18. On February 24th 1987, a supernova was seen in the constellation of Dorado, in
the vicinity of the Tarantula nebula in the Large Magellanic Cloud. Neutrinos
from Supernova 1987A reached Earth travelling a distance of 55 kpc.
(a) The neutrino flux from SN 1987A was estimated to be $1.3 \times 10^{10}$ cm$^{-2}$ at
the location of Earth. If the average energy per neutrino was approximately
4.2 MeV, estimate the amount of energy released via neutrinos during the
supernova explosion.
(b) The neutrinos were found to have energies in the range 6-39 MeV. If the
spread of 12s in arrival times was caused by neutrinos of different energies
traveling at different speeds, show that the neutrino mass cannot be much
more than about 20 eV.