Transcript Document 7129388

Cross Section
Total
,3n
,4n
,2n
,n
Alpha particle energy
One of the most practical nuclear reactions results from the
compound nucleus that results from A>230 nuclei absorbing neutrons.
Often split into two medium mass nuclear fragments
plus additional neutrons.
NUCLEAR FISSION
1930 Bothe & Becker
Studying -rays bombarding beryllium
produced a very penetrating non-ionizing form of radiation
-rays?
Irène and Frédéric Joliot-Curie
knocked protons free from paraffin targets
the proton energy range revealed
the uncharged radiation from Be
to carry 5.3 MeV
1932 James Chadwick
in discussions with Rutherford
became convinced could not be s
Assuming Compton Scattering
to be the mechanism, E>52 MeV!
Neutron
chamber
ionization
(cloud)
chamber
Replacing the paraffin with other light substances,
even beryllium, the protons were still produced.
Nature, February 27, 1932
Chadwick developed the theory explaining the phenomena
as due to a 5.3 MeV neutral particle
with mass identical to the proton
undergoing head-on collisions with nucleons in the target.
1935 Nobel Prize in Physics
9Be
has a loosely bound neutron
(1.7 MeV binding energy)
above a closed shell:
4
He Be C  n
9
5-6 MeV 
from some
other decay
12
Q=5.7 MeV
Neutrons produced by many nuclear reactions
(but can’t be steered, focused or accelerated!)
Natural sources of neutrons
Mixtures of 226Ra ( source) and 9Be 
~constant rate if neutron production
also strong  source
so often replaced by 210Po, 230Pu or 241Am
Spontaneous fission, e.g. 252Cf ( ½ = 2.65 yr)
only 3% of its decays are through fission
97% -decays
Yield is still 2.31012 neutrons/gramsec !
A possible (and observed) spontaneous fission reaction
U 2 46 Pd
238
119
92
8.5 MeV/A
7.5 MeV/A
Gains ~1 MeV per nucleon!
2119 MeV = 238 MeV
released by splitting
119Pd
238U
Atomic (chemical) processes ~few eV
Fission involves 108 as much energy as chemical reactions!
Yet
U 2 46 Pd
is a rare decay:  ½ = 1016 yr
238
119
92
not as probable as the much more common -decay
 ½ = 4.510 9 yr
From the curve of binding energy per nucleon the most
stable form of nuclear matter is as medium mass nuclei.
Consider:
M ( A, Z )  M ( A1 , Z1 )  M ( A2 , Z 2 )
The Q value (energy release) of this process is
Q  B( A1 , Z1 )  B( A2 , Z2 )  B( A, Z )
The mass differences cancel since the total number of constituents remains unchanged.
For simplicity, if we assume the protons and neutrons
divide in the same ratio as the total nucleons:
A1 / A  Z1 / Z  y1
A2 / A  Z 2 / Z  y2
y1  y2  1
The difference in binding energy comes from the
surface and coulomb terms
so the energy released can then be expressed in terms of the
surface energy Es and the coulomb energy Ec
of the original nucleus (A,Z).
Q  ES (1  ( y1 )  ( y2 ) )  EC (1  ( y1 )  ( y2 ) )
2/3
2/3
5/3
maximum Q is found by setting dQ/dy1
Note:
y1  y2  1
maximum occurs when y1
=0
dy2 / dy1  1
= y2 = 1/2.
Q  0.37 EC  0.26ES
5/3
Fission into two equal nuclei (symmetric fission)
produces the largest energy output or Q value
The process is exothermic (Q > 0) if Ec/Es > 0.7.
in terms of the fission parameter, x
2
( Z / A)
>0.35
x  EC /(2 ES )  ( Z / A)(2aS / aC ) 
50
2
Suggesting all nuclei with (Z2/A) > 18 (ie heavier than 90Zr)
should spontaneously release energy
by undergoing symmetric fission.
However
Half-life of spontaneous fission as a function of x
where
Z2 / A
x 2
( Z / A)critical
and
( Z 2 / A)critical  49
R.Vandenbosch
and
J.R.Huizenga.
Nuclear Fusion,
Academic Press,
New York, 1973.
There is
a competition between
the nuclear force
binding the nucleus together
and the
coulomb repulsion
trying to tear it apart
Induced fission as nuclear reaction
n 92 U  92 U  57 La  35 Br  2n
235
236
139
95
n 92 U  92 U 37 Rb 55 Cs  2n
235
236
93
141
suggests the absorption of the neutron (and its energy)
may induce such distortions/vibrations in the nucleus.
The surface if any arbitrary figure can be expanded as

