an-x-ray-photon-with-a-wavelength-of-0240-nm-scatters-from-a-free-electron-at-rest-the-scattered-pho

Question

An X-ray photon with a wavelength of 0.240 nm scatters from
a free electron at rest. The scattered photon moves at an angle of
$125^{\circ}$ relative to its incident direction. Find (a) the initial momentum and (b) the final momentum of the photon.

Zulfiqar Ali · Accepted Answer

Revenant off extra food on lender is equal to zero point 240 nana meters. This is equal to 0.24 Zito multiply by 10 to the power minus nine meters. You are initial momentum off. Electron is equal to zero and angle of the scattered foot on angle of the scattered for dawn Peter is equal to 1 25 degrees. Artie here. What is the initial momentum off the foot on? Well, let&#x27;s calculate change in valence. Change in violent equals. It&#x27;s divided by Mars. Off electron multiply. They speed off light into one minus co Sign off. Peter, who signed Tita and Changing Dublin, equals it is Ah, 6.63 multiplied by 10 to the power of minus 34. Divided by mass off electron is 9.1, multiplied by 10 to the power minus 27. Ah, sorry. It&#x27;s minus 31 27. It&#x27;s minus Ah um minus cutie bun minus 31. Multiply the speed of light is three. Multiply may tend to devour eight meters per second. One minus school signed theories 25 Big rates change in gavlin is equal to zero point free. 81 multiplied by 10 to the power minus 11 meters. And this gives us, uh, three point H one multiplied by 10 to the power minus two out majors. This is the change in violent. We know they changing. Valent equals lander prime minus lender Linda Prime is the prevalent after the foot on scatters the prevalent of scattered foot on is Lambda Crime. Well changing babble in these three point 81 multiplied by 10 to the power minus 12 is equal to Lambda Prime minus Landa land, a zero point 240 multiply by 10 to the power minus line and therefore Lambda Prime equals 2.44 multiplied by 10 to the power minus. Then maters no, let&#x27;s calculate initial momentum off dawn. So Manta Michel&#x27;s age, divided by Lambda, it is playing constant 6.63 Multiply by 10 to the power minus 34. Divided by Lambda and lander is 0.240 Multiply. We tend to the bar minus nine, and this gives us 2.8. Multiply by 10 to the power minus 24 minus 24. Kimmel Graham Major for a second and final moment. Um, momentum off the foot on after it scatters, it is etched divided by land, a prime. Let&#x27;s plug in the values, which is 6.63 Multiply return to the father minus 34 divided by lender Prime is a 2.4 forward. Multiply me 10 to the power minus 10 and then four. Final momentum is Ah, 2.7, multiplied by 10 to the power minus 24 kill around meter or second.

