Question

State which of the following reactions are allowed by conservation laws and which is forbidden, and give the reasons in either case:

1-

State which of the following reactions are allowed by conservation laws and which is forbidden, and give the reasons in either case: 1- pi^0 arrow e^++e^- 2- P arrow n+e^++ve 3- mu^+ arrow e^++e^-+e^+ 4- mu^+ arrow e^+ + gamma

2- $P\rightarrow n+e^{+}+\upsilon{_{e}}$

3- $\mu ^{+}\rightarrow e^{+}+e^{-}+e^{+}$

4- $\mu ^{+}\rightarrow e^{+}+\gamma$

Answer 1

Answer 2

Conservation of Baryon Number Nature has specific rules for particle interactions and decays, and these rules have been summarized in terms of conservation laws. One of the most important of these is the conservation of baryon number. Each of thebaryons is assigned a baryon number B=1. This can be considered to be equivalent to assigning each quark a baryon number of 1/3. This implies that the mesons, with one quark and one antiquark, have a baryon number B=0. No known decay process or interaction in nature changes the net baryon number. The neutron and all heavier baryons decay directly to protons or eventually form protons, the proton being the least massive baryon. This implies that the proton has nowhere to go without violating the conservation of baryon number, so if the conservation of baryon number holds exactly, the proton is completely stable against decay. One prediction of grand unification of forces is that the proton would have the possibility of decay, so that possibility is being investigated experimentally. Conservation of baryon number prohibits a decay of the type but with sufficient energy permits pair production in the reaction B1+111-1 The fact that the decay is observed implied that there is no corresponding principle of conservation of meson number. The pion is a meson composed of a quark and an antiquark, and on the right side of the equation there are only leptons. (Equivalently, you could assign a baryon number of 0 to the meson.) Conservation of Lepton Number Nature has specific rules for particle interactions and decays, and these rules have been summarized in terms of conservation laws. One of the most important of these is the conservation of lepton number. This rule is a little more complicated than the conservation of baryon number because there is a separate requirement for each of the three sets of leptons, the electron, muon and tau and their associated neutrinos. The first significant example was found in the decay of the neutron. When the decay of the neutron into a proton and an electron was observed, it did not fit the pattern of two-particle decay. That is, the electron emitted does not have a definite energy as is required by conservation of energy and momentum for a two-body decay. This implied the emission of a third particle, which we now identify as the electron antineutrino. nep te The assignment of a lepton number of 1 to the electron and -1 to the electron antineutrino keeps the lepton number equal to zero on both sides of the second reacton above, while the first reaction does not conserve lepton number. The observation of the following two decay processes leads to the conclusion that there is a separate lepton number for muons which must also be conserved. The first reaction above (decay of the pion) is known to be a two-body decay by the fact that a well-defined muon energy is observed from the decay. However, the decay of the muon into an electron produces a distribution of electron energies, showing that it is at least a three-body decay. In order for both electron lepton number and muon lepton number to be conserved, then the other particles must be an electron anti-neutrino and a muon neutrino .