These situations are respectively called subcritical, critical,and supercritical.If
two neutrons from each fission in an atomic bomb induce further fissions in
10 ^8 s, a chain reaction starting with a single fission will give off 2 1013 J of
energy in less than 10^6 s.12.10 NUCLEAR REACTORS
E 0 mc^2 $$$A nuclear reactor is a very efficient source of energy: the fission of 1 g of^235 U per day
evolves energy at a rate of about 1 MW, whereas 2.6 tons of coal per day must be
burned in a conventional power plant to produce 1 MW. The energy given off in a
reactor becomes heat, which is removed by a liquid or gas coolant. The hot coolant is
then used to boil water, and the resulting steam is fed to a turbine that can power an
electric generator, a ship, or a submarine.
Each fission in^235 U releases an average of 2.5 neutrons, so no more than 1.5 neutrons
per fission can be lost for a self-substaining chain reaction to occur. However, natural
uranium contains only 0.7 percent of the fissionable isotope^235 U. The more abundant(^238) U readily captures fast neutrons but usually does not undergo fission as a result. As
it happens,^238 U has only a small cross section for the capture of slowneutrons, whereas
the cross section of^235 U for slow neutron-induced fission is a whopping 582 barns.
Slowing down the fast neutrons that are liberated in fission thus helps prevent their
unproductive absorption by^238 U and at the same time promotes further fissions in
(^235) U.
To slow down fission neutrons, the uranium in a reactor is mixed with a moderator,
a substance whose nuclei absorb energy from fast neutrons in collisions without much
tendency to capture the neutrons. While the exact amount of energy lost by a moving
body that collides elastically with another depends on the details of the interaction, in
general the energy transfer is a maximum when the participants are of equal mass
454 Chapter Twelve
Neutrons produced
during fission
Fissionable
nucleus
Stray neutron
Lighter nuclei
Figure 12.21Sketch of a chain reaction. The reaction is self-sustaining if at least one neutron from
each fission event on the average induces another fission event. If more than one neutron per fission
on the average induces another fission, the reaction is explosive.
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