A neutron initially at rest, decays into a proton, an electron and an antineutrino. The ejected electron has a momentum of `1.4xx10^-26` kg-m/s and that of antineutrino `6.4xx10^-27` kg-m/s. Find the recoil speed of the proton a. if the electron and the antineutrino are ejected along the same direction and b. if they are ejected along perpendicular directions. Mass of the proton `1.67xx10^-27`kg.

Explanation

Mass of proton =`1.67xx10^-27`kg
`Let V_P` be the velocity of proton. Given, moment of electron
`=1.4xx10^-26kgm/sec `
and momentum of antineutrino
`=6.4xx10^-27kgm/sec`

a. The electron and the antineutrino are ejected in the same direction.
As the total momentum is conserved the proton shoud be ejected in the opposite direction.
`1.67xx10^-27xxV_P`
`=1.4xx10^-26+6.4xx10^-27`
`=20.4xx10^-27`
`:. V_P=(20.4/1.67)`
`=12.2m/sec` in the opposite direction.
b. the electron and ntineutrino are ejected perpendicular to each other.
Total momentum of electron and antineutrino
`=sqrt((14)^2+(6.4)^2)xx10^-27kgm/s `
`rarr V_P=(15.4xx10^-27kg-m/sec)/(1.67xx10^-27kg)`
`:. V_P=9.2m/s`