l
R  R0 [1     lmY (, )]
l 0 m   l
m
l
If lm time-independent: permanent deformation of the nucleus
If lm time-dependent: an oscillation of the nucleus
The Spherical Harmonics Yℓ,m(,)
ℓ=0
ℓ=1
1
Y00 
4
3
Y11  
8
3
Y10 
4
sin 
15
4
2
Y21  
15
8
i
e
Y32 
2
sin 
e
2i
sin  cos 
3

Y20 
cos2 

4  2
15
Y33  
cos 
1
Y22 
ℓ=2
ℓ=3
i
e
1
 
2
1
35
4
4
1
105
4
2
Y31  
3
sin 
3i
2
sin  cos 
1
21
4
4
e
2i
 i

sin  5 cos2   1 e
5

Y30 
cos3 

4  2
7
e
3

 cos  
2

ℓ=0
z

Nuclear Charge Density
R ~ 1  sin 
ℓ=1
R ~ 1  cos 
Lowest order to be considered:
ℓ=2
quadrupole deformation
For which we write the nuclear radius
2
R  R0 [1    2 mY2 (, )]
m
m  2
The l=2, m=0 mode:
1/ 2
5 

R (t )  R0 [1   20  
 16  
2
( 3 cos   1)]
Z

1/ 2
5 

R (t )  R0 [1   20  
 16  
2
( 3 cos   1)]
Nuclei do show spectra for such vibrational modes
Example of a vibrational spectrum (levels denoted by the number of phonons, N)
O.Nathan and S.G.Nilsson, Alpha- Beta- and Gamma-Ray Spectroscopy,
Vol.1, (K. Siegbahn, ed.) North Holland, Amsterdam, 1965.
We can approximate any small elongation from a spherical shape by
semi-major axis
a  R0 (1  )
semi-minor axis b
1
 R0 (1  2 )
The semi-empirical mass formula
B  aV A  aS A  asym (Z  N ) A  aC Z A
2
B
(Z  N )
1 / 3
2
4 / 3
 aV  aS A  asym
 aC Z A
2
A
A
2/3
From which:
1
2
ES  aS A (1    )
1 / 3
2
5
2
EC  aC Z A (1    )
2
1 / 3
1
5
2
2
1 / 3
With the surface energy (strong nuclear binding force) proportional to area
E  EC  ES
 aC Z A
2
1 / 3
1
(5
 )  aS A
2
2/3
Coulomb force
deforming nucleus
where
  [aC Z A
> 0
Notice
(so the Coulomb
force wins out) for:
1
5
2
2
1/ 3
 )
2
surface tension
holding spherical
shape
which we can write in the form
E  
2
(5
2
 2aS A
2/3
]
Same fission parameter
Z
2 aS
when

 49. introduced
estimating available Q
A aC
in symmetric fission
E  
2
comes from considering small perturbations from a sphere.

V(r)
r
for small r
As long as these disturbances are slight, the
Separation, r, of distinct fragments linearly follows
r  2
 r 
V (r )  Q   
4  R0 
At zero separation the potential
just equals the release energy Q
separation r
For Z2/A<49,
 is negative.
2
While for large r, after the fragments have been scissioned

V(r)
r
for small r
r
r
Z1 Z 2 e
V (r ) 
r
for large r
separation r
2
For such quadrupole
distortions the figure
shows the energy of
deformation (as a factor
of the original sphere’s
surface energy Es)
plotted against 
for different values of
the fission parameter x.
When x > 1
(Z2/A>49)
the nuclei are
completely unstable
to such distortions.
Z2/A=36
such unstable states
decay in characteristic
nuclear times ~10-22 sec
Z2/A=49
Tunneling does allow spontaneous
fission, but it must compete with
other decay mechanisms (-decay)
The potential energy V(r) = constant-B
as a function of the separation, r, between fragments.
No stable states
with Z2/A>49!
Tunneling
probability
drops as
Z2/A drops
(half-life
increases).
At smaller values of x, fission by barrier penetration can occur,
However recall that the transmission factor (e.g., for -decay) is

