Find the kinetic energy of the recoil nucleus in the positronic decay of `N^(13)` nuleus for the case when the enrgy of positrons is maximum.

Explanation

The `K.E` of the positron is maximum, when the enrgy of neurino is zero. Since the recoil energy of the electron is quite small, it can be calculated by successibe approximation.
The reaction is
`n^(13) rarr C^(13)e^(+)+V_(e )`
The maximum enrgy available to the postiron(including its rest enrgy) is
`c^(2)("Mass of " N^(13) "nucleus-Mass of " C^(13)"nucleus")`
`=c^(2)("Mass of "N^(13) "atom-Mass of " C^(13) "atom" -m_(e ))`
`0.00239c^(2)-m_(e )c^(2)`
`=(0.00239xx931-0.511)MeV`
`=1.71MeV`
The momentum corresponding to this enrgy is `1.636MeV//c`.
The recoil energy of the nucleus is then
`E=(p^(2))/(2M)=((1.636)^(2))/(2xx13xx931)= 11 eV= 0.111 keV`
on using `Mc^(2)= 13xx931MeV`