCI
– Gen-IV
– Nuclear Power 2010
Why nuclear?
• Power density
– 1000 MW electric
• 10 000 ttons off coall per DAY!!
• 20 tons of uranium per YEAR (of which only 1 ton
is U
U-235)
235)
A typical pellet of uranium weighs
about 7 grams (0.24ounces). It can
generate as much energy as……
3.5 barrels of oil or……
17,000 cubic feet of natural gas, or…..
1,780 pounds of coal.
Why nuclear?
• Why still use coal
– Capital cost
– Politics
– Public perception of nuclear
nuclear, nuclear waster
issue
50%
What do you think is the biggest barrier to constructing the
next U.S. nuclear power plant?
40%
Nuclear Waste
Political
Disposal
Resistance to
Issues
Nuclear Energy
Cost of
Nuclear
Power Plant
Construction
Fear of
Nuclear
Accident
14%
10%
0%
15%
10%
16%
20%
44%
30%
Other
Image by MIT OpenCourseWare.
- 2008 surveyy of
energy professionals
“Eighty-two
Eighty two percent of Americans living in
close proximity to nuclear power plants
favor nuclear energy
energy, and 71 percent are
willing to see a new reactor built near
them, according to a new public opinion
them
survey of more than 1,100 adults
nationwide.
nationwide ” – NEI,
NEI September 2007
Basic Principles of Nuclear Reactor
• Simple device
– Fissioning fuel releases energy in the “core”
– Heat is transported away by a coolant which
couples the heat source to a Rankine steam
cycle
– Very similar to a coal plant, with the exception
of the combustion process
– Main complication arises from the spent fuel,
a mix of over 300 fission products
Public domain image from wikipedia.
Main
Turbine
Electric
Generator
Discharge
Main Condenser
Large Body of Water
(Ocean, Lake, etc.)
Intake
Circulating
Water Pump
• Power plants will often
often
discharge their circulating
water directly back to the
ocean
– Strict environmental
prottecti
tion regullatitions
– Temperature increases by
5-10
10 Farenheits
Image by MIT OpenCourseWare.
Main
Turbine
Electric
Generator
Cooling
Tower
Main
Condenser
Circulating
Water Pump
Image by MIT OpenCourseWare.
• If far from a water source,
cooliling towers are used
d to
transfer the heat to air.
– Water vapor is visible at the
contact of the warm wet air
inside the tower with the cool
dry air outside
Reactors Concepts
• Fuel
– Uranium
– Plutonium
– Thorium
• Moderator (optional)
–
–
–
–
Light water
Heavy water
Graphite
Be
• Coolant
–
–
–
–
–
–
–
–
Light water
Heavyy water
Sodium
Molten salt
Helium
CO2
Lead-Bi
d Bismuth
th
…
M
Macroscopic
i tto microscopic
i
i world
ld
Cutaway of PWR pressure vessel and
Internals.
Fission chain reaction
Public domain image from wikipedia.
Public domain image from wikipedia.
Shield Wall
Reactor Vessel Wall
Control Rod
Moderator (Water)
Neutrons in a reactor
Fuel Rods
Image by MIT OpenCourseWare.
Nomenclature Isotopes
Nomenclature--Isotopes
A
Z
12
6
X such as C or
235
92
Z is the atomic number
A is the atomic mass
N = A-Z is the number of neutrons
Nuclei with the same Z and different A
are called isotopes.
238
U
and
E.g. 235
92 U
92
1
1
H and 12 H and 13 H
U
Nuclear Stability
Image removed due to copyright restrictions.
• As Z increases, the
long range Coulomb
repulsion between
protons is balanced
by the presence of
additi
dditionall neuttrons to
provide additional
short--range attractive
short
nuclear forces.
