Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

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.

•• Consider the α decay of a nucleus X at rest, X → Y + α, where Y denotes the offspring nucleus, (a) Prove that because the α is much lighter than Y, almost all the available kinetic energy goes to the α; specifically, prove that

[Hint: Use conservation of momentum and treat all particles nonrelativistically.] (b) In the α decay of a typical naturally radioactive nucleus, what percentage of the available kinetic energy does the alpha particle take? (c) Assuming that β decay has the form X → Y + e, use the relation corresponding to (17.86) to find what percentage of the available kinetic energy goes to the electron. (Your answer here is really an upper bound, since some energy can go to the neutrino. It is also only approximate since the electron can be fairly relativistic.)