03 - Nuclear Energy
Summary
The strength of the nuclear force leads to enormous energies. These can be released when there is a change in nuclear profile. In the last section, we saw α, β, and γ radiations with energies of the order of 1MeV. Energies of around 200MeV can be released when a heavy nucleus splits (fission), and ten times more when light nuclei combine (fusion).
In this section, we’ll look at the physical sources of these energies, specific examples of nucleear reactions involving them, and the uses they have been put to.
Contents
- Nuclear Fission
- Nuclear Fusion
Nuclear Fission
During Fission, a heavy isotope splits into two or more fragments , this binding energy is released during the process. Nuclear reactors and Atomic bombs make use of this. A typical reaction is 1n+235U→236U→141Ba+92Kr+31n
Approximately 200 MeV of energy is released per fission
- B/A for 235U = 7.59MeV, for 141Ba = 8.8MeV, for 92Kr = 7.83MeV
Reason for Nuclear Fission
Coulomb repulsion is at the heart of nuclear fission
remember, the binding energy per nucleon curve only dips down, giving a maximum around 56Fe, when we introduce the Coulomb repulsion term
a large nucleus can deform, no longer spherical. The increase in surface energy being offset by a larger distance between protons
consider the reaction above. If the 141Ba and 92Kr nuclei are just touching, their separation will be 1.2×3√141+1.2×3√92=11.66nm
the potential energy will be given by E=14πϵ0q1q2r≈250MeV where the charge on 141Ba is 56×e and on 92Kr is 36×e
During fission several neutrons are emitted by each nucleus and these cause further fission
- can cause a chain reaction
- reason for neutron emmission is to maintain proton/neutron ratio appropriate for atomic mass
- fission products tend to be β emitters
number of neutrons (k) that propagate reaction is crucial
- if k < 1 then reaction dies out
- if k > 1 then explosion
- if k ≈ 1 then controlled power plant
control rods made from Cadmium can be used to absorb neutrons, keep k close to 1
surface to volume ratio important
- critical mass (about 50kg for 235U)
Fission bomb types
- gun type (Little Boy dropped on Hiroshima)
- implosion type (Fat Man dropped on Nagasaki)
The large numbers of neutrons produced in a reactor can be used to produce nuclear transformations in suitable elements producing radioisotopes for therapy, tracing etc.
Neutrons in Fission
absorbtion of neutron is what triggers fission
235U is even-odd, 236U is even-even
- lots of energy released into nucleus which bubbles inside before splitting it apart
neutron absorbtion is much more probable for slow (thermal, ~10eV) neutrons
- but neutrons emitted in fission are hot (~MeV)
- slow down by collisions with light nuclei
- moderator, usually water (contains 1H+) or graphite carbon
Fission Reactors
natural Uranium is about 1% 235U (mostly 238U)
reactor grade is about 20% 235U
weapons grade is about 85% 235U
239Pu also fissionable
4th Generation Reactors - SMR
small and modular can be transported by road
higher temperatures so more efficient
liquid salt coolant (Natrium type) can act as energy reservoir
continuous fuel feed so no need to shut down to service
238U act as neutron absorber to control reaction rates
build on sites of old coal plants
cost about €3B, take ~ 10 years
typically 80-300MW per reactor
Proton-Proton Cycle
1H+1H→2H+e++μ
2H+1H→3He+γ
3He+3He→4He+21H++γ
$N(t) = N_0;e^{-t} $
t1/2=loge2λ=0.693λ
ℏ=1.0546×10−34Js
Fusion Reactors
use 3T or 2D (tritium or deuterium)
2D naturally occuring (1 in 6,500 water molecules)
3T is not, 12 year half-life
need temperatures of about 150 million ∘C
laser induced fusion (pulse of 2 MJ)
magnetic confinement (20T) in a Tokamak (doughnut shape)
Large science effort, current leaders are Lawrence Livermore in California (laser) and ITER in Cadarache in France (tokomak)
Equations
References
Nuclear Physics