Distribution of Stable Nuclides
A
Z
N
# nuclides
Even
Even
Even
159
Odd
Even
Odd
53
Odd
Odd
Even
50
Even
Odd
Odd
4
266
Nuclear Collision Reactions
a+b
1
0
c+d
n+
235
92
U→
235
92
a(b, c)d
236
92
U +g
236
92
U (n, g ) U
Fundamental Laws
• Conservation of nucleons
– Total “A” remains the same
• Conservation of charge
– Total “Z” remains the same
• Conservation of momentum
gy
• Conservation of Energy
– Energy, including rest mass, is conserved
Rest Mass
_
2
2 2
E (pc) = (mc )
2
Mass is a characteristic of the total energy and momentum of an object or a system
of objects that is the same in all frames of reference.
2
m0 = E/c
The invariant mass of the system is equal to the total system energy divided by c2.
This total energy in the center of momentum frame, is the minimum energy which
the system may be observed to have.
Special Relativity Mass
m=
m0
2
_
ν
1
/c
2
A body’s mass increases when it is in motion with speed v
relative to an observer at rest.
Q - value
Exothermic reaction produces energy
Endothermic reaction requires energy
An exothermic reaction is defined with Q < 0 therefore it is
important to understand the concept:
E = mc2
Q = [(Ma + Mb) _ (Mc + Md)]c2
Q > 0 exothermic
Q < 0 endothermic
Ea + Eb + Mac2 + Mbc2 = Ec + Ed + Mcc2 + Md c2
Examples of Q-value
Exothermic
_
_
(
Be)
+
M
(
He
)
M
(
C)
mn]c2
Q = [M
_
Q = [9.012182u + 4.002603u 12.000000u
_ 1.008664u]931.5MeV/u
9
4
4
2
12
6
Q = 5.702MeV
9
Be
4
+
4
He
2
12
C
6
+
1
n
0
Examples of Q-value
Endothermic
13
_
_
Q = [M ( O) + mn M ( 6C) M(42He)]c2
16
8
_
Q = [15.994915u + 1.008664u 13.003354u
_ 4.002603u]931.5MeV/u
Q = _2.215MeV
16
8O
+
1
n
0
13
C
6
+
4
He
2
Examples of Q-value
16
16
8O(n,p) 7N
Assumption
Q = ⎡⎣ mn + M ( 168O ) − M ( 167 N ) − mp⎤⎦ c 2
Why is this incorrect?
1
0
n + 168 O → 167 N + −10 e + 11 p
This is approximately equivalent to
1
0
n+ O → N + H
16
8
16
7
1
1
Q = ⎡⎣ mn + M ( 168 O ) − M ( 167 N ) − M ( 11H )⎤⎦ c 2
Most important Reactions
An Example
235U
92
+ 10n
129
53I
1n
+ 104
Y
+
3
39
0
Nuclear fission (n, fission)
1
0
n + ZA X →
A1
Z1
X + ZA22 X + neutrons + 200MeV
Radiative Capture
An Example
238
92U
+
1
0n
239
( 92U)*
Radiative capture (n, γ)
1
0
n+ X →(
A
Z
A+1
Z
239
92U
X) →
*
A+1
Z
+
0
0γ
X +g
Scattering
Examples
elastic 126C + 10n
1
inelastic ( 240
Pu
+
94
0n
12
1
C
+
6
0n
240
1
Pu)*
+
94
0n
240
0
1
Pu
+
β
+
94
0
0n
Scattering (n, n) or (n, n')
1
0
1
0
A
Z
1
0
A
Z
1
0
A
Z
n+ X ν n+ X
elastic scattering (n,n)
n + X ν n + ( X ) ν 01n + ZA X + γ
A
Z
*
inelastic scattering (n,n')
Beta decay
When the weak interaction converts a neutron into
a proton and emits an electron and an anti-neutrino,
Beta (minus) decay occurs. This happens when an
atom has an excess of neutrons.
A
Z
0
−1
X → e+
Cs
137
55
A
Z +1
_
Y + u + Energy
_
137
0
56Ba + -1e + υ
Positron Emission
Positron emission cannot occur in isolation unlike Beta decay.
This happens because it requires energy (the mass of the neutron
is greater than the mass of the proton).
Positron emission happens inside the nuclei when the absolute
value of the binding energy of the mother nucleus is lower than
that of the daughter nucleus.