X e
where
2
 
h
2m[V (r )  E]dr
while for  particles (m~4u)
this gave reasonable, observable
probabilities for tunneling/decay
for the masses of the nuclear fragments we’re talking about,
 can become huge and X negligible.
Neutron absorption by heavy nuclei can create
a compound nucleus in an excited state
above the activation energy barrier.
As we have seen, compound nuclei have many final states into which they can decay:
n 92 U  92 U * 55 Cs 37 Rb  2n
235
236
141
93
n 92 U  92 U * 57 La 35 Br  2n
235
236
139
95
n 92 U  92 U *.  54 Xe38 Sr  2n
235
236
139
95
..
in general:
n 92 U  92 U *Z 1 X  Z 2Y  n
235
236
A1
A2
where Z1+Z2=92, A1+A2+=236
PROMPT
NEUTRONS
Experimentally find the average A1/A2 peaks at 3/2
Thermal neutrons
E< 1 eV
Slow neutrons
E ~ 1 keV
Fast neutrons
E ~ 100 keV – 10 MeV
“Thermal neutrons”
(slowed by interactions
with any material they
pass through) have been
demonstrated to be
particularly effective.
Cross section 
The incident neutron itself need not be of high energy.
Typical
of decay
Products
& nuclear
reactions
incident particle velocity, v
This merely reflects the general ~1/v behavior
we have noted for all cross sections!
At such low excitation there may be barely enough available
energy to drive the two fragments of the nucleus apart.
Division can only proceed
if as much binding energy as possible
is transformed into the kinetic energy separating them out.
(so MOST of the available Q goes into the kinetic energy of the fragments!)
Thus the individual nucleons
settle into the lowest possible energy configurations
involving the most tightly bound final states.
There is a strong tendency to produce a heavy fragment of
A ~ 140 (with double magic numbers N = 82 and Z = 50).
A possible (and observed) spontaneous fission reaction
U 2 46 Pd
238
119
92
8.5 MeV/A
7.5 MeV/A
Gains ~1 MeV per nucleon!
2119 MeV = 238 MeV
released by splitting
119Pd
238U
238 MeV represented an estimate of the maximum available energy
for symmetric fission.
For the observed
distribution
of final states
the typical average is
~200 MeV per fission.
This 200 MeV is distributed approximately as:
Fragment kinetic energy
Prompt neutrons
Prompt gamma rays
Radioactive decay fragments
165 MeV
5 MeV
7 MeV
25 MeV
235U
Isobars off the valley of stability
(dark squares on preceding slide)
b-decay to a more stable state.
 and b decays can leave a daughter in an excited nuclear state
1/2
187W
2
b
b
198Au
0.68610
0.61890
b
1.088 MeV
b
0.20625
0.412 MeV
0.13425
5/2
187Re
0
198Hg
n 92 U  92 U * 56 Ba36 Kr  3n
235
236
143
90
With the fission fragments radioactive, a decay sequence to stable nuclei must follow
Ba

Kr

143
56
90
36
La  e  
143

Ce  e  
58
143

Pr  e  
59
143

Nd  e  
59
90

Rb  e  
37
90

Sr  e  
38
90

Y e 
39
90

Zr  e  
40
143

57
n 92 U  92 U * 60 Nd  40 Zr  8e  8  3n
235
236
143
90
n 92 U  92 U * 55 Cs 37 Rb  2n
235
236
141
93
With the fission fragments radioactive, a decay sequence to stable nuclei must follow
141
55
Cs

