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Problem 50 Hard Difficulty

A $\mathrm{K}^{0}$ particle at rest decays into a $\pi^{+}$ and a $\pi^{-} .$ The mass of the $\mathrm{K}^{0}$ is 497.7 $\mathrm{MeV} / c^{2}$ and the mass of each pion is 139.6 $\mathrm{MeV} / c^{2} .$ What will be the speed of each of the pions?

Answer

Therefore, the speed of each pion is 0.8279$c$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

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Marshall S.

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Video Transcript

this question is looking at the K off a que on into a positive pie own and a negative pile. So the key thing to note waas the ko indicate when he was at risk, which means that the momentum off this system is zero. And so after the decay, my Thomas frees us. Well, the next thing I know is that both off this pylons f t c miss, you have to say mess as seen from the same rest energy and given that he had to see Miss and that momentum total momentum must be zero you meet. They must move in equal and opposite directions if equal speeds in order to can so each other's momentum out right to give a total mental to be zero and since they have equal speed, they must carry equal energy. So the energy off each pion must simply be half the initial amount off energy. The initial amount of energy county come from the rest energy off our chaos. So rest energy of K on Stephen be 4 97.7 every V. So this is the energy off each pilot to find the speed off the pie on We know that the total energy it's related to its rest energy by the full in creation comma times rest, energy, labour s you not despite so rest. Energy off the pi Onus given us 139.6 MVV no, we can find. What is the speed, right? Since we have our energy of the pie. Yes, well, I mean, she's over here using or Gamma. So come on. Yes. T. Lawrence Fekter given s one. Over. Screw it off. What? Minus square C squared. Rearranging this equation. Bit of fine. Comer square. One of work on muskrat goes to minus square was square fee. Be close to see time's skirt off. One minus. Come on, square. And God, Musgrave, we can obtain from over here where I got my Sequels to total energy off Pion divided by the arrest Energy. All right, so we have to substitute this in and all. Finance overpay 2.8 to 7. Nine. See, in terms off the speed off light. So about 0.2. What was the 0.83 times the speed effect

National University of Singapore
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Zachary M.

Hope College