A
ZX
+ Energy
22
11
Na
22
10
A
Z-1Y
0
1
+
0
1e
Ne + e + υ
+υ
Capture of Electron
A
ZX
+
0
-1e
+ Energy
A
Z-1Y
+u
In cases where ß+ decay is allowed energetically, it is accompanied
by the electron capture process.
22
Na
11
+
0
-1e
22
10Ne
+u
If the energy difference between initial and final states is low
(less than 2mec2), then b+ decay is not energetically possible and
electron capture is the sole mode decay.
Alpha Decay
Coulomb repulsion increases ~ Z2
Alpha decay occures only in heavy atoms (A > 100 amu )
Alpha particle has small mass relative to parent nucleus and
has very high binding energy
Nuclear binding force increases ~ A
A
ZX
a+
238
92U
A-4
Z-2Y
+ Energy
234
90Th
+a
Gamma decay
60
Co
27
eV β
1.17 MeV γ
0.31 M
1.33 MeV γ
5.26 a
Ni
60
28
Image by MIT OpenCourseWare.
• Gamma decay is the emission of a gamma ray (photon) from a
nucleus
• Occurs when nucleus transitions from a higher to lower energy state
• Energy of photon(s) equal to the change in energy of nuclear states
• Nuclear structure does not change so parent and daughter are the
same
Predicting type of decay
90
α
80
Proton Number (Z)
70
60
ure
50
+
β
40
or
n
ro
ect
El
pt
Ca
Line of Stability
β
−
30
20
10
0
0
10
20
30
40
50
60
70
80
90
100 110 120 130 140
Neutron (N)
Image by MIT OpenCourseWare.
Binding Energy
D = ZMp + NMn - MX
The weights of these constituent masses exceeds the weight of the nucleus
if we add the masses of Z protons and N neutrons that make up a nucleus.
The difference is the mass defect which is positive for all nuclides. Multiplying
by c2 yields the binding energy of the nucleus.
When the nucleus is formed, the loss in mass is due to the conversion of mass
to binding energy. It is defined as the energy that is supplied to a nucleus to
completely separate its nucleons.
A measure of nuclear stability is obtained when the binding energy is normalized
to the number of nucleons.
Calculate mass defect and binding
f uranium-235
i
23
energy for
Mass of neutron 1
1.008665
008665 amu
Mass of proton 1.007826 amu
Mass
off one atom
off U
U-235
235.043924
M
t
235 235
043924
Binding energy = mass defect x c2
• Mass defect = 1
1.91517
91517 amu
• BE = 1
1.91517
931.5
MeV
91517 amu x 931
5M
V / 1 amu
• BE = 1784 MeV
1 amu = 1.66054
1 66054 x 10-27kg = 931.5
931 5 MeV / c2
Binding Energy Curve
• Exothermic reactions
result in reaction
products with higher
binding energy
ti
• T
Two options
– Fission of heavy
nuclides
– Fusion of light
nuclides
First-Order
First
Order ODE - Review
• Appendix A of Lewis + Handout
Radioactive Decay
• Lewis
Lewis, Section 1
1.7
7
Decay chain
(a) λB = 5 x λA; t1 = 5 x t1
2
Normalized activity
1
A
2
0.75
0.5
0.25
0
0
1
2
t
3
4
(b) λB = λA /5; t1 = t1 /5
2
A
2
(c) λB = λA; t1 = t1
B
0.75
0.5
0.25
0
0
1
2
t
3
2
1
Normalized activity
Normalized activity
1
B
4
A
2
B
0.75
0.5
0.25
0
0
1
2
t
3
4
AA (t)/AA (0)
AB (t)/AA (0)
Image by MIT OpenCourseWare.
Decay Chains
Definition of Decay Chain: The radioactive decay of different discrete
radioactive decay products as a chained series of transformations.