b,
25 sec
0.03%
141
56
Ba
Cs  n 
b,
65 sec
140
55
93
37
Rb

b,
18 min

b,
6 sec
1.40%
92
37
93
38
Sr

7 min
b,
Rb  n 
b,
5 sec

b,
140
La
Ba
13 d
57
b,
140
56

141
4 hr
141
93
Y
39

b,
92
38
Sr
10 hr

3 hr
b,
58
57
Ce
La
93
40
Zr
92
Y
39

b,
141

b,
140
33 d
40 h

b,
106 yr

b,
4h
59
58
Pr
Ce
93
Nb
41
92
40
Zr
n 92 U  92 U * 58 Ce 59 Pr  8e  8  8  2n
sometimes  3n or  4n
235
236
140
141
For 235U fission, average number of prompt neutrons ~ 2.5
n 92 U  92 U * 56 Cs 36 Kr  3n
235
236
143
90
n 92 U  92 U * 55 Cs 37 Rb  2n
235
236
141
93
n 92 U  92 U * 57 La 35 Br  2n
235
236
139
95
n 92 U  92 U * 54 Xe38 Sr  2n
235
236
139
95
with a small number of additional delayed neutrons.
with every neutron freed comes the possibility of additional fission events
This avalanche is the chain reaction.
235U
will fission (n,f)
at all energies of the absorbed neutron.
It is a FISSILE material.
However such a reaction cannot occur in
natural uranium (0.7% 235U, 99.3% 238U)
Total (t) and fission (f) cross sections of 235U.
1 b = 10-24 cm2
Notice:
238U
has a threshold for fission (n,f) at a neutron energy of 1MeV.
The difference between these two isotopes of uranium
is explained by the presence of the pairing term
in the semi-empirical mass formula.
   a pair A
3 / 4
  a pair A
0
3 / 4
for Z even, N even
for Z odd, N odd
for A odd
Like nucleons couple pairwise into especially stable configurations.
Note the strong
resonant capture of
neutrons (n, ) in
the energy range
10-100 eV
(particularly
for 238U
where the
cross-section
reaches
high values)
The fission neutron energy spectrum peaks at around 1 MeV
At 1 MeV
the inelastic
cross-section
(n,n') in 238U
exceeds the
fission
cross-section.
This effectively
prevents fission
from occurring
in 238U.
only
the
Natural uranium (0.7% 235U, 99.3% 238U)
undergoes thermal fission
Fission produces mostly fast neutrons
Mev
but is most efficiently
induced by slow neutrons
E (eV)
Consider fission neutrons created deep enough
in a lump of natural uranium
that we’ll just (for now) ignore that
some neutrons may simply escaping from the sample.
100
10
1
Cross-section (barns)
1000
The processes competing with
neutron-induced fusion
have approximate cross-sections
(read from the graphs at right) of
235U
(n,n) elastic scattering ~ 5 barn
(n,n’) inelastic scattering ~ 3 barn
(n,)
~0.2barn
(n,f) fission
~ 2 barn
238U
(n,n) elastic scattering ~ 5 barn
(n,n’) inelastic scattering ~ 2 barn
(n,)
~0.2barn
(n,f) fission
~0.6barn
1000
100
10
1
0.1
Cross-section (barns)
10000
Giving a relative probability to each of:
235U
238U
(n,n) elastic scattering
(n,n’) inelastic scattering
(n,)
(n,f) fission
6.7
1.7
0.3
3.3
(n,n) elastic scattering
(n,n’) inelastic scattering
(n,)
(n,f) fission
8.3
3.3
0.3
1
 0.7/99.3
Of the first 100 fission neutrons we start with
~98 are captured in the dominant 238U
238U
235U
(n,n) elastic scattering
(n,n’) inelastic scattering
(n,)
(n,f) fission
63
25
2
8
(n,n) elastic scattering
(n,n’) inelastic scattering
(n,)
(n,f) fission
1
0
0
0
With 2-3 neutrons generated by each fission,
only ~20 neutrons in the second generation
- this is insufficient to sustain a chain reaction.
only 8 of
these
captures
result
in fission
FAST REACTOR
Enriching the 235U content
a 50-50 mix of the two isotopes will sustain a chain reaction
(most fission events occurring now in 235U
by neutron energies in the range 0.3 - 2.0 keV.
THERMAL REACTOR moderating the neutrons to thermal speeds
mixing natural uranium with a material to slow
(but not absorb) neutrons to lower energies
where the fission cross-section for 235U is large.
Most fissions are then induced by neutrons
with thermal energies (~0.025 eV).
Granulated powders can be mixed for this purpose.
Powdered uranium
Or blocks of uranium fuel can be alternately stacked
with graphite to form a nuclear pile.
FUEL
Moderator
(Graphite)
FUEL
1. Starting with  neutrons/fission
2. Avg of  neutrons after fast fission
3. p survive thermalization
4. pf number captured in 235U
238U
Moderator
(Graphite)
FUEL
5. k = pf(f /total)
number producing fission
235U
