A neutron striking a nucleus won't make it fall apart and release more
neutrons unless the nucleus is one of the types that does that. Most
don't. The ground contains very few nuclei of the types (e.g. U235)
which sustain a chain reaction, so on the average each neutron in the
ground will release much less than one new neutron, and the reaction
quickly stops.
There are several ways a nuclear chain reaction in concentrated
fissile material can stop. One is that the material may heat up and
blow apart, more or less violently, so that the neutrons from one part
no longer are likely to hit the nuclei of the other parts. Another is
that enough of the material is used up that the remainder no longer
generates more than one new neutron for each neutron released.
In a more relaxed and commonplace application, nuclear chain
reactions are taken advantage of to generate power. In this case, the
intention is to keep a chain reaction going at a slow, controlled rate.
The fissile material is kept mixed in with other atoms which do not
support the chain reaction -- materials which slow down neutrons, or
which absorb them. Water, heavy water, and graphite are good materials
for slowing down neutrons, and atoms with heavy nuclei have good
neutron capture cross-sections and can absorb neutrons quickly. These
materials are used in control rods.
The time dependence of the reaction rate is an exponential with an
adjustable sign in the exponent -- it can either react more and more,
exponentially getting bigger, or the reaction rate can gradually slow
down. Another piece of the puzzle is the constant production of new
neutrons as the atoms spontaneously decay. That way, if you put enough
neutron-slowing materials and enough neutron-absorbing materials around
so that chain reactions never exponentiate off in the increasing
direction, they will still be kept going at a lower level because of
the natural decay processes.
Mike W. and Tom J
(published on 10/22/2007)