Let each fission event in a chain reaction give rise on average to k neutrons that in turn cause further fission.
a. (i) Show that the number of neutrons after n generations is Nn=N0kn, where N0 is the initial number of neutrons.
b. (ii) Using the result, write the conditions on k for (a) a steady, (b) a dying out, and (c) a rapidly growing chain reaction.