One fission event produces
k = pf(f /total)
secondary fission events.
k is the reproduction factor.
A chain reaction requires k1.
If k=1 the core is “critical” and self-sustaining.
Typical values for natural uranium/graphite piles are
  2.47
f  0.88
  1.02 p  0.89
 f /  t  0.54
k=1.07
Uranium is not dumped into the core like coal
shoveled into a furnace. Instead it is processed
and formed into fuel pellets (~pencil eraser size).
The fuel pellets are stacked inside hollow metal
tubes to form fuel rods 11 to 25 feet in length.
Before it is used in the reactor, the uranium fuel is not very radioactive.
The fuel rods are arranged in a regular lattice inside the moderator.
The rods are typically 2-3 cm in diameter and
spaced about 25 cm apart.
The rods metal sheath or cladding –
most commonly stainless steel or alloys of zirconium.
This cladding supports the fuel mechanically,
prevents release of radioactive fission products into the coolant stream and
provides extended surface contact
with the coolant in order to promote effective heat transfer.
A single fuel rod cannot generate
enough heat to make the amount of
electricity needed from a power
plant. Fuel rods are carefully
bound together in assemblies,
each of which can contain over
200 fuel rods. The assemblies hold the
fuel rods apart so that when
they are submerged in the reactor core,
water can flow between them.
In nuclear power plants, the moderator is often water
(though some types do still use graphite).
Fuel cell channels
in face
of reactor core.
Control rods
slide in or out between the fuel rods
to regulate the chain reaction.
contain cadmium or boron (high cross section
for neutron absorption, without fission).
e.g., natural Boron is 20% 10B
with a cross section
for thermal neutrons of
3840 b for the process
10
B  n Li * 
7
Control rods act like sponges to absorb excess neutrons.
When the core temperature drops too low,
the control rods are slowly pulled out of the core,
and fewer neutrons are absorbed.
When the temperature in the core rises,
the rods are slowly inserted.
To maintain a controlled nuclear chain reaction,
the control rods are manipulated until each fission
results in just one neutron on average, all other
neutrons effectively absorbed by the control rods.
Temperature changes in the core are generally very gradual.
However should monitors detect a sudden change in temperature,
the reactor immediately shuts down automatically by dropping
all the control rods into the core. A shutdown takes only
seconds and halts the nuclear chain reaction.
This very common type makes use
of the excellent properties of water as
both coolant and moderator (ordinary
water does absorb neutrons –
converting hydrogen into deuterium).
The Boiling Water Reactor (BWR)
allows the water to boil in the reactor
core and uses the steam to drive the
turbines.
The highest temperature possible for liquid water (critical temperature
374°C) is a limitation for devices that use water to convey heat.
The core must be contained within a pressure vessel of welded steel
(typically withstanding pressures of about 1.55 x107 Pa or 153 bar.
Furthermore recall: the Carnot engine efficiency  is
  1  T2 / T1
In this ideal case the heat is received isothermally (the working fluid at T1)
but rejected isothermally (at T2) with all processes reversible.
No real power plant operates on an ideal Carnot cycle, but the expression
shows the higher T1, the higher the efficiency (T2 cannot be lower than
the outside temperature).
1st land based pressurized water reactor: Shippingport USA (1957).
Pressure vessels are enormous
with 9 inch thick walls, often
weighing more than 300 tons.
The pressure vessel surrounds
and protects the reactor core,
providing a safety barrier and
holding the fuel assemblies,
control rods, and coolant.
Pressure vessels are made of carbon steel and lined with a layer of
stainless steel to prevent rust. The pressure vessel is located inside
the containment building, a thick concrete structure reinforced with
steel bars.
A Fast Reactor has no moderator
