Observations of neutrinos emitted by the supernova SN1987a p

Observations of neutrinos emitted by the supernova SN1987a place an upper limit of 20 eV on the rest energy of the electron neutrino. If the rest energy of the electron neutrino were, in fact 15 eV, what would be the speed difference (in terms of cm/s) between light and a 1.8 MeV electron neutrino?

Solution

energy of neutrino = 20 ev

actual rest energy = 15 ev

E = gamma*mc^2

=> gamaa = sqrt ( 1- v^2/c^2) = 15/20

=> v^2/c^2 = 0.437

=> v = 0.6610 c

difference in speed , c - 0.6610c = ( 1- 0.6610)*3*10^8 = 10^8 m/s OR 10^10 cm/s