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.
•• The positive pion decays into a muon and a neutrino, π+ → μ+ + ν. The pion has rest mass mπ = 140 MeV/c2, the muon has mμ = 106 MeV/c2, while the neutrino has mν ≈ 0. (Strictly speaking, there are several kinds of neutrino; the one discussed here is denoted νμ to indicate that it is the one produced with a muon.) Assuming the original pion was at rest, use conservation of energy and momentum to show that the speed of the muon is given by
Evaluate this numerically.
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