# Confusion on conservation of energy in the beta decay process

In a question,regarding the beta decay process, it is given that.

Assuming the anti-neutrino to be massless and possessing negligible energy and the neutron to be at rest, momentum and energy are conserved and,from the calculations, the maximum kinetic energy of an electron was found to be $$0.8 * 10^6 ev$$, Now suppose the anti neutrino has a mass $$3ev/c^2$$, find the new range of kinetic energy for the electron and maximum energy of the anti neutrino.

The answer given was that the anti neutrino could possess an energy of nearly $$0.8 *10^6 ev$$,

It was also given that the new kinetic energy range for electron is 0 to $$0.8 *10^6 ev$$. Which implies that the anti neutrino should possess a kinetic energy of $$0.8 *10^6 ev$$.

But the maximum kinetic energy (assuming the antineutrino to be travelling at the speed of light) is merely $$1.5 ev$$ due to this,I am puzzled as to how the anti neutrino could possess $$0.8 *10^6 ev$$.

• If the antineutrino has mass (which it does) it cannot travel at c, but in either case (positive or zero mass) there's no intrinsic limit on its KE, or its momentum. How did you come up with that figure of 1.5 eV? You have to use relativistic formulae, not $E_k = \frac 1 2 mv^2$ – PM 2Ring Apr 22 '19 at 14:44
• Oh. I see, by the relativistic formula kinetic energy can tend to infinity. I think that is where I made a mistake. – Vaishakh Sreekanth Menon Apr 22 '19 at 15:16