Each of the following reactions is missing a single particle. Calculate the baryon number, charge, strangeness, and the three lepton numbers (where appropriate) of the missing particle, and from this identify the particle. (a) p + p S p + Λ0 + ?; (b) K- + n S Λ0 + ?; (c) pbar + p S n + ?; (d) n barm + p S n + ?

For every reaction, 4-protons are “used up,” meaning they are unable to participate in future reactions. How much mass does this correspond to that is being “used up” each second? (you may use mH that was shown in class and express your answer in kg)

(a) The most common decay mode of the Ξ− particle is Ξ− → Λ0 + π− . Using the quantum numbers in the table given above, show that strangeness changes by 1, baryon number and charge are conserved, and lepton family numbers are unaffected.                                                                                      (b) Is the decay K+ → μ+ + νμ allowed, given the quantum numbers in the table given above?

Problem 9. Explain why the fact that the electron emitted in the decay of a neutron has a range of energies rather than En - Ep (apparently violating energy conservation) led to the discovery of the neutrino.