Lecture 11
Nuclear Physics Part 3
Nuclear Reactions
Fission
Nuclear Reactor
Fusion
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David Milstead
Nuclear Reactions
Radioactivity will convert one nuclide into another.
We can artificially do this in the lab via nuclear reactions
Eg, first artificially induced transmutation (1919)
4
2
α +
14
7
N→
17
8
O + 11 p
General form of a nuclear reaction in which particle a, interacts
with nucleus X, producing particle b and nucleus Y.
a+X→ Y +b
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David Milstead
Reaction energy Q, determined by mass difference
between the initial and final sets of particles
Q = ∆mc2 = (ma + mX − mY − mb )c 2
(11.1)
If Q>0, reaction is exothermic (energy released as
kinetic energy and γ-rays)
If Q<0, reaction is endothermic. There is a threshold
of the energy of the incoming particle to make the
reaction happen.
Q=0 is elastic scattering. Total kinetic energy remains
constant.
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David Milstead
First controlled ’atom smasher’ experiment by Cockcroft
and Walton.
1
1
p+
7
3
Li →
4
2
He + 42 He
Q=17.3 MeV.
Incoming proton had energy of 0.125 MeV.
First direct experimental check of E=mc2
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David Milstead
Question
A generic fission event is
1
n+
235
U → X + Y +2 n
1
Which of the following pairs cannot represent
X and Y
(a) 141Xe, 93 Sr (b) 139 Cs, 95 Rb (c) 156 Nd, 79 Ge
(d)
121
In,
113
Ru
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David Milstead
Question
When 7Li is bombarded by a proton, two alpha-particles
are produced. Check that the reaction energy is 17.3 MeV..
Masses
: 11 H
:
7
3
Li
:
4
2
He
1.007825u
7.016004u
4.002603u
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David Milstead
Artificially create radioactive isotopes by nuclear
reactions.
Eg
27
13
Al + α →
30
15
P decays quickly vi a beta decay
30
15
+
P → 30
Si
+
β
+ν e
14
30
15
P+ n
1
0
Artificially induced radioactivity practical importance as
biological and chemical ’tracers’ in analysing complex
reactions and processes.
Firing neutrons into nuclides leads to artifically induced
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radionuclides which can lead to fission.
David Milstead
Fission
Discovered in 1938 by Otto Hahn, Fritz Strassman and Lise Meitner
Uranium exists as two isotopes
238
U(99.3%) and
235
U(0.7%)
Both isotopes easily split by neutron bombardment (induced fission)
1
0
n+
235
92
U→
236
92
89
1
U * → 144
Ba
+
Kr
+
3
56
36
0n
1
0
n+
235
92
U→
236
92
94
1
U * → 140
Xe
+
Sr
+
2
54
38
0n
Highly unstable, excited
236
92
U * state actually fissions.
Around 200 MeV energy released as kinetic energy.
Note also: 1 neutron goes in, 2 to3 neutrons go out! Fyu02- Kvantfysik
David Milstead
Primary fission fragments have neutron excess and
release around 2.5 ’prompt’ neutrons
Cascade of radioactive decays
Xe→ Cs→ Ba→ La→ Ce
140
54
140
55
16s
140
56
66s
140
57
13d
140
58
40h
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David Milstead
Over 100 different nuclides from 20 different elements
have found as fission products
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David Milstead
Why is energy released during fission ?
1
0
n+
235
92
U→
236
92
Kr
89
1
U * →144
Ba
+
Kr
+
3
56
36
0n
Ba
fission
U
fusion
The lighter nuclei: Ba and Kr have larger binding energies/nucleon
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than U
David Milstead
Binding energy per nucleon for uranium ≈ 7.6 MeV
Binding energy per nucleon (for nuclei between
90 and 150) ≈ 8.5 MeV
Energy released ≈ 236 × (8.5 - 7.6) = 200 MeV
70% carried away as kinetic energy of fission fragments,
30% shared by emitted neutrons, β , λ particles.
Compare with ’chemical energy’ of uranium:
Combustion process of U+O2
UO2
Energy released 11eV per atom, 20 million times
less than fission!
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David Milstead
Understanding Fission with the
Liquid Drop Model of the Nuclei
Consider nucleus as an electrically charged liquid drop
(a) A 235U absorbs a neutron and becomes 235U*
(b) Excess energy causes oscillations
(c) Repulsion between two ’lobes’ causes a split
Fission
fragment
n
n
n
Fission
235U
(a)
.
fragment
(b)
(c)
.