and consequently a much smaller core.
The very high power involved means that
liquid metals have to be used as coolants!
Liquid sodium is the most common but
has the disadvantage of becoming
radioactive itself through
23Na(n, )24Na.
As well as generating power
fast reactors are used for
breeding fissile material.
If uranium fission reactors used as sole source of
electrical power needs
all high-grade ores used up within a few decades!
Breeder Reactors
Fermi, Zinn (1944)
Can fissile nuclei be grown? (the result of any nuclear reaction)
Can we create fissile material as a by product of any reaction?
The parent nuclei that spawns the fissile material
is described as being a fertile nuclide.
Example: build a reactor core that runs on 239Pu (the fuel)
packed within a bed of 238U (the fertile nuclide)
• =2.91 fast neutrons/239PU fission
Only one of these on average producing an additional fission
is sufficient for sustainability.
If the rest are incident on 238U there’s a chance of inducing
n U  U  
238
239
U
1/2= 25 min
b
239
239
Np
1/2= 2.3 days
b
239
A well designed breeder reactor
can double the amount of fissile material
in 7 – 10 years.
Pu
While neither natural Uranium cannot maintain a chain reaction
even small lumps of pure 235U or 239Pu cannot explode
simply because of the number of neutrons that escape
before inducing fission.
Recall we need k = pf(f /total) > 1
A large enough (critical) mass of 235U or 239Pu can chain react
and the reaction set off by any accidental initial neutron
(even from a rare spontaneous fission event).
If N neutrons (initially even 1 or 2) are present at time t
their number will increase during the next moment dt by
dN  Ndt
where  is related to k and obviously depends on
the fissile material and its geometry.
For critical samples of 235U ~108 Hz.
As long as we can
treat as a constant
N (t ) 
t / where  =1/ is the
N ( 0) e
“generation time.”
Uranium- 233: fissile, weapon-useable isotope, derived from irradiating
232Th with neutrons, 
½ =160,000 years; 10-20 kg required for a
nuclear device; less common than U-235 for making nuclear explosives.
Uranium-235: best suited for fission bomb (or fast reactor) when enriched
to > 90% purity; 6-25 kg required for a nuclear bomb; “significant quantities”
standards (for UN inspections) is as little as 3 kg; a recent international study
estimates 1,750 tons of highly enriched 235U have been produced worldwide.
Five grades of uranium are commonly recognized:
1. Depleted uranium: containing < 0.71% 235U.
2. Natural uranium: containing 0.71% 235U.
3. Low-enriched uranium (LEU), between 0.71 – 20% 235U.
• commercial power reactors use 2-6 % 235U fuels.
• cannot be used to make nuclear explosives
4. Highly enriched uranium (HEU): containing > 20% 235U.
Research and naval reactors use either LEU or HEU fuel.
5. Weapon-grade uranium: HEU containing > 90% 235U.
Plutonium-239: Highly carcinogenic  ray emitter.
Unlike uranium, all (but trace quantities) of Pu are manufactured.
239Pu is produced in nuclear reactors when 238U is irradiated with neutrons.
½ = 24,000 years, and it is a fissile material.
Subsequent neutron captures lead to accumulations of 240Pu, 241Pu and 242Pu.
241Pu is fissile, but 240Pu and 242Pu are not. However, all are fissionable by
fast neutrons, and can be used either in combination or alone in nuclear explosives;
best fission explosive nuclear material.
3-8 kg required for nuclear explosive; "significant quantities standard" 1 kg.
The bomb dropped on Nagasaki contained 6.1 kg.
There are about 1,200 metric tons of Plutonium on our planet of which some
230 tons have been produced for military purposes.
Plutonium is ~10 times more toxic than nerve gas. When inhaled, the smallest
particles cause cancer: inhaling 12,000 micrograms (millionths of a gram) causes
death within 60 days. The dispersal of 3.5 ounces of plutonium could kill every-one
in a large office building.
For weapon production, plutonium has to be at least 93% enriched. Plutonium
technology for bomb construction is judged to be more difficult than 235U techniques.
