Beta decay is the process by which a neutron decays to a proton (which typically stays in the original nucleus) an electron, and neutrino (if we’re being technical, this is an electron-antineutrino). This is one of the processes by which a heavy nucleus with many neutrons can move back towards stability. Carbon-14 decays to Nitrogen-14 via this process. The electron and neutrino are emitted in opposite directions. The electron momentum is 1.1 x 10-22 kg m/s and the neutrino has a momentum of 5.4 x 10-23 kg m/s. a. What is the linear momentum of the nucleus after the decay? Take the electron direction to be in the positive x-direction.
b. If the mass of the residual nucleus is 2.34 x 10-26 kg, then what is the kinetic energy (in Joules) of the recoiling nucleus? In real life, the recoiling nucleus and the electron would be measured, allowing one to infer the momentum of the neutrino (this incidentally was the reason the existence of the neutrino was proposed).