Sustainable Nuclear Reactions 

M is the average distance a neutron must travel before getting absorbed. 
k is the neutron multiplication factor or how many come out compared to put in.

  A part of the problem when generating nuclear energy is finding an element that will generate more neutrons than put in to keep the reaction going. At the start of the nuclear age, many were skeptical about whether or not they could find an element that would produce more neutrons than it absorbed.   After much experimentation uranium isotope, 235 was chosen as the most usable isotope of an element for a nuclear reactor (before the synthesis of plutonium).  because on average this Isotope generated 2.45 neutrons per fission. Once an element or isotope is found that has a larger neutron emission then absorption there are other challenges to overcome. One being the purification of that element as well as the orientation or geometry the reactor must be in in order to have the maximum absorption of neutrons to the nucleus's of the Atoms nearby to maximize the number of fissions. When a reactor becomes self-sustaining or critical this means that there is no longer a need to fire neutrons into the reactor, the neutrons produced are great enough to keep the reaction going by itself.  This can be thought of as the worlds largest domino effect only with atoms and large amounts of energy. The reactor criticality equation is shown left. Once the neutron multiplication factor is greater than one the reaction has gone critical and is now producing more energy than put in to start the reaction this leads us to nuclear reactors in power plants.