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A neutron at rest decays. Assuming the resulting proton to remain at rest, too, find the kinetic energy of the electron and the energy of the antineutrino. |
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Answer» `Deltaepsi=(m_(n)-m_(p))xx931.6-938.2=1.4MeV` This energy is shared by the electron and the antineutrino: `Deltaepsi=epsi_(e)+epsi_(v)`, where the total energy of the electron is the sum of its rest energy `epsi_(0)` and its KINETIC energy `K_(e)`, i.e. `epsi_(e)=epsi_(0)+K_(e)`. In accordance with the law of conservation of momentum for a proton at rest `p_(e)-p_(v),orepsi_(v)/e=1/esqrt(epsi_(e)^(2)-epsi_(v)^(2))` SUBSTITUTING the value of the neutrino energy, we obtain after simple transformations `epsi_(e)=((Deltaepsi)^(2)+epsi_(0)^(2))/(2Deltaepsi),K_(e)=((Deltaepsi-epsi_(0))^(2))/(2Deltaepsi),epsi_(v)=((Deltaepsi)^(2)-epsi_(0)^(2))/(2Deltaepsi)` |
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