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Determine which of the reactions below can occur. For those that cannot occur, determine the conservation law (or laws) that each violates.

$$

\text {(a)} \mathrm{p} \rightarrow \pi^{+}+\pi^{0} \quad \text { (d) } \mathrm{n} \rightarrow \mathrm{p}+\mathrm{e}^{-}+\overline{\nu}_{\mathrm{e}}

$$

$$

\text {(b)} \mathrm{p}+\mathrm{p} \rightarrow \mathrm{p}+\mathrm{p}+\pi^{0} \quad \text { (e) } \pi^{+} \rightarrow \mu^{+}+\mathrm{n}

$$

$$

\pi^{+} \rightarrow \mu^{+}+\nu_{\mu}

$$

(a) Conservation of charge/baryon number is violated. (b) Allowed (c) Allowed (d) Allowed (e) Conservation of baryon number/lepton number is violated

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Hope College

University of Sheffield

McMaster University

this question. We have this following five reactions and the mean whether take and occur or not. So we're gonna look at the conservation laws. I'm Syria, that the violators So the tree, different steps we're gonna use for all of distractions is gonna look at conservation off charge and then conservation off, bury on number. And then finally, conservation off the left on number. If there are any left, owns involved indirection, right? So they're starting with your first question. First off the charge on the left in sight. It is a trash plus one for the proton on the right. The pi plus in pi zero. So told her trashes pass one. So that's conserved for the barrel number. Boat on heavy baron number off plus one body baron number 40 pion zero. Right, cause the army zones so they have zero by barrel number and so barren number is not conserved. So it violates number two. Moving on the Knicks creation. Total charge is plus two plus two. So is conserved 40 baron number. It's also plus two and pass to. That's fine. The electron number. There's no laptops involved, So this is a lot so this question must be allowed next one charge plus one plus one. So that's fine. Burial number. They have no Barents. So it's fine for lepton number. Phone number for me, One for the anti me one. This is minus one for the neutrino. This is plus one. So it is a total zero. Never inside definable Lipton's. So there is zero as well. So it is conserved. So this is allowed knicks for the fourth equation. The church is zero left on the right. The proton is plus one in. Actually, it's my different. So total is zero s Well, so that's good is conserved the barrel number there is plus one from the neutron and plus one for the proton and so they're both conserve. Then you're looking at the lepton number the electron, his elect a number off plus one and the anti neutrino Yes, a left on the both minus one. So that is conserved. This gives zero, which is zero on the left hand side as well because they're store left turns over there So it is conserved Next The last equation the church It's plus one plus one on both sites. So that's called served for the barrel number. The pie plastics Amy's own. So there's no baron anyone see? No, it's a left on, so there's no burial number, but the neutron you see barrel right. So there's a burnable plus one. You can see the bear and the boys plus one on the right, but zero the left so barren number is not conserved, so it violates number two. And furthermore, it also violates the lepton number, right, because there's a leapt on over here. I mean and team your own. So this is a minus one told number. But on 11 site, there's no left aunts. So actually, he also violates our left on conservation. Yes, well.

National University of Singapore