In the bets decay of `Na^(24)`, the combined electron neutrino momentum has a magnitude equal to `4MeV//c.`What is the recoil energy of daughter nucleus , given that its mass `23.99u`? Take `c=3xx10^(8)m//s` and `1u=1.66xx10^(-27)kg`.

Explanation

Here, momentum of electron neutrino pair,
`p=4(MeV)/(c)=(4xx1.6xx10^(-13))/(3xx10^(8))kgm//s`
`p=2.13xx10^(-21)kgm//s`
As parent nucleus decay at rest, according to the law of conservation of linear momentum, momentum of daughter nucleus`=` momentum of electron neutrino pair
`p=2.13xx10^(-21)kgm//s`
As mass of daughter nucleus,
`m=23.99u=23.99xx1.66xx10^(-27)kg`
`:.` Recall energy of daughter nucleus
`E=(p^(2))/(2m)=((2.13xx10^(-21))^(2))/(2xx23.99xx1.66xx10^(-27))J`
`=(4.53xx10^(-15))/(3.32xx23.99xx1.66xx10^(-13))MeV`
`E=3.55xx10^(-4)MeV`