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.

••• Observations show that if there were no neutrino, β decay would violate conservation of momentum, as well as energy. For example, in a decay of 6He at rest, the two final charged particles were observed with momenta as shown in Fig. 1. (a) Show that this decay would violate conservation of momentum if there were no neutrino involved, (b) Assuming that a neutrino is ejected and that total momentum is conserved, calculate the momentum (magnitude and direction) of the unobserved neutrino, (c) Assuming conservation of energy, find the neutrino’s energy, (d) Show that your answers in parts (b) and (c) are consistent with the neutrino’s having zero rest mass (within the accuracy of the given numbers).

FIGURE 1