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04moving electron collides with stationary electron and an electron-positron pair comes into being as ? result (1 positron is posluvely charged electron) When all l...

Question

04moving electron collides with stationary electron and an electron-positron pair comes into being as ? result (1 positron is posluvely charged electron) When all lout particles have the same velocity altet the collisu: the kirietic energy required Tor Khis process IS nninum Uc reltastic eculation toshow Aitetu Gma" where ml thc resl nass ofithe clecrron

04 moving electron collides with stationary electron and an electron-positron pair comes into being as ? result (1 positron is posluvely charged electron) When all lout particles have the same velocity altet the collisu: the kirietic energy required Tor Khis process IS nninum Uc reltastic eculation toshow Aitetu Gma" where ml thc resl nass ofithe clecrron



Answers

A $0.110-\mathrm{nm}$ photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backwards. Find the momentum and kinetic energy of the electron.

Discussion of you have a photo on coming in and striking a electron in action that is at rest. This is initially not moving, but subsequently, uh, the fort on get scattered backwards. And he seemed direction that it came from 50 Elektron actually moving forward, so it gains some momentum. So we want to find what is Steve Momentum and kinetic energy for this electron kinetic energy s various. Its momentum we're gonna do is we're gonna use the conservation off momentum. Yes, well, as conservation of energy, you know, they find this too. Varies. So start off we use you can use d Compton scattering creation. All right, that is I'm the frying may know slum. They're not. I saw this is the after the whistling. After the collision, we think before the collision, she goes to each off minutes off this object, which is the electron. So the electron time see times one minus call science teacher Ready, dicey and go off defection. So in this case, the angle deflection is 180 degrees. So I is for originally in the positive, right. What's direction Then it becomes left. So he told a change in the Anglo is 180 degrees. Now we can actually find this change. Do we thank for us, my nurse. Co sign 180 degrees. This is it. Close to 4.6% Poll menace. Shoaf Just now we are given that the original we've thanks is 0.11 NATO meet us 1.1 to understand Cold minus 10. Tito therefore, we can actually find what s D with length off our fort on after the collision. All right, we just at this over to the right hand side. Get about 1.15 I'm sent home minus 10. And why do we need to use this? Well, we can use this to find what if the momentum off the fort on Given that I'm dicey close to each overpay, therefore piece goes to each other. Lunda used to use to find momentum before and after the collision. Right, sweetie? Momentum since they must be conserved, right? Initial momenta must be closely final winter, plus the momentum off our electron so we can find what is the final momentum taking each front of idee. Hey, thanks for USD 1.15 Instead, call minus 10. Excuse us. My 0.76%. Almost so. Modesty. Momentum after rental before we just have to use the orginal reef length right and the overall momentum off this system must add up to be the origin of momentum. So the current momentum for the electron is toasty, right? This in the positive direction. But our momentum for the photons afterwards SCV negative direction. So therefore e minus away the final momento. What you fought on must be closed toe the original momentum. This is in terms off magnitudes, so you can ignore these signs. Therefore, find more mental electron right to desist. E went off the electron, not defining kinetic energy. We can use the conservation off energy that s t energy off the four time it is stuck equals to the energy to the photo on afterwards, after the collision plus t kinetic energy off our electron Kenya Energy. Just the jury photo on this lady. Final energy off the photo and we can actually find this from the momentum PC energy only for their own testicles to its momentum about C. So from a previous answers, we just take this car by C plus this so, uh, minus minus A We they're smart. Bye bye. See? Frieze this you give us both some point. Eat. Stand, Paul minus 17. Use rich or in terms off. Natural in votes can invite the spy 1.6 sent home minus 19 Juice, baby. Give us for it. Textron votes.

