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Problem 38 Hard Difficulty

An electron has a speed of 0.750$c.$ (a) Find the speed of a proton that has the same kinetic energy as the electron. (b) Find the speed of a proton that has the same momentum as the electron.


a) $1.5119$
b) $0.0236 \mathrm{~c}$


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Video Transcript

Well, according to given problem uh, kinetic energy electron is equal to Connecticut Energy of Proton. Let's plug in the values. Oh, kinetic energy Electron e's M E time C square M is the most of electrons. His the speed of light into latticed ick factor for electron minus one is equal to moss of proton Time C square into relativistic factor for proton minus want Well, In this case, we have M E square, which is equal to 0.511 mega electron Walt. And also we have MP time see scare and it's equal to 9 28 1,000,000 electron Walt. A leftist ick factor for electron is equal to one minus, uh, 0.7 Zito Hold square on then we have square root and solving this We get 1.5 119119 This through logistic factor for electron and no lamest ick factor for baton is equal to, uh, one place mass of electron times Cease creator into our logistic factor of electron minus one divided by ah muscle proton Time C square and let's plug in the values One place most of electron time. C square is 0.511 1,000,000 Electron won't into well, relentless tick factor for electron 1.5 119 minus one divided by 9 38 and therefore latticed ick factor for the tall is equal to 1.0 279 279 But ah, logistic factor we're put on is equal to one divided by r squared Rudolph one minus. We lost your proton squared divided by C suite and solving for Have you lost your proton? We can't see into square root off one minus our latest ick factor for proton minus ah two holes here and therefore we lost. Your proton is equal to zero point zero to tree six times the speed of light.

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