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.

••• In an observed β decay of a nucleus X that is exactly at rest, it happens that the electron is also exactly at rest. For this special case, derive an exact (relativistic) expression for the energy of the in terms of mX, mY, and me (assuming that the mass of the neutrino is negligible). Show that to an excellent approximation, the neutrino takes all of the available kinetic energy, ΔMc2, when the electron is at rest. In a typical case [mx ≈ 200 u and (mX − mY) ≈ 0.001 u] how good is this approximation? (Give your answer as a fractional error.)