Problem

What is the kinetic energy in MeV of a $\pi$ -mes…

04:03

Problem 56 Hard Difficulty

A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet, they annihilate, converting all of their mass into energy. (a) Find the energy released, assuming negligible kinetic energy before the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is velocity? (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity?

Answer

(a) $1.64 \times 10^{-13} \mathrm{J},(\mathrm{b}) 1.34 \times 10^{7} \mathrm{m} / \mathrm{s},(\mathrm{c}) 2.89 \times 10^{8} \mathrm{m} / \mathrm{s}$

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Physics 103

College Physics for AP® Courses

Chapter 28

Special Relativity

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Video Transcript

Well, uh, wrist muscles. One electron m is equal to buying 0.11 multiplied by 10 to the power minus 30 bond kilogram and speed off light C equals 3.0 multiplied by 10 to the power eight meter per second and ah, the total rest mass energy off the electron positron pair. Ah, total energy is a cool too. Two times months off electron times C square and this is equal to to multiply by Most of electron is 9.11 multiplied by 10 to the power minus 31 Motive live I see his 3.0 Multiply by 10 to the barber ate all square and therefore total energy off the pair Physical to 1.64 Multiply by 10 to the power minus 13. Jules All right. Uh, no. Ah! Kinetic energy e is equal to gamma minus one times M c square, M C square. And here I am is the moss of proton. Therefore, we have m mass of raton and most of Britain is a call to 1.6 multiplied by its must've positron, not proton. Excuse me. 1.6 multiply returned to the power minus 27. Um, well, Soling for, uh, gamma. We have gamma physical, too divided by ah moss off Rosie Traum. Time C square less one. And this uses 1.64 multiplied by 10 to the power minus 13. Do you find it by the most of positron is 1.6. Multiply by 10 to the power minus 27. Multiply by three molted live I tend to the bar for eight whole square and therefore got more is equal to 1.1 No, we have Ah, gamma is equal to well, one divided by one divided by a squared Rudolph one minus. We squared, divided by C square and solving for re we have we is equal to see into square rode off one minus one minus one divided by normal square Let's plug in values we equals three multiply by tend to devour it into one minus one, divided by 1.1 all square and therefore we is equal to well, we is equal to 1.34 Multiply by 10 to the power seven leader for a second. Hence the velocity of the proton will be Ah, one point. Ahh. 34 multiplied by 10 to the power seven leader per second on. Right? No. Let's. Um um uh, let's find out. Uh, the gamma Well, we know that gamma can be regiones e divided by most of electron times C square. And we know that on plus one as well. And we know that he divided by massive electron time C square is equal to two. And therefore we have gamma physical 22 plus one and excuse us train. And hence the velocity off the electron will be We is equal to see into one minus, uh, one divided by gum square. Deal for V equals three. Multiply by 10 to the power eight into one minus one, divided by three square on This gives us 2.89 Multiply by 10 to the power eight meter per second. Eight meter per second.

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