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Taking the value of atomic masses from the tables, calculate the kinetic energies of a positron and a neutrino emitted by c^(11) nucleus for the case when the daughter nucleus does not recoil. |
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Answer» Solution :We assume that the parent nucleus is at rest. Then since the daughter nucleus does not RECOIL, we have `vec(P)= -vec(P)_(v)` i.e., positron & `v` momentum are EQUAL and opposite. On the other hand `sqrt(C^(2)p^(2)+m_(e )^(2)c^(4))+cp=Q=` TOTAL energy released. (Here we have used the fact that energy of the neutrino is `|vec(P)_(v)|=cp`) Now `Q=[ ("MASS of "C^(||)"nucleus")-("Mass of "B^(||)"nucleus")]c^(2)` `=["Mass of " C^(||)"atom-Mass of " B^(||)"atom"-m_(e )]c^(2)` `=0.00213 am uxxc^(2)-m_(e )c^(2)` `=(0.00213xx931-0.511)MeV= 1.47MeV` Then `c^(2)p^(2)+(0.511)^(2)=(1.470cp)^(2)=(1.47)^(2)-(1.47)^(2)-2.94cp+c^(2)p^(2)` Thus `cp= 0.646 MeV=` energy of neutrino Also `K.E`. of electron `=1.47-0.646-0.511= 0.313MeV` |
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