In the β disintegration considered in Exercise 1, the electron has a mass equivalent to a rest energy of 0.511 MeV, while the neutrino has essentially no mass. What are the total energies carried away by the electron and neutrino? What fraction of the nuclear mass is converted into kinetic energy (including the electron rest energy)?
Exercise 1
A nucleus, originally at rest, decays radioactively by emitting an electron of momentum 1.73 MeV/c, and at right angles to the direction of the electron a neutrino with momentum 1.00 MeV/c. (The MeV, million electron volt, is a unit of energy used in modern physics, equal to 1.60 × 10−13 J. Correspondingly, MeV/c is a unit of linear momentum equal to 5.34 × 10−22 kg•m/s.) In what direction does the nucleus recoil? What is its momentum in MeV/c? If the mass of the residual nucleus is 3.90 × 10−25 kg what is its kinetic energy, in electron volts?
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