Decay Chains
_ Thorium series or 4n
_ Neptunium series or 4n + 1
_ Uranium or Radium series 4n + 2
_ Actinium series or 4n + 3
Chart of Nuclides
3
He
in
−
t out
β out
p in
d in
n out
Original
Nucleus
n in
d out
p out
β out
+
α in
t in
α, 3n
p, n
γ, n
n, 2n
He
out
He, n
α, n
p, γ
d, n
3
He, np
a, np
t, n
3
He, p
d, p
Target
Nucleus n, γ
t, np
γ, np
γ, p
n, α
n, He
3
α out
α, 2n
3
t, p
n, p
3
Image by MIT OpenCourseWare.
Chart of Nuclides
• Gray shaded square (stable nuclide)
Symbol, mass number
Pd 108
Percent abundance
26.71
Activation cross-section in
"bars" to two isomers
Mass (C-12 scale)
σ (0.2 + 12)
107.9030
Fission product, slow
neutron fission of U-235
Image by MIT OpenCourseWare.
• White or "color" square: ( Artificially
Produced Radioactive Nuclide))
Symbol, mass number
Half life
Modes of decay, radiation,
and energy in MeV. ( ) means
radiation from short-lived
daughter.
Disintegration energy in MeV.
Fe 52
Fe852
h
B 0.80, (263), ε
γ 0.17, 380, (1.43)
E 2.38
Image by MIT OpenCourseWare.
Chart of Nuclides
• Black rectangles across the top of square
– On gray-shaded square: Radioactive nuclide with
long half life (Considered Stable)
Symbol
Ce 142
11.07
Half life
Thermal neutron
absorption cross-section
in barns
Percent abundance
5x1015yrs
α, 1.5
Modes of decay
σ1
141.9090
Mass
Image by MIT OpenCourseWare.
– On white square: Radioactive nuclide found in
nature with relatively short half life
Chart of Nuclides
• Smaller black rectangle
g near top
p of square
q
((Nuclide is a
member of a natural radioactive decay chain)
Po 218
Symbol
Ra A
Modes of decay
and energies
α 6.00
β
3.05m
218.0089
Symbol, mass
number
Half life
Mass
Image by MIT OpenCourseWare.
• Black triangle at bottom corner of square (nuclide is
formed by
y fission of U-235 or Pu-239))
Pd 108
Percent abundance
26.71
σ (0.2 + 12)
Mass (C-12 scale)
Symbol, mass
number
107.9030
Activation cross-section
in "bars" to two isomers
Fission product, slow
neutron fission of U-235
Image by MIT OpenCourseWare.
Chart of Nuclides
• Verticallyy divided square
q
– Two isomeric states, one stable
Sn 117
Symbol
Percent abundance
7.61
Half life
Modes of decay
radiation, and
energies in Mev
14 d
IT 0.159
γ 0.161
e-
Mass
116.9031
Radioactive upper isomer Stable lower isomer
Image by MIT OpenCourseWare.
– Two isomeric states, both radioactive
Pm 145
Symbol
? 16d
β+ 0.45
Radioactive
upper isomer
Half life, ?
means uncertainty
18y
ε ,eγ 0.068, 0.073
E 0.14
Modes of decay
radiation, and
energies in Mev
Disintegration
energy in Mev
Stable lower isomer
Image by MIT OpenCourseWare.
Neutron Sources
Definition of Spontaneous Fission
Spontaneous fission (SF) is a form of radioactive decay characteristic for
very heavy isotopes. In practice, only energetically feasible for atomic
masses above 230 amu. It is theoretically possible for any atomic nucleus
with mass >= 100 amu.
Radioisotopes for which spontaneous fission is a nonnegligible
decay mode may be used as neutron sources notably Cf-252
(half-life 2.645 years, SF branch ratio 3.09%)
Intensity (ARB. UNITS)
102
101
100
1
2
3
4
5
Neutron energy (MeV)
Measured neutron energy spectrum from the spontaneous fission of
252Cf.
Image by MIT OpenCourseWare.
• Alpha Neutron Source
– Neutrons are produced when alpha particles impinge upon any
of several low atomic weight isotopes
• beryllium, carbon and oxygen
• Must have loosely
y bound neutron
– Alpha emitters must be long-lived
• Radium, polonium, plutonium, americium
– The low A material and alpha emitter are usually mixed in
powdered form
– Typical emission rates for alpha reaction neutron sources range
from 1×106 to 1×108 neutrons per second.
