from where does the beta(negative) particle get velocity from?

Question

a neutron decays into a electron a proton and an antineutrino,the proton stays in the nucleus,why does the electron come out though it is attracted by the positively charged nucleus,from where does it gain energy to come out of the nucleus?

Answer 1

The kinetic energy arises because the rest mass of the neutron is larger than that of a proton.

Add up the rest masses of the decay products. The difference between the resulting rest mass and the initial rest mass is available as kinetic energy to the decay products.

Answer 2

The neutron's rest mass is more than that of the sun of the particles produced on its decay. This mass defect appears as the kinetic energy of the electron and antineutrino, the antineutrino getting the major share of the energy, for purposes of momentum conservation. The electron escapes the electrostatic potential barrier of the positive nucleus as if by ionisation of an atom, the requisite ionisation energy being supplied by its kinetic energy. The neutron can be visualized as a proton-electron (H-atom) system, from which the electron escapes if it has the requisite 13.6eV energy for ionisation. The electron and antineutrino are the decay products of an intermediate virtual W^- boson, so the decay is governed by the weak force and the proton is held in the nucleus by the strong force, to which the electron and antineutrino, being leptons, are not subject.