Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
•• To improve the chance that the neutrons produced in fission will themselves induce further fissions, it is important to slow them down. A moderator is a substance with which neutrons can collide and lose energy. It must be chosen so that the neutrons lose as much energy as possible (but are not actually captured). In practice the best process for reducing the neutrons’ energy is an elastic collision. Consider a head-on elastic collision between a neutron (mass m) and a nucleus (mass M). (a) Use conservation of energy and momentum (nonrelativistic) to derive an expression for the neutron’s fractional loss of energy, ΔK/K, as a function of the mass ratio μ = m/M. (b) Show that the loss is maximum when the masses are equal (μ = 1). (c) This result suggests that hydrogen — in water, for example — would be the best moderator. Unluckily, ordinary hydrogen, 1H, has the disadvantage that it can capture neutrons readily to form deuterium. Two practical alternatives with masses at least fairly close to the neutron mass are deuterium (in “heavy” water) and carbon (in the form of graphite). What is ΔK/K for these two moderators?
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