Th size
i and
d costt off these
th
t
l comparable
bl
– The
neutron
sources are also
to spontaneous fission sources.
– Usual combinations of materials are plutonium-beryllium (PuBe),
americium-beryllium (AmBe)
(AmBe), or americium-lithium (AmLi)
– Radium is not used as much now because of its high gamma
emission rate
Relative neutron intensity (MeV-1)
8
6
Stilbene
4
Emulsions
2
0
2
4
6
8
10
Neutron energy (MeV)
Measured energy spectra for neutrons from a 239 Pu/Be source containing 80g of the isotope.
Image by MIT OpenCourseWare.
• Photoneutrons
– A photon that is absorbed by the nucleus creates an excited
state from which a neutron is emitted. There are two such
sources:
– 9Be + >1.7 Mev photon → 1 neutron + 2 4He
– 2H (deuterium) + >2
>2.26
26 MeV photon → 1 neutron + 1H
– The resulting neutron energies are discrete if the photons are
ti R
hl one gamma ray iin 106 interacts.
i t
t S
monoenergetic.
Roughly,
So,
the gamma ray source needs to be very large (as in a fission
reactor) for these sources to be appreciable. The most common
use is the deuterium reaction as a source of neutrons for the
startup of light-water reactors. The source of the photons would
be fission products. (Note: Sufficient D2O exists in light water for
this source to be effective in LWRs.)
•
•
•
•
Accelerated charged particles
Fission
Fusion
F i
…
Fission
• Consider the following
g example
p of U-235 fission
• From binding energy curve, energy released is about
~200 MeV (235*(8.9 – 8))
– Most of the energy leaves in the form of kinetic
energy of the fission products
– Rest goes to particles emitted during fission
•
A distinction must be made between energy produced and energy recuperated
– Fission products are large ionized particles that travel a short distance, thus
energy is deposited locally
– The electrons released by beta decay of the fission products are also
absorbed locally.
– The gamma rays (photons) travel much greater distances and are sometimes
b b d by
b th
t shield.
hi ld
absorbed
the reactor
– The neutrinos escape entirely
Energy Released
Energy Recuperated
168
168
Beta (FP)
8
8
Gamma (FP)
7
7
Neutrinos
~12
-
Prompt Gammas
7.5
7
Prompt Neutrons
5
5
(n, gamma)
-
3-12
~207
198-207
Fission Products
Image by MIT OpenCourseWare.
• For fission to occur, we must provide some energy to the
nucleus. A potential
p
barrier exists that p
prevents
spontaneous fission from happening very frequently.
• Liquid drop model: A water drop doesn’t separate in two
spontaneously even if its energetically favorable
favorable. The
superficial tension of the drop acts as a barrier that tries
to keep the fragments from splitting.
Liquid Drop Model of Fission
A
+
+B
B
+
+
C
Image by MIT OpenCourseWare.
•
In nuclear fission, the short nuclear bonds of the nucleons keeps the
together. Initially
Initially, the potential energy of the nucleus is
nucleus together
equal to the binding energy of the nucleons (no kinetic energy). To
deform the nucleus, energy must be provided in an effort to increase
the average distance between the nucleons, thus increasing the
nucleus. However
However, the strong nuclear forces
potential energy of the nucleus
are very short. Thus when the separation starts, the repulsive
forces diminish and the potential energy diminishes as well. There
is thus a threshold energy required (about 6 MeV) for fission
t
h i also
l explains
l i h
t
fifission
i can
• Q
Quantum
mechanics
how spontaneous
happen, but with very-low probability, thru a tunnelling effect without
any energy input.
