PHY 1020 Lecture 22

NUCLEAR REACTIONS

first ``artificial'' nuclear reaction:
Rutherford's proton discovery 1919:

is artificial transmutation of N isotope into O isotope
one of the reactions in Chadwick's neutron discovery:

converts beryllium into carbon;
conservation laws:
in nuclear reactions, nucleon number, charge and energy is conserved (energy = kinetic energy plus mass energy)
energy and mass:
- according to special theory of relativity, mass is a form of energy
  
  = ``rest energy"
- energy of a nucleus or particle = rest energy + kinetic energy + ..
- binding energies in nuclei are much larger than in atoms;
- masses of nuclei smaller than sum of masses of constituents;
  difference is = binding energy;
- the bigger the binding energy of a nucleus, the smaller the mass of the nucleus, compared to the mass of the constituents;
- if the total binding energy in the ``final state'' is bigger than in the initial state, energy is released in reaction;
  released energy = ``Q-value of reaction''
  = [(sum of masses before) - (sum of masses after)]times
  
  the energy Q is in the form of kinetic energies of the particles in the final state of the reaction.

BINDING ENERGY AND STABILITY OF NUCLEI

the binding energy per nucleon is a measure of the stability of a nucleus;
the bigger the binding energy per nucleon, the more energy has to be put into the nucleus in order to kick a nucleon out
binding energy per nucleon vs mass number:
has maximum at position of iron (``iron plateau'');
with rather steep rise to plateau from lower mass numbers, and gentle fall-off towards higher mass numbers;
energy is set free when nuclei heavier than iron break up into nuclei in the iron plateau, (``fission'')
but also when very light nuclei combine to form heavier nuclei (``fusion'').

NUCLEAR FISSION

``fission'' is a process in which a heavy nucleus is split into two intermediate-size nuclei, with emission of neutrons and conversion of mass into energy.
``induced'' fission of U-235:
- U-235 nucleus can absorb neutrons -- formation of U-236
- U-236 is unstable: absorption of neutron deforms nucleus, resulting oscillations lead to further deformation and eventual break up;
  U-236 nucleus decays (``fissions'') into two lighter nuclei (called ``fission fragments''), accompanied by emission of several neutrons and release of energy:
- some fission processes:
  
  (this last reaction was the one observed by Hahn and Strassmann in 1938, and explained by Meitner and Frisch)
features of U-235 fission processes:
- many different fission processes, resulting in emission of different pairs of nuclei between ;
- fission products are radioactive (due to excess neutrons), sometimes with long half-lives;
- neutrons are released;
- rather large amount of energy released (approximately 200 MeV per fission);
- energy appears as kinetic energy of fission fragments, neutrons, beta rays, gamma rays, and neutrinos
- note that this is ``induced fission'' caused by absorption of neutrons by original nucleus, i.e. neutrons are needed to make U-236;
other fissile nuclei: U-233, Pu-239

CHAIN REACTIONS

neutrons emitted in a fission process may be captured by another fissile nucleus fission more neutrons more fissions, ....
``chain reaction''
chain reaction is self-sustaining if, on average, one neutron released in each fission event causes another fission event
(factor k = 1'')
conditions for self-sustaining chain reaction:
- enough neutrons made
- sufficiently many neutrons must be captured by fissile nucleus
- sufficiently many excited nuclei undergo fission
critical mass:
= the minimum amount of fissile material necessary to sustain chain reaction (i.e. to make k = 1);
subcritical mass:
not enough or unfavorably distributed fissile material neutrons escape before they can be absorbed (reproduction factor smaller than 1) chain reaction dies out;
supercritical mass:
on average, more than one fission reaction caused by every fission ( k > 1 ) ``runaway chain reaction'' - explosion
nuclear bomb:
two subcritical pieces of fissile material brought together very rapidly to produce strongly supercritical mass (use conventional explosive charge to ``shoot them together'');
main problem in making nuclear bomb: produce enough pure U-235 (is only 0.7% of natural uranium)

NUCLEAR REACTORS:

natural uranium: 0.7% U-235, 99.3% U-238 (1 : 138)
absorption of neutron by U-238 does not lead to fission
fast neutrons (e.g. those from fission) can be absorbed equally well by U-238 and by U-235 no chain reaction in natural uranium;
slow neutrons mostly absorbed by U-235
to make sustained chain reaction in natural uranium, have to slow neutrons down so that they are captured by U-235 rather than U-238
``moderator'' = material that slows neutrons down (e.g. carbon, ``light'' or ``heavy'' water)
nuclear reactors use ``enriched uranium'' (i.e. 2 to 3 % U-235) as fuel,
water as coolant and moderator
and boron or cadmium as material for ``control rods''
control rods'' made from material that absorbs neutrons; can be pushed in or pulled out to change reproduction factor.
(Enrico Fermi's first reactor used graphite as moderator and cadmium for control)
coolant carries heat from reactor to heat exchanger where heat is transferred to working substance (usually also water) of heat engine which drives electric generator.

FUSION

fusion is a process in which light nuclei combine to form heavier ones, with the release of energy.
fusion is the source of energy of the sun and other stars
fusion of H into He:
proceeds in several steps from H to He; net reaction is

energy liberated per reaction = 24.7 MeV = kinetic energy of reaction products
1 kg of He contains He atoms if we make 1 kg He from protons, we generate

compare: burning of 1 kg of coal yields ! (in sun, about 600 million tons of hydrogen are ``burned'' per second)
for fusion to proceed, the nuclei must get close enough to each other for strog force to become effective must overcome electric repulsion must have enough kinetic energy
in addition, density must be high enough so that nuclei collide frequently
to start and maintain fusion, must have high temperature and high density - plasma must be ``confined''
these conditions are present in interior of sufficiently massive star.
hydrogen bomb:
= a bomb in which deuterons are fused to He; fusion initiated by a fission bomb
controlled fusion: not yet proved practical (so far, energy input needed to maintain necessary conditions is higher than energy output).
confinement problem:
main problem in controlled fusion is to reach high temperatures and to keep hot plasma confined after fusion process starts
Tokamak: = a fusion reactor in which magnetic confinement is used to keep plasma together and away from any material
breakthrough of 1993: at Princeton Plasma Physics Laboratory, deuterium and tritium fused in magnetically confined plasma; produced energy, but energy needed to initiate reaction = four times energy output!
potential advantages of fusion:
- low cost and abundance of deuterium: can be (cheaply) extracted from ocean water
  -- uranium is expensive, scarce, hazardous to mine
- fewer nuclear waste disposal problems: fusion by-products have short half-lives
- no run-away accidents possible
but - fusion plants will be more expensive to build than fission reactors,
-- still a long way to go until fusion becomes practical

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Tue Nov 19 08:52:41 EST 1996