Nuclear 2
Fission and Fusion
History
1896: Becquerel discovers radioactivity
1898: Marie & Pierre Curie discover radium
1911: Rutherford discovers nucleus
1932: Chadwick discovers neutrons
1933: Hitler becomes Chancellor
1934: Joliot-Curies and Fermi induce “artificial”
radioactivity via alphas and neutrons
1938: Hahn and Strassman show that Fermi
had observed fission.
More History
1938: Meitner and Frisch describe fission
theoretically, and show large amounts of energy
can be released
1938: Szilard confirms energy release
experimentally, and demonstrates possibility of
nuclear chain reaction.
1938: Nazis invade Czecholslovakia
1939: Nazis invade Poland
1939: Einstein-Szilard letter to Roosevelt
Energy of the nucleus
Energy and mass are equivalent according to
E = mc2
c = 300,000 km/s = speed of light
Energy (nucleus: Z protons and N neutrons)
= Z mp c2 + N mn c2 - Binding Energy (N,Z)
Binding Energy (N,Z) = BE (A Chemical Symbol)
Binding Energy : energy required to completely
decompose nucleus into its constituents
Determines the possibility (energy) of fission or fusion
Binding energy per nucleon
BE/A
⇑
Fusion
region
Fission
region
Number of nucleons in nucleus (A)
Key Facts
Nuclei “want” to be in states of lowest energy.
Lowest energy means largest binding energy (because of the
minus sign in definition of binding energy).
Nuclei in the middle have the highest binding energy per
nucleon.
Lighter nuclei go to lower energy states by combining (fusion)
Heaviest nuclei can lower their energy by coming apart (fission).
Nuclei around Iron are most stable.
Fission of U-235
Atomic numbers of
fission products are
distributed among all
possibilities.
Split into exact
halves is not most
likely process.
Fission energy
Energy considerations make fission possible:
Heavy nucleus
two smaller nuclei
Example: split 240Pu into two 120Ag nuclei
240
94
120
Pu146 ⇒120
Ag
+
47
73
47 Ag 73 + fission energy
Look up : BE(240Pu) = 1813 MeV
BE(120Ag) = 1008 MeV
Energy balance :
Initially ⇒ 94 mp c2 + 146 mn c2 - 1813 MeV =
Finally ⇒ 2 x (47 mp c2 + 73 mn c2 - 1008 MeV) + fission energy
Solve for fission energy : fission energy = 203 MeV (enormous)
Fission
Fission is nuclear energy from splitting heavy nuclei
Spontaneous fission is very improbable
Fission can be induced!
1934
Fermi: n + U
elements heavier than U (transuranics)
1938
Hahn & Strassmann 1938/9 Frisch & Meitner
n + 235U ⇒ Barium ???!!!???
understand that fission occurs!
Two nuclei yield fission with high probability (are fissile)
when bombarded with low energy neutrons
235U
occurs naturally but in small amounts
239Pu
not available before 1940!!
Fusion energy
• Fusion occurs in the sun
• Hydrogen or thermonuclear bomb
Example of fusion reaction :
2H
2
H+ 2 H⇒ 3 He + n + fusion energy
contains 1 p and 1 n and is called a “deuteron”
Look up : BE (2H) = 2.2245 MeV
BE (3He) = 7.718 MeV
Energy balance :
Initially ⇒ 2 x ( mp c2 + mn c2 - 2.2245 MeV) =
Finally ⇒ 2 mp c2 + mn c2 - 7.718 MeV + mn c2 + fusion energy
Solve for fusion energy : fusion energy = 3.269 MeV (a lot ...)
Picture of a fusion reaction
Deuterium and
Tritium are isotopes
of Hydrogen.
D has 1 neutron; T
has 2.
Final result is He-4 +
a neutron.
Self-sustaining Nuclear Reactions
Neutrons induce
fission.
More neutrons can
lead to more fission
events, leading to
more neutrons, and so
on.....
This is known as a
chain reaction
Another view of a chain reaction
http://lectureonline.cl.msu.edu/~mmp/applist/chain/chain.htm
More on chain reactions
Self-sustaining chain reaction :
• Each fission event must produce 1 or more free neutrons :
average 2.5 for 235U & 3 for 239Pu
• One or more of these n must induce another fission event
Fate of n : - leaves the sample ⇒
make sample larger
use n reflectors
- n may be absorbed ⇒
minimize surface (sphere)
compress sample (bombs)
purer 235U (enrichment)
Still more ...
Naturally occurring Uranium : 99.3 %
238U
and 0.7 % 235U
• Weapons-grade uranium
⇒ enriched to 95 %
• Reactor-grade uranium
⇒ enriched up to 4 %
Capability of sample to sustain chain reaction characterized by
k ⇒ multiplication factor
Example: - throw 100 n in sample and wait 10-8 s for their fate
- then check how many free n there are : x
- k = x / 100
What will k be for a -bomb ?
As large as possible
1
-reactor ?
and more ...
k = 1 critical point between a reaction that grows or dies out
So mass of fissile material with k ≥ 1 is called critical mass
(actually depends on geometry of material- more later)
Time step for next fission events :
n from fission ⇒ fast neutrons with kinetic energy of about 1 MeV
1 MeV
= 0.5 mn v2 = kinetic energy
So mn c2 = 939 MeV
= 0.5 mn c2 v2 / c2
v2 / c2 = 2 / 939 or v = √(2/939) * c = 1.4 107 m/s
Assume n in pure 235U ⇒ sphere with 0.1 m radius
will induce fission within t = 0.1 m / v ≈ 10-8 s
So time step is only about 10-8 s !!
Growth of released energy
Assume half of the n
lead to fission (180 MeV)
N generation Time (μs)
# neutrons
Energy
(MeV)
0th
0.00
1
0
1st
0.01
2.7
245
2nd
0.02
7.4
910
3rd
0.03
20.0
2720
10th
0.1
2.2 x 104
3.1 x 106
20th
0.2
4.9 x 108
6.9 x 1010
50th
0.50
5.2 x 1021
7.4 x 1023
56th
0.56
2.1 x 1024
3.0 x 1026
57th
0.57
5.7 x 1024
8.1 x 1026
Exponential growth!
1 kiloton TNT = 2.6 x 1025 MeV
How much fissionable material is needed?
Pure 235U
critical mass ≈ 20 kgsize of softball
Pure 239Pu
critical mass ≈ 10 kgsize of baseball
Still, it is difficult to make bombs ...