Transcript Ch.8 Nuclear Physics Applications 8.1 Fission – splitting

Ch.8.Nuclear Applications
• 8.1 Nuclear Fission - release of energy due to splitting of
heavy elements into two parts
(atomic bomb and nuclear reactors)
• 8.2 Nuclear Fusion - fusion of light nuclei into heavier with
release of energy (creation of heavy elements inside the
stars – burning of hydrogen in the core of Sun)
• 8.3 Nuclear weapons (fission and fusion devices)
• 8.4 Biomedical applications : radiation therapy, Medical
imaging, tomography, magnetic resonance
• 9.7 Nuclear medicine cancer therapy
• 9.8 Power production and Nuclear Waste
Nuclear fission, chain reactions
Atomic bomb
Ch. 8 Fission and fusion
Fusion
AX
->
Fission
A2X
2+
A1X
1
+ Qf – fission – splitting of heavy nucleus into two parts
with release of enormous of energy Qf
M(A,Z)–[M(A1,Z1)+M(A2,Z2)] = A1B(A1,Z1)+A2B(A2,Z2)-AB(A,Z)=Qf
B(A,Z)=aVA – aSA2/3-aCZ(Z-1)A-1/3 – aA(Z-A/2)2/A – aPA-1/2
2
Nuclear fusion
Nuclear fusion occurs in the core of the Sun,
giving out heat and light. The reaction takes
place continuously for billions of years.
(Photo
credit: US
NASA)
Neutron-Induced Fission
The neutrons do not feel the Coulomb repulsion, only the nuclear attraction. Therefore nuclear
reactions can be induced by neutrons of arbitrarily low energies.
1932: discovery of neutrons by James Chadwick
1932: experiments on neutron bombardment of uranium and observation of
induced radioactivity in stable elements by Enrico Fermi (Nobel 1938)
1933: Leo Szilard proposed nuclear chain reaction
1938: discovery of neutron-stimulated nuclear fission of 235U
by Otto Hahn (Nobel 1944), Fritz Strassmann,
Lise Meitner, and Otto Frisch
1942: the first artificial chain reaction (Enrico Fermi)
1945: first nuclear explosion in Alamogordo (New Mexico, USA)
Neutron-Induced Fission of 235U
Heavy nuclei (e.g., 238U) undergo fission when it acquires enough excitation energy (typically a few MeV
or so). A few nuclei, notably 235U, are sufficiently excited by the mere absorption of a neutron (even this
is just a thermal neutron). 235U absorbs the neutron to become 236U, and this new nucleus is so
unstable that it “explodes” into two fragments.
94
38
Sr
n
n
stable
235
92
n
U
an average 2.5
neutrons per
fission
236
92
U
high excitation and
strong oscillation
formation of a neck (electrical
repulsion pushes the lobes
apart)
140
54
Xe
Because heavy nuclei have a greater n/p ratio than the lighter ones,
the fragments contain an excess of neutrons. To reduce this excess,
two or three neutrons are emitted instantly (instant neutrons), and
subsequent beta decays and neutron emission (delayed neutrons)
bring the n/p ratios in the fragments to stable values.
Fission Barrier
U
Fission occurs if an excitation
energy is greater than the
potential barrier that separates
the
two
configurations
(fragments inside the same
nucleus
and
completely
separated fragments) or if there
is an appreciable probability for
tunneling through the potential
barrier.
barrier
UB
total energy of
fragments
range of the
nuclear force
~1/r electric
potential
energy
r0
r
Spontaneous fission occurs via a quantum mechanical tunneling through the fission barrier.
Spontaneous fission is possible only for elements with A  230 and x  45.
Ground states spontaneous fission half-lives for
(9.8  2.8) x 1018 y
238U: (8.2  0.1) x 1015 y
235U:
238Pu:
(4.70 0.08) x 1010 y
254Cf: 60.7 y
256Fm:
2.86 h
260
106Sg: 7.2 ms
Ch.8 Nuclear Physics Applications
8.1 Fission – splitting of the heavy nuclei into 2 parts
Fission is energetically favourable - it reduces Coulomb energy
E.g. 238U  2 114 Pd , Q  214 M eV - lots of energy libirated
92
46
λ
- lim itte d b y C o u lo m b b a rrie r
fi s s i o n
2m b
-2 G
1 / 2
P e
, w ith G =
dr
a [V (r) - Q ]
2
2 h
Z Z c
1 2
V (a) =
- fra g m e n ts t o u c h in g
C
4πε (R + R )
0 1
2
Fission is tunneling of the
fragments through potential
barrier
Actually: Diffuse barrier, gradual shape evolution of nucleus
Activation energy Eact < VC(a)-Q
b=R/(1+ε)1/2
a =R(1+ε)
V=4/3πR3
V= 4/3πab2
Binding energy depends on deformations:
Surface energy: ES=aSA2/3 (1+2/5 ε2 +…)
Coulomb energy: EC=aCZ2A-1/3(1-1/5 ε2 +…)
ΔB=B(ε)-B(0)= 1/5ε2 (2aSA2/3 –aCZ2 A-1/3) =0 for Z2/A~47
if ΔB<0 – energy lost by increasing ε : Eact >0
if ΔB>0 – energy gain by increasing ε : rapid fission
8.1 Fission (cont’s): some features
Cold nuclei (δE- n-induced ):
Asymmetric fission (A1≠ A2) due to shell effects
Hot nuclei :
Symmetric fission (A1≈ A2 ≈Amother/2)
Neutron-rich fragments:
eeνe
νe
Prompt neutrons Delayed neutrons Closer to stability:
Statistical emission after β-decay
long-lived
Multiplicity
Steep mass parabola, β-activity
distributionP(ν) β-daughters must have Ex>Sn
Neutrons may trigger new fissions -> chain reaction!
Used in reactors and atomic bombs
Neutron induced fission cross section:
σn->F (En)=σn (En) P(Ex) with Ex~En +Sn(n+1X)
σn (En) ~1/vn neutron capture cross section
P(Ex) ~1 – fission probability for Ex > Eact
235U: E
236U) (even-even) – needs <E >~kT~0.025eV
act < Sn(
n
238U: E
239
U) (odd) – needs fast neutrons
act ~1.2MeV+Sn(
Chain Reactions
Because fission reaction produce neutrons, a self-sustained sequence of fissions is possible. The
threshold for such a chain reaction: one neutron from each fission strikes another 235U nucleus and
