A neutron can decay into a proton, an electron, and an electron antineutrino. Th

Question

A neutron can decay into a proton, an electron, and an electron antineutrino. The antineutrino has a very, very small mass (we will take it to be zero).

a. If the neutron is at rest originally, how much energy is it possible for the three decay particles to have? The mass of the proton is 1.6726 x 10-27kg, the mass of the neutron is 1.6749 x 10-27kg, and the mass of the electron is 9.1094 x 10-31kg. Explain

b. If thepanti-?e= 3.1 x 10-22kg m/si-hat, the electron momentum ispe= 2.4 x 10-22kg m/sj-hat, and the antineutrino kinetic energy is 9.3 x 10-14J. What is the kinetic energy of the proton and the electron? Explain.

c. Would any of the decay particles (proton, electron, and electron antineutrino) be relativistic? Explain how you would find out.

Explanation / Answer

In developing the standard model for particles, certain types of interactions and decays are observed to be common and others seem to be forbidden. The study of interactions has led to a number of conservation laws which govern them. These conservation laws are in addition to the classical conservation laws such as conservation of energy, charge, etc., which still apply in the realm of particle interactions. Strong overall conservation laws are the conservation of baryon number and the conservation of lepton number. Specific quantum numbers have been assigned to the different fundamental particles, and other conservation laws are associated with those quantum numbers. From another point of view, it would seem that any localized particle of finite mass should be unstable, since the decay into several smaller particles provides many more ways to distribute the energy, and thus would have higher entropy. This idea is even stated as a principle called the "totalitarian principle" which might be stated as "every process that is not forbidden must occur". From this point of view, any decay process which is expected but not observed must be prevented from occuring by some conservation law. This approach has been fruitful in helping to determine the rules for particle decay. Conservation laws for parity, isospin, and strangeness have been developed by detailed observation of particle interactions. The combination of charge conjugation (C), parity (P) and time reversal (T) is considered to be a fundamental symmetry operation - all physical particles and interactions appear to be invariant under this combination. Called CPT invariance, this symmetry plumbs the depths of our understanding of nature. Another part of the high energy physicist's toolkit in anticipating what interactions can be expected is "crossing symmetry". Any interaction which is observed can be used to predict other related interactions by "crossing" any particle across the reaction symbol and turning it into it's antiparticle.

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