Weapons can be made out of plutonium with low concentrations of 239Pu and high
concentrations of 240Pu, 241Pu, or 242Pu.
The plutonium used in nuclear weapons typically contains mostly 239Pu and
relatively small fractions of other plutonium isotopes. Plutonium discharged in power
reactor fuel typically contains significantly less 239Pu and more of other
plutonium isotopes.
The following grades of plutonium are widely used:
1. Weapon-grade plutonium: containing < 7% 240Pu.
2. Fuel-grade plutonium: 7 - 18 % 240Pu.
3. Reactor-grade plutonium, containing over 18 percent 240Pu.
The term "super-grade plutonium" is sometimes used to
describe plutonium containing less than 3 percent plutonium 240.
The term "weapon-usable plutonium" is often used to describe
plutonium in separated form and, thus able to be quickly turned
into weapons components
Before triggering, fissile material is kept in subcritical quantities
to prevent accidental explosions. An electrical trigger sets off
chemical explosives that drive the subcritical parts together.
Propellant
Tamper
Active Material
each 2/3 critical
Gun Trigger Assembly
Tamper
Enola Gay
Little Boy
Hiroshima
Size:
length - 3 meters,
diameter - 0.7 meters.
Weight: 4 tons.
Nuclear material:
Uranium 235.
Energy released:
equivalent to
12.5 kilotons of TNT.
Code name:"Little Boy"
N ( t )  N ( 0) e
t /
Once triggered the
chain reaction
builds exponentially.
Note logarithmic scale!
After ~50 generations
(0.50 msec) the energy
released is increasing so
rapidly it heats the
material to the point
it expands explosively.
This scatters the remaining
fissile material in subcritical
quantities, and the chain
reaction ends.
Dropping the first atomic bomb
At 2:45am local time (August 6, 1945), the Enola Gay, a B-29 bomber
took off from the US air base on Tinian Island in the western Pacific.
6½ hours later, at 8:15 A.M. Japan time, its atomic bomb was dropped
and exploded a minute later at an estimated altitude of 58020 meters
over central Hiroshima.
Initial explosive conditions
Maximum temperature at burst point: several million degrees C.
A 15m radius fireball formed in 0.1 millisecond, with a temperature of
300,000o C, and expanded to its huge maximum size in one second.
The top of the atomic cloud reached an altitude of 17,000 meters.
Black rain
Radioactive debris fell in a “black rain” for > hour over a wide area.
Damaging effects of the atomic bomb
Thermal heat
Intense thermal heat emitted by the fireball caused severe burns and loss of eyesight.
Thermal burns of bare skin occurred as far as 3.5 kilometers from ground zero (directly
below the burst point). Most people exposed to thermal rays within 1-kilometer radius
of ground zero died. Tile and glass melted; all combustible materials were consumed.
Blast
An atomic explosion causes an enormous shock wave followed instantaneously by
a rapid expansion of air (the blast); these carry ~half the explosion's released energy.
Maximum wind pressure of the blast: 35 tons per square meter.
Maximum wind velocity: 440 meters per second.
Wooden houses within 2.3 km of ground zero collapsed. Concrete buildings near
ground zero (blast from above) had ceilings crushed, windows and doors blown off.
Radiation
Exposure within 500 meters of ground zero was fatal. People exposed at distances of
3-5 kilometers later showed symptoms of aftereffects, including radiation-induced cancers
Deaths
With an uncertain population figure, the death toll could only be estimated.
According to data submitted to the United Nations by Hiroshima City in 1976,
the death count reached 140,000 (plus or minus 10,000) by the end of December, 1945.
Active Material
(235U or 239Pu)
each 1/3 critical
chemical
explosive
electrical
trigger
chemical
explosive
Active Material
(235U or 239Pu)
subcritical density
Implosion Assembly Designs
Fat Man
Nagasaki
The atomic bomb dropped on Nagasaki exploded at 11:02 A.M. on August 9.
Using 6.1 kg of 239Pu it delivered the explosive power of 20 kilotons of TNT-equivalent,
And left an estimated 70,000 dead by the end of 1945.