Question

A neutron is an electrically neutral subatomic particle with a mass just slightly greater than that of a proton. A free neutron is radioactive and decays after a few minutes into other subatomic particles. In one experiment, a neutron at rest was observed to decay into a proton (mass 1.67××10−27−27 kgkg) and an electron (mass 9.11××10−31−31 kg). The proton and electron were shot out back-to-back. The proton speed was 5.0 ××1055 m/sm/s and the electron speed was 3.0 ××1077 m/sm/s. No other decay products were detected.

How much momentum did this neutrino “carry away” with it?

Answer 1

(1) Mass of proton Mp = 1.67 x 10^{−27} kg;

Mass of electron Me = 9.11 x 10^{-31} kg;

Initial momentum is zero as neutron was at rest.

since, neutron was observed to decay into a proton and electron, due to the force of attraction they will move towards each other therefore if speed of proton is in -ve direction then speed of electron will be in +ve direction. Thus;

final speed of proton Vp = - 5 x 10^5 m/s;

final speed of electron Ve = 3 x 10^7 m/s;

Solution:

momentum of proton;

momentum of electron;

let the momentum of neutrino carry away is Pn, therefore applying conservation of momentum;

final momentum of {electron + proton + neutrino} = Initial momentum of neutron