initiates another fission.
Neutron multiplication factor: f
Sub-critical regime (f < 1): if too few
neutrons initiate fissions, the reaction
will slow down and stop.
Critical regime (f = 1): precisely one
neutron per fission causes another
fission, energy is released at a constant
rate (nuclear reactor).
Super-critical regime (f > 1): more than
one neutron per fission causes another
fission, the frequency of fission increases
exponentially, and an explosion occurs
(atomic bomb).
8.1 Induced Fission and chain reactions
8.1 Induced Fission and chain reactions
<n>=Σn=1∞np(1-p)n-1=p∂/ ∂q Σn=1∞qn=
=p ∂/∂q 1/(1-q)=p/(1-q)2 =1/p, where q=1-p
Nuclear Reactors
For a self-sustained chain reaction, the multiplication factor f should be =1. What are the factors that
control f ?
1. The probability of absorbtion of a neutron by 235U nuclei is large only for slow neutrons. The
neutrons produced by fission have too much energy. A moderator should be used to slow them
down. An effective moderator should contain nuclei whose mass is close to that of neutrons.
Hydrogen would be a good moderator, but it absorbs neutrons to form deuterium. Deuterium does
not absorb neutrons, it is used as a moderator in the form of heavy water. Another common
moderator – graphite.
2. Neutrons can produce reactions other than further fission. For example, 238U can absorb neutrons
to form 239U. Naturally occurring uranium contains 99.3% 238U and only 0.7% of fissionable 235U enrichment is required to increase the percentage of 235U. A reactor that uses highly enriched
uranium can use ordinary water (instead of heavy water) as a moderator.
3. Neutrons can escape from the reaction zone (the mean free path  the size of the zone). Thus the
mass of the nuclear fuel must be sufficiently large for a self-sustained chain reaction to take place
(critical mass). The value of the critical mass depends on the fuel and the moderator (typically, a few
kg).
To maintain critical regime (f = 1), the reactors should have a negative feedback. They are equipped
with movable control rods (usually made of cadmium or boron) whose function is to absorb neutrons
(if the rods malfunction – Chernobyl !). The time constant of the feedback loop can be reasonably
long due to an existence of delayed neutrons (~1% of the total amount of neutrons) emitted by
neutron-rich fission fragments having lifetimes on the order of seconds (even thermal neutrons move
with v ~ 2km/s, so without delayed neutrons, the feedback should operate on the time scale ~
0.1m/2000m/s ~10-4 s !)
8.1 reactors (cont’s)
Chain Reactions
Because fission reaction produce neutrons, a self-sustained sequence of fissions is possible. The
threshold for such a chain reaction: one neutron from each fission strikes another 235U nucleus and
initiates another fission.
Neutron multiplication factor: f
Sub-critical regime (f < 1): if too few
neutrons initiate fissions, the reaction
will slow down and stop.
Critical regime (f = 1): precisely one
neutron per fission causes another
fission, energy is released at a constant
rate (nuclear reactor).
Super-critical regime (f > 1): more than
one neutron per fission causes another
fission, the frequency of fission increases
exponentially, and an explosion occurs
(atomic bomb).
How does an A bomb work?
To realize a super-critical regime, we need a critical mass of the material that undergoes fission (~
1kg for pure 235U) (the critical mass depends on the probability of capture of neutrons by the nuclei
that undergo fission, i.e. on the mean free path of neutrons in the material).
Assuming that each fission produces 2 neutrons, and
both neutrons cause further fission reactions (an ideal
chain reaction), let’s find the time T required to split all
235U nuclei:
~10-7 s is the mean life-time of
neutrons in 235U
A – the number of generations
T  A
N  2  2  2  ....  2  2
2
3
A
A 1
1st gen. 2nd gen. 3d gen.
the number of fission reactions should be
equal to the total # of U atoms in 1kg
N 
1kg
235 1.66  10
 27
kg 
 2.6  10
24
2
time 
# of neutrons 2
81
ln 2 .6  2 4 ln 1 0  x ln 2
- this means that the last generation will have the number 80

The energy
24
E

2.6

10
release:
  2  10
8
M eV
 1.6  10
2
22
3
23
The total time of the explosion:
T  80 1  10 s   8  s
7
 19
J / eV   8  10 J
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A-bomb race – the heavy water saga
A-bomb race – the heavy water saga
A-bomb race – the heavy water saga
Hiroshima and Nagasaki
How does an A bomb work?
Nagasaki
before
and after
bombing
Chernobyl 26.05.1986
Leonid Telyatnikov
(1951-2004) decorated
The nuclear reactor after the disaster. Reactor 4
the lava under the Chernobyl-4 Lumps of graphite moderator ejected
•
Chernobyl 26.05.1986
Nuclear power is the use of sustained Nuclear fission to generate heat and do useful work. Nuclear Electric Plants,
Nuclear Ships and Submarines use controlled nuclear energy to heat water and produce steam, while in space,
nuclear energy decays naturally in a radioisotope thermoelectric generator. Scientists are experimenting wit fusion
energy for future generation, but these experiments do not currently generate useful energy
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