Jayashree Behera · Answer

So we know that an idea off a foot on Misic Waldo plant constant time frequency off the bone. And since frequency can visit and as C over Lando&#x27;s so we can use this expression as well to find energy off before dawn? No, by competent effect, they have this equation where each over emcee is a constant and that is that constant cannot separate. And as Lambda see standing forward, the Compton equivalent Lander dash is the reverend off the scattered for Don Don Geiss of England off the original photo on that, that is just a scattering angle and m iss the electron breast mass. Also, the momentum off a fort on can be found by dividing the energy off food on with speed off light On using this to expressions. Over here we find mo mentum bagel toe edge F oversee or etch over Landa and being able to get over Lambda. So that&#x27;s a very common expression. That civilian probably are prevalent in question, so you must be familiar off the this aggression before. So no, let&#x27;s jump overto the first part of the problem. So with the news question, do here. So according to a Christian, too. You can find London us to be called to land a plus. Lambda. See dying&#x27;s one Linus, close fight. Andi five is 1 80 degree over here, Lando, See, is one old large Landis E. Is it or what? M. C. It is planned concert, and this is equal to 6.626 times 10 to the five, minus 34 jewels seconds and is 9.1 times 10 to the minus 31. Kid. Jeez, saving the speed off life is equivocal. Three times the money me defense ticket and Landa is given Toby 0.990 meter. So this is lamb. 1,000,000,000 units off meters. Tsunami can substitute all these values over here on that gives us Lambda Dash. Toby Mine point 485 signs tend to the part minus 11 meter. So now that we have land a dash, which is energy off the skater photo on, we can find the Surya landed ash is the equivalent off the scattered photo. So now they can use a question one another to find the energy off the scattered for Tom. So e dash is it&#x27;s the overland a dash. So We&#x27;re using a question one over here on DDE again substituting the values. We get this on Serge to be don&#x27;t bind Cedo 942 times tend to the bar minus 15 minutes. So that&#x27;s the energy. And then three dads can be found by using good question trees. This is equal. Do you dash oversee on it over land a gash And that comes out to be six point 986 time stent of the bond minus 24. They gave me double a second. So, Dex, the first part to the problem. So instead of finding e dash on, then finding the momentum, you can definitely find B dash Bye. Using the second part off the Arctic Ocean. So by the day, broadly reverend equations appease equal to theta Rolanda. So once you have Lambert Dash, you can directly use the question three in order to find me dash without without our doing no without finding the energy. So this process is actually not me daily conveniently use readers. She could do it over land. Redash on, find this answer now in the second part So we have e want to be equal to energy off the scattered forth on less kind of energy. So, Katie, then we goto e one minus e dash and e one is and a g off the original for dawn on e dish is energy off the scattered for dawn so that I already found over here. But if you are are directly going from a question one to question tree, then you might need to find a potential here as well. This is basically it&#x27;s your body and then he dishes. It&#x27;s It&#x27;s you, Belinda Dash. So now you can against substitute Landa and landed us over here. Orlando and E Dash over here. If you already have in Dash calculated and sold for the kind of dependency and doing so you&#x27;ll find this value. Toby. 1.1296 times 10 to the barge minus 16. Jules on DDE. We know that the one electron volt is 1.6 years two times tended upon minus 19 jewels so we can divide this factor over here on fight. The kind of dignity in units off electron volts on DDE that comes out to be 705 struggles. So the energy off the incident for dawn is 13.8 killer yet strong, bold on dhe. Therefore, only 5% off its energy is transferred to the electron in down in your so as the kind of big energy off the electron.

Katie Mcalpine · Answer

Okay, so in this problem, we have an incident. X ray photonic has a wavelength of 0.900 So I&#x27;ll write that down. Lambda equals 0.900 nano meters and we know it&#x27;s scattered 180 degrees and that&#x27;s the incident. Proton. So 5 180 degrees. And we want to know how much momentum does the electron get? So, um so basically, the photons kind of coming in getting back scattered out, and then the electron leaves with some energy. So whatever changing moment of the photons has will be picked up by the electrons. Let&#x27;s find the change in momentum by the proton. First, let&#x27;s get the wave like that. This photons. We want to use that with the usual Compton scattering for So Lamda Final isn&#x27;t Lambda initial plus each over M c. Ramus Mass of the electron C is the speed of light times one minus the co sign him the angle between the initial and final momentum vector. And that&#x27;s gonna be FIEs kind of be 1 80 So that&#x27;s gonna make this whole thing, too, because the coastline of one eighties negative 11 my segment was too. So plugging all of that into a calculator I decorated beforehand I get that the wave like this 0.94859 point five nano meters and all around The final answer to, um I guess it should have 36 figs. Um, open the tomb. Very nineties there. Yes, Wonderful. Um And so now let&#x27;s calculate the change of momentum. So the momentum of a foe time, as shown in the book, is each over Lambda. So the change in momentum is gonna be each over Lambda Final Tau Lambda Final. Let&#x27;s say that this direction is negative in this direction is positive. Um so let&#x27;s just kind of calculate the magnitude of the change of momentum. And then we could say that that&#x27;s the change of much of the electron, its insurgents at rest. That&#x27;s what the electron will gain. Um, and I&#x27;ll probably see that again towards the end. So it&#x27;s gonna be Lambda final, and then this. I&#x27;m just gonna use the magnitude of blamed a final, and then Lambda Final is in. It&#x27;s gonna be the negative direction. And then Lambda initial is gonna be in the positive direction but we want to subtract it, because in general, if you&#x27;re finding the change in the quantity of quantity, you want to subtract final minus initial. So, um so that&#x27;s what we want to evaluate. And then when I did that, I got 1.435 times, 10 to the minus 23 kilogram meter per second. And then if we want to get the, um, energy of the electron we want, I just use the formula. K e is so it&#x27;s one. Haven&#x27;t be square, but if you put in terms of momentum given them, momentum is empty. You get that? It&#x27;s equal to P squared. One formula is peace. Word over to M. So plugging in p here, What I got is, um seven, 701 e b. And then I guess I should I should only use 3366 So, yeah, I will stick with 701 p p dodge of my calculations. Nine 0.430 I didn&#x27;t actually used to write the work six weeks here. That so my I might need to update my answer where sometimes six. He Oh, Okay, So I actually got 705 now, So I&#x27;m gonna go ahead and update

