Phase diagram of water

B/A
Fusion
Binding Energy of Nuclei
Fission
Mass Number A
MeV
Above mass ~20 approximately constant binding energy per nucleon
However: more stable nuclei can be formed either by:
i) Fusion (combining 2 nuclei with low mass number A)
ii) Fission (breakup of large A nucleus into lower A fragments plus
release of neutrons)
8
6
4
2
0
In fission
A 1 → A 2 + A 3 + neutrons,
where A 2 and A 3 are the final
stable nuclei, the total energy
release E R is approximately
E R = A 2 {b(A 2 ) − b(A 1 )} +
A 3 {b(A 3 ) − b(A 1 )}.
Basic Ideas : Fission Reactors
141
Ba 56
n
n
235 236
U U n
92 92
n
neutron
92
Kr
absorption
36
fission
n + 235 U 92 141 Ba 56 + 92 Kr 36 + 3n
Change in mass, δm = 3.6 10 −28 kg
Energy released, E = (δm)c 2
= (3 10 8 ) 2 3.6 10 −28
= 3.2 10 −11 J
⇒ chain reaction
cf chemical combustion
C + O 2 CO 2 E = 7 10 −19 J
Energy release from 1 uranium nucleus = 5 10 7 carbon atoms
1 tonne of 235 U = 2.7 10 6 tonnes of coal
U is 0.7% 235 U so 1 tonne U ≡ 20,000 tonnes of coal
Naturally-occurring uranium consists of
• fissile isotope 235 U
• stable isotope 238 U }ratio = 1/138 ~ 0.7%
In a reactor, neutrons are lost by :
1) absorption by 238 U 239 U 239 Pu
2) absorption by 235 U 236 U (18% for thermal n)
3) absorption by moderator
4) absorption by reactor structure
5) escape from reactor core
Not enough n to continue chain reaction with H 2 O moderation
enrichment necessary to increase ratio 235 U/ 238 U 3%
Note: the naturally-occurring ratio was higher in the past
%
Oklo ‘reactor’ (Gabon)
3
0.7
−2.10 9
−10 9
0
years
β
nb t 1/2 of
235
U = 7.1 10 8 years
cf t 1/2 of
238
U = 3 10 9 years
Fuel Enrichment
Enrichment is process of increasing proportion of fissionable nuclei
in natural uranium (0.7% 235 U)
Methods of enrichment
1 Electromagnetic Separation
accelerating
electrodes
B
mv 2 /r = qBv r = mv/qB
vacuum chamber
heavy isotope
light isotope
Used for Manhattan project (1g/day) and by Iraq before Gulf War