2. An electron neutrino is produced in a nuclear reaction in the sun, with an energy E = 200 KeV. (a) In terms of the neutrino mass eigenstates (v1), [v2), describe the wave function of the neutrino when it is produced. (b) What is the probability of detecting this neutrino as a muon neutrino after it is produced, as a function of time? Give your answer in terms of the energies E1, E2 of the two neutrino mass eigenstates, and the weak mixing angle 0. (c) The sun is approximately 1.5 x 108 km from earth. Since neutrinos are very light, they travel at velocities roughly the speed of light, i.e. 3 x 108 m/s. Your neutrino detector finds that upon reaching the earth's surface, 1/9 of these electron neutrinos are detected as muon neutrinos. If the neutrino mass difference obeys (m? - m?) = 2.0 x 10-64 kg, what is the weak mixing angle 0