The $\beta$ -decay process, discovered around 1900, is basically the decay of a neutron (n). In the laboratory, a proton (p)
and an electron ($e^{-}$) are observed as the decay products of the neutron. Therefore. considering the decay of a neutron as a
two-body decay process, it was predicted theoretically that the kinetic energy of the
electron should be a constant. But experimentally, it was observed that the electron kinetic energy has a continuous
spectrum. Considering a three-body decay process, i,e., $n \rightarrow p+e^{-}+v_{e'}^{-}$, around
1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino ($\overline{v_{e}}$) to be massless and possessing negligible energy., and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is
0.8 x 106 eV. The kinetic energy carried by the proton is only the recoil energy.
If the anti-neutrino had a mass of $3eV/c^{2}$ (where c is the speed of light) instead of zero mass, what should 'be the range of the kinetic energy K, of the electron?