• When a neutron interacts with a nuclide, it forms a
compound
d nucleus.
l
Energy
E
is
i given
i
to
t the
th nucleus
l
b
by
the binding energy of the incident neutron and its kinetic
energy
– If the binding energy is sufficient to get above the fission
threshold of the nuclide, than the nuclide is fissile to thermal
neutrons
– If it requires additional kinetic energy, than it is said to be fissile
to ffast neutrons or ffissionable
• Fissile nuclides
–
–
–
–
U-235: only naturally occurring fissile isotope
P 239 radiative
di i capture off U
238
Pu-239:
U-238
U-233: radiative capture of Th-232
Pu-241: radiative capture of Pu-240
Critical Energy
Critical Energies Compared to Binding Energy of Last Neutron
Target
Nucleus
Critical Energy
Ecrit
Binding Energy of
Last Neutron BEn
BEn _ Ecrit
232
90 Th
7.5 MeV
5.4 MeV
-2.1 MeV
238
92U
7.0 MeV
5.5 MeV
-1.5 MeV
235
92U
6.5 MeV
6.8 MeV
+0.3 MeV
233
92U
6.0 MeV
7.0 MeV
+1.0 MeV
239
94Pu
5.0 MeV
6.6 MeV
+1.6 MeV
Image by MIT OpenCourseWare.
Fission cross sections for
fi i
bl nuclei
l i
fissionable
3
236U
240Pu
238U
234U
232Th
σf , barn
2
242Pu
1
0
0
2
4
6
8
10
Neutron energy, Mev
Image by MIT OpenCourseWare.
Fertile Materials
• Materials that can undergo transmutation
to become fissile materials.
233
239
92
94
U
β-
N
Pu
β-
233
239
91
93
Pa
N
β232
90
Th
N
n,
Np
β-
233
238
90
92
Th
U
n,
239
92
U
N
Image by MIT OpenCourseWare.
Fission Products
• Generally observe only two fission
fragments
– Note the logarithmic scale
10
Fission Yield, %
1
0.1
0.01
14 MeV
Thermal
0.001
0.0001
70
90
110
130
150
170
Mass Number
Image by MIT OpenCourseWare.
Stability of fission products
Image removed due to copyright restrictions.
• Neutron rich
fission products
beta decay
towards stability
Criticality – Neutron Multiplication
k ≡ multiplication factor ≡
•
•
•
number of neutrons in one generation
number of neutrons in preceding generation
Critical, k=1
Sub-critical k<1
Super-critical k>1
1
235U
N(t)
Supercritical
X
238U
2
235U
X
k>1
N(0)
k=0
Critical
3
235U
235U
k<1
Subcritical
t
Image by MIT OpenCourseWare.
Neutron generation
• Lewis
Lewis, p
p.12
12
Neutrons released from fission
• Prompt
– Spectra
– Average energy
• Delayed
– Delay discussion to kinetics
Neutrons released from fission
5
v
233U
4
Pu-239 produces
more neutrons
per fission than U-235.
239Pu
v
3
235U
2
0
v49 = 2.874 + 0.138 E
v25 = 2.432 + 0.066 E (0 < E < 1)
= 2.349 + 0.15E (E > 1)
23
v = 2.482 + 0.075 E (0 < E < 1)
= 2.412 + 0.136 E (E > 1)
5
10
v(E)=average number
of neutrons produced
per fission
15
E (MeV)
Image by MIT OpenCourseWare.
Fission prompt neutron
energy spectrum
χ (E ) = 0.453e
−1.036E
χ ( E )dE ≡
0.5
Average number of
fission neutrons emitted
with energy in E to
0.4
E + dE per fission
neutron.
sinh 2.29E
χ (E)
0.3
0.2
0.1
0
1
2
3
4
5
E (MeV)
Image by MIT OpenCourseWare.
Delayed fission neutrons
87
Br 55s
β
β
(87Kr)*
Neutron
Less than 1% of neutrons from fission
87
are considered delayed. Delayed neutrons
appear long after the fission event through the
emission
86
Kr + Neutron
Kr
β
decay of certain fission products, also called neutron
precursors. These delayed neutrons are essential to
the control of nuclear reactors since they appear many
orders of magnitude later than the prompt neutrons.
87
Rb
β
87
Sr
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MIT OpenCourseWare
http://ocw.mit.edu
22.05 Neutron Science and Reactor Physics
Fall 2009
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