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Problem 47 Hard Difficulty

Integrated Concepts The primary decay mode for the negative pion is $\pi^{-} \rightarrow \mu^{-}+\overline{\nu}_{\mu}$ (a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much $\pi^{-}$ is at rest when it decays? You may assume the muon antineutrino is massless and has momentum $p=E / c,$ , just like a photon.

Answer

a. 33.90 $\mathrm{MeV}$
b .4.12 $\mathrm{MeV}$ 29.78 $\mathrm{MeV}$

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Physics 103

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Chapter 33

Particle Physics

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Video Transcript

I'll minus. They came to mule plus the mu neutrino count entertainer And we want to know what is the energy release in? Maybe investigate. But the energy release will be the difference in the rest mess. We are so many of them. Very nice massless. So we have that don't energy is mass of the bio minus minus mass off the mule I'm say square and then this is just one under 39 seven my eyes 105.65 and maybe And this gives a difference in energy off 33.9 maybe no for but be wanting to know what is the energy off the moon and the move Anti neutrino using that the conservation of momentum and that the under neutrino is massless So we have from conservation on the form off the former mental we have that the in form a mental off the pile knew Is it going to the formal mental off the mule plus the former mental off the continue training And for the zero component this is just the energy. So we have m pile is equal toe energy off the human minus plus energy off new you and then for the special part This guy doesn't have any momentum. And then this is masculine. So we have that zero Izzy Goto if you view minus bless you me bar you So can you things too. So for the momento off the meal so we can write this us even you minus minus mu minus. Now we can use the iisten relation for the energy off the mule. So we have that and you Minuses square isn't goto e new miners square minus b New mind square we can write. Rearrange this So let me right here The questions have you So we have this equation e meu minus minus minus. And I will have new square is equal to the new minus where managers, people, new minds square You could write this us in you minus less being you minus even you minus minus B minus. We solicited this fire here and then we find a relation. So with president here and there some to find that e meu minus is 1/2 and bile plus m u square over empire. So we using the values that we got, we have energy off 109. When? 77 And maybe so. This is the total invasion. We have to remove the rest mass initial toe. Find a kinetic energy for the more so we have for the mule in the kinetic energy is 109.77 That this day, Dr Energy mine is 105.65 So you have any off 4.12 maybe. And then the other energy we found by using the the relation that view new miners is equal to minus He knew bar. And then this is equal to minus work. Huh? Off we have to. We have this relation here. We have toe to track this. So we have and muse where? Minus m pi minus and by and then this gives us the energy off 29 0.7 night. And maybe so. This is the energy for the pile. And this is the energy for the internal Torino

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