Question

Consider a hypothethical experiment where a burst of 10 MeV neutrinos is observed in 1 hour after the light has been detected from a supernova explosion at a distance of 10^(22) m. Estimate the neutrino mass.

Answer 1

Given kinetic energy of the neutrinos is K = 10 MeV, the distance between the supernova and earth is d = 10^22 m, also given that the neutrions take 1 hr more than light to reach us, Therefore, As we know the total energy for a particle moving relativistically is
, where is the rest mass energy of the neutrinos.

as the rest mass energy of neutrinos is very small compared to the kinetic energy, we can approximate as



using bionomial expansion to get rid of the exponent 1/2, and get that

Now as we also know that the distance d is covered by light 1 hr faster than neutrinos, so it can be express as

where v is the velociity of neutrinos and solving this we can get v as

Now equating v from both the above equations we get that

Therefore the rest mass of the neutrinos is


Calculating all these value the rest mass of neutrinos is
.