Most of the energy released in the collapse of a massive star to a neutron star (a core-collapse supernova) is in the form of neutrinos. (a) If the newly-formed neutron star has mass M = 1.4 M and radius R = 10 km, estimate the mean number density of neutrons. Find the mean free path of a neutrino inside the neutron star, using the density you just found, and assuming the cross section for a neutrino to scatter off a neutron in the star is sigma ~ 10^-42 cm^2.