A neutron is an electrically neutral subatomic particle with a mass just slightl

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 1.67×1027kg) and an electron (mass 9.11×1031kg). The proton and electron were shot out back-to-back. The proton speed was measured to be 1.2×105 m/s and the electron speed was 3.1×107 m/s . No other decay products were detected.

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

Express your answer using two significant figures.

Explanation / Answer

If the neutron had zero velocity, then the momentum of the system was zero and must remain zero after the decay. So

p(proton) + p(electron) + p(neutrino) = 0
p(proton) + p(electron) = -p(neutrino)
(1.67x10^-27kg * 1.2*10^5 m/s) + (9.11x10^-31 kg * -3.1x10^7 m/s) = -p(neutrino)
(2.004x10^-22kg m/s) + (-2.82x10^-23kg m/s) = -p (neutrino)
1.722x10^-22kg m/s = -p(neutrino)

Because of the sign, the neutrino is moving in the direction opposite the proton.

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