In this problem I can write the value of the initial Is equal to two multiplication MEC Square by under hood one minus p square by c square. On simplification. I can write the expression as to multiplication point wipe 11 M. Maybe by Underwood. 1 -1999 sq. I forget to write one more night. So on solving it I get the evaluation to multiplication .511 x zero food. Food seven mm. P. Return simplification. I get devaluated 2-8.635mm. Maybe now calculating the value of the final. So here I can write the valuable. The final is equal to two multiplication. Relativistic energy. Single immune. So I can die to multiplication kinetic energy plus raised energy. Which on further simplification I can write the expression age to multiplication K plus €1.5.7 M. E B. From conservation of energy. I can write the value of E I. Is equal to E F. On further simplification, I can write 2-8 .635 mm P is equal to two multiplication K plus one day to fight .7 M. Maybe on solving it further, I can write the expression age two K is equal to 2 to 8.635 M e b minus 211 point food m e B. On solving it further. Finally, I get the value Kid 8.6175 M e B as the kinetic energy.

Here for the solution Wavelength Lambda for Tony 0.11 and M, which is equal to 0.11 multiplied by 10 to the power minus 9 m. Frank Constant is magical to 6.63 Multiply by 10 to the power my 34 j s mass. That is M see off a me off electron that 9.11 multiplied by 10 to the power minus 31 kg. Charge E on electron is 1.6, multiplied by 10 to the power minus nine. See scattering angle. Tita is equal to 1 80 degree now if Lambda equal to act by m Easy, then we can write the shift Delta Lambda is given by the Delta Lambda is equal to Lambda See Bracket one minus cost 1 80 degree hair by soldiers. We get 0.486 and m. Now the is scattered wavelength that is Lambda tm will be Lambda is equal to Lambda Plus Delta Lambda is equal to 0.110 plus 0.486 and which is equal to 0.115 n. M. The kinetic energy that s k off the recall electron will be That s K is equal to FC Lambda Delta Lambda Divide by Lambda Lambda Days. Now here we substituted the values off. Everybody will that etc Delta, Lambda, Lambda and Lambda Desk. And by calculating this, we get 478 Evie. So now the Mo mentum p off the recoil electron will be p equal to on the road. Um, e k g Here we substituted the values and sold for this. We got 1.18 multiply by 10 to the power minus 23 kg meter per second. And this is our final answer. So this is a complete solution. The step by step in until please go through this.

Hello, Josh. Here we have a 30 g V electron hitting a stationary positron. It's like an electron, but it is positive. Okay, Now we need to figure out what the available energy is for this particular reaction and to find that we can apply Equation 44.10. We have this equation here that says E a squared is equal to two m c squared times e m plus M c squared. OK, let's look at this term were quick E m is 30 g v m C squared is, uh, 0.5 11 any V or 5 11 K V. So let's read it over here. So electron rest mass is 511 times 10 to the third e v. Percy squared OK or 511. Okay, 1000 Electron bowl. Percy squared. All right, this G here means times 10 to the nine. All right, we have times 10 to the nine and times 10 to the third. That means that the force your G V is about six orders managed to larger. That means it's about 1,000,000 times larger. So this equation here is approximately well, yea is approximately equal to two m c squared times e m. And that is a good approximation. Now, if I plug in my values here, M C squared is 5 11 times end of the third evey time C squared. So it's an energy and e m is 30 g v or 30 times 10 to the ninth. Okay. Ah, and this would be under a radical if we take the skirt of both sides. Of course. Okay, So for part A, it asks for this calculation than E A is approximately ah, route too. Times 5 11 times. 10 to the third times 30 times 10 to the ninth. This is all in unit C V and that all this is under squared as well. And that is going to you 175 times 10 to the sixth e V or equal to 175 1,000,000 electron volts. Okay, Part B says, well, hey for a glider and I don't want to hit a stationary target. What energy would each incoming beam? I gotta beam of electrons coming in and I got a beam of positrons coming in. What I need to do well in a collider, all the available energies in the beam, so simply each beam would just need half of this value. Right? So the available energy, it's simply 175 divided by two mega electron volts or 87.5 mega electron volts. Okay. Thank you.


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