Give the reasons forbidding each of the following decays: (a) n →p+e^-; (b) n →π^++e^-; (c) n →p

Give the reasons forbidding each of the following decays:...

Key Concepts

Conservation Laws

This concept involves the preservation of fundamental quantities such as energy, momentum, electric charge, baryon number, and lepton number in any particle interaction or decay. In analyzing decay processes, one must check that these conservation laws hold; if any are violated, the decay is forbidden regardless of other considerations.

Beta Decay and Neutrino Emission

In weak interaction processes like beta decay, a neutron transforms into a proton with the simultaneous emission of an electron and a neutrino (or antineutrino). The neutrino is essential not only to conserve lepton number but also to balance momentum and energy. Omitting it disrupts these conservation requirements, rendering the decay process forbidden.

Energy and Momentum Conservation (Kinematics)

Every decay process must obey energy–momentum conservation. This means that the rest mass of the initial particle must be sufficient to account for the masses (and the kinetic energies) of all the final state particles. If the mass difference between the initial and final particles does not accommodate the production of a new particle or provided kinetic energy, then the decay cannot occur.

Angular Momentum and Parity Selection Rules

Decays must also satisfy the conservation of angular momentum and parity. In processes involving particles with intrinsic spin and associated angular momentum (such as photons, which are spin?1), proper matching of total spin states and parity before and after the decay is required. If the transition would violate these quantum number rules, the decay is forbidden even if other conservation laws are met.

Transcript

00:01 In this question we are given five different reactions and decays and want to determine what conservation laws are violated for these different decays because we are given that they are forbidden decays so the four different conservation laws are listed on the right and this is what we will check them against to see which one they actually violate starting from the easiest which is the charge followed by barren number then laptop number and finally the strangeness value so for the first decay very obviously we see that the charge is the same both are minus one but and there's no barons involved only lapton's and we see that there's only one of each type of one of muon, one electron.

01:02 And so definitely we would know that the muon laptop number as well as the electron number will not be conserved.

01:12 So this actually violates number three.

01:17 For the second equation, we are looking at decay of the neutron.

01:24 For the charge is neutral, so zero on both sides.

01:30 Now looking at the lepton number, the electron on the right gives a electron lepton number of plus one.

01:43 The neutrino also gives plus one, so we have a total of plus two on the right hand side, but on the left we have no leptons.

01:53 So the lepton number is not a conserved again, so it violates number three.

02:00 For the next equation we see very obviously that there's a positive charge on the proton on the right -hand side on the left is neutral so this actually violates charge conservation and also furthermore it also called it actually also violates strangeness because our lambda barion contains a strange quark which means that its strangeness value is minus 1 but on the right there's no more strange clock so stranger's value is 0 and so it also violates number 4 now moving on the default equation we see that the charge is both positive 1 on both sides the barrel number however the proton is a barrel so we have have barrier number one...

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