A free neutron at rest decays spontaneously into a proton, an electron, and an antineutrino. Given the following rest masses: Mass of neutron, m_ n = 1.00866 u Mass of proton, m_ p = 1.00727 u Mass of electron, m_ e = 0.00055 u ( 1 u = 931.5 MeV/ c² ) The maximum possible kinetic energy of the emitted electron is approximately:

Step-by-step solution

The spontaneous decay of a free neutron is given by the equation: n p + e⁻ + _ e The Q -value of the reaction is determined by the mass defect m : m = m_ n - (m_ p + m_ e ) m = 1.00866 - (1.00727 + 0.00055) m = 1.00866 - 1.00782 = 0.00084 u Converting the mass defect into energy: Q = m 931.5 MeV/u Q = 0.00084 931.5 0.782 MeV The energy Q is shared among the proton, the electron, and the antineutrino as kinetic energy. The maximum kinetic energy of the electron occurs when the antineutrino carries away negligible en