A neutron initially at rest, decays into a proton, all electron and an antineutrino. The ejected electron has a momentum of 14 × 10-28 kg-m/s and the antineutrino
6.4 × 10-27 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 = 1.67 × X 10-27 kg.
Let the velocity of proton be ‘v’ m/s
(a.) Applying conservation of momentum,
Initial momentum of neutron = momentum of electron + momentum of proton + momentum of antineutrino
0 = 1.67 × 10-27 × v + 1.4 × 10-27 + 6.4 × 10-27
–1.67 × 10-27 × v = 20.4 × 10-27
v =–12.2 m/s
Velocity of proton is 12.2 m/s in direction opposite to electron and antineutrino.
(b.) Resultant momentum of electron and antineutrino
Applying conservation of momentum,
Initial momentum of neutron = momentum of electron + momentum of proton + momentum of antineutrino
0 = 1.67 × 10-27 × v + 1.4 × 10-27 + 6.4 × 10-27
-1.67 × 10-27 × v = 1.4 × 10-27 + 6.4 × 10-27
v = -9.2 m/s
Velocity of proton is 9.2 m/s in opposite direction to resultant of momentums of electron and antineutrino.