InterviewSolution
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InterviewSolution
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A stationary positive pion disintergrated into a muon and n nertrino. Find the kinetic energy of the moun and the energy of the neutrino. |
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Answer» Solution :Energy-momentum conservation implies `O=vec(P)_(mu)+vec(pv)` `m_(pi)c^(2)=E_(mu)+E_(v) or m_(pi)c^(2)-E_(v)=E_(mu)` But `E_(v)=c|vec(p_(v))|=c|P_(mu)|`. THUS `m_(pi)^(2)c^(4)-2m_(pi)c^(2).c|vec(p)_(mu)|+c^(2)p_(mu)^(2)=E_(mu)^(2)=c^(2)P_(mu)^(2)c^(4)` Hence `c|vec(p_(mu))|=(m_(pi)^(2)-m_(mu)^(2))/(2m_(pi)).c^(2)` Substituting `m_(pi)c^(2)= 139.6MeV` `m_(mu)c^(2)= 105.7MeV` we GET `T_(mu)= 4.12 MeV` Also `E_(v)=(m_(pi)^(2)-m_(mu)^(2))/(2m_(pi))c^(2)= 29.8MeV` |
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