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A neutron of the right speed hits a Uranium atom. This splits into 2 pieces plus 2 or 3 neutrons. Of the three neutrons, one or two may miss, but one or two hit other Uranium atoms, causing them to split, each again releasing several neutrons.
if the reproduction rate is greater than 1, then the number of neutrons increases rapidly, a chain reaction.
For a bomb, the reproduction rate is high, so most of the uranium atoms fission quickly, producing a lot of heat, ie, the explosion.
In a fission reactor, moderators (rods inserted into the core) absorb a lot of the neutrons. The amount of moderation is adjusted by moving the rods in or out of the core, keeping the reproduction rate at 1.000.