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David Milstead
Fission Chain Reaction
1 neutron goes in, 2-3 neutrons go out! They can also
go on to induce fission
Critical mass needed to allow process to increase with time.
Depends on material, geometry, and apparatus.
Used in nuclear reactors and bombs!
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David Milstead
Animation of Fission Chain Reaction
http://lectureonline.cl.msu.edu/~mmp/applist/chain/chain.htm
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David Milstead
Controlled Fission – Nuclear Reactor
On average, each 235U fission produces 2.5 free neutrons.
40% are needed to sustain a chain reaction.
Fission takes place in the reactor core, which is water cooled.
Control rods (boron) absorb neutrons which slow down the reaction
Slow neutrons more likely to cause fission. Collisions with a
moderator slow neutrons down.
Reactor heats water, and steam drives turbines which generate power.
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David Milstead
What can go wrong ?
15% of energy comes from β decays of fission fragments.
Following halt of chain reaction with control rods, heat continues
to be produced.
For 3000-MW reactor, 200 MW comes from this source.
If cooling water is disabled this can cause a melt-down.
Partial meltdown in Three Mile Island accident (1979)
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David Milstead
The worst of all - Chernobyl
April 1986, Ukraine.
Test of emergency core cooling
System.
Unstable design, human error.
Too many control rods withdrawn
To compensate for build-up of
neutron absorbers 135Xe.
Power rose from 1% of normal
to 100 times normal in 4 seconds.
Steam explosion blew reactor concrete cover.
Graphite moderator caught fire.
Meltdown occured.
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David Milstead
Interactive Nuclear Power Station
http://lectureonline.cl.msu.edu/~mmp/applist/chain/chain.htm
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David Milstead
Question
What mass of 235U has to undergo fission each day to provide
3000 MW of thermal power ?
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David Milstead
Fusion
Binding energy/nucleon increases with A for lighter nuclei
Fusion of lighter nuclei into larger nucleus releases energy.
What happens!
For nuclei to fuse, they must overcomeCoulomb
repulsionfield and becomebound by thestrong nuclearfield.
Electrostatic energyof 2 21H (deuterium) at 4 ×10-15 m separation.
ke2 9 ×109 ×1.6 ×10−19
−14
U=
=
=
6
×
10
J ≈ 400 keV
15
r
4 ×10
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David Milstead
Potential energy
≈ 4 × 10 −15 m
separation
Deuterons need 200 keV to achieve overcome potential
barrier and become confined by the strong force
Possible at high temperature (kT=200 keV)
Needs temperature of 2x109 T
Interior of the sun at 1.5x107T
kT=1.3 keV.
Fusion only takes place in the sun due to low probability
energy fluctuations and quantum mechanical tunneling.
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David Milstead
The proton - proton cycle in the Sun
1
H+1H→2 H + e+ +ν e
Q = 0.4 MeV
1
H+ 2 H→3 He + γ
Q = 5.5 MeV
3
He+ 3 He→4 He+1H+1H
Q = 12.9 MeV
Total energy=24.7 MeV, distributed as
kinetic energy among reaction products.
More energy released with e+e- annhilation.
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David Milstead
Fusion as an enenrgy source ?
Fusion is an attractive energy production mechanism:
no atmospheric pollution,
abundant fuels,
safe to operate,
radioactive waste decays rapidly.
Following mechanisms under study:
2
2
3
1
H
+
H
→
He
+
Q = 3.27 MeV
1
1
2
0n
2
1
H+ 21H→31 H+11H
Q = 4.03 MeV
H+31H→42 He + 01n
Q = 17.6 MeV
Require: high temperature (>108 K) at which atoms are stripped
of electrons and ionised gas is a plasma.
:high particle density (n particles/vol)
:long confinement time τ to allow reaction to occur
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Lawson’s criteria nτ>1020 s/m3
(11.2)
David Milstead
2
1
Fusion in the Lab.
Joint European Torus (JET):
the world’s largest nuclear fusion
research facility, Oxford Uk.
Plasma confined by magnetic
field and heated to
temperatures of 40-50 million degrees.
As yet, no success in producing a net surplus of usable energy
(always 10 years away!).
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David Milstead