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.

Explanation

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`