Elan Stopnitzky · Answer

All right. So this is the formula that relates on the change in wave length to the scattering angle. And we&#x27;re told that the wavelength after scattering is 0.830 Nana meters, Um, we&#x27;re told that the photon is sent back in the same direction that it started in, so the scattering angle is 180 degrees or pie pi ratings. So one minus co sign pi equals one minus negative one, which is too. Okay. So if we want to know the original wavelength we have land is equal to land the prime minus two h over M C and his 9.11 times 10 to the negative 31 kilograms h is 6.63 10. Send the negative 30 for Jules Doc seconds and C is three times entity meters per second. So if we plug everything in what we get is that the new or sorry that the original wavelength is 0.781 Nana meters pretend to the negative nine medals in part B. We want to know what Mo mentum is imparted by the electron. Sorry, what moments was imparted to the electron by the scattering of the photons. So basically, by momentum conservation, the mo mentum change of the photons has to be compensated for by the moment and change with the electron. So using the grubbly relation we have adult pee is equal to each overland minus negative h over land of crime. And we have the negative in here because Momenta me&#x27;s a vector. Quantity is we need to be careful about signs so plugging everything in What we get is that this is 1.65 times 10 to the negative 23 killer grounds. Times means per second. Now, if we want to know their kinetic energy of the electron that&#x27;s given by p squared over to m plugging in the value of P that we got in part B and the value of M for an electron that I&#x27;ve written up here. What this comes out toe 1.49 times 10 to the negative 16 Jules

Zulfiqar Ali · Answer

we&#x27;ll x ray put on scattered it 100 five degrees relented ve to the incident direction Um, and the foot on skaters from ah free electron addressed. So 115 degrees is the scattering Advil, uh, part of it, Reverend Off Scattered foot on is 0.3 to 0 nanometers, so wrap laid off. Scattered for tone Lambda Prime equals zero point preto zero nanometers and to the 0.3 to 0 nanometers. Eyes equal to zero point tree, too. 00 multiplied by 10 to the power minus nine meters. Well, now let&#x27;s calculate incident for Don&#x27;s lab lint, you&#x27;ll find on lender land Land days The Babel int off incident for dawn We know that change in Dublin equals It&#x27;s divided by months off electron times speed off light into one minus go sign pita. And in this case, theta equals 115 degrees are here for ich divided by Marcel&#x27;s electron times A speed of light into one minus Go sign off 115 degrees and this gives us I delta lambda change in Dublin vehicles each divided by mass of electron times. Speed off light into one. Uh plus zero point four on. Then we have changing. Bubbling equals 1.4, multiplied by 6.63 Multiply by 10 to the power of minus 34. Divided by mass off electron is 9.1, multiplied by 10 to the power minus 31. And then speed off light is a three month supply. Me 10 to the power eat meter where second and then forward changing Devlin. Uh, it&#x27;s equal to 3.4 Tradepoint for multiply my 10 to the power minus 12 minus 12 meters. Okay, well changing. Revel in candy regiones Alemdar prime minus lambda. And therefore lander, you choose that little incident for dawn equals, um lived a prime minus change in javelin. And this gives us Lambda equals. Let the prime is all zero point zero point tree to zero little 0.3 to 0. Multiply my 10 to the power. My niece is mine minus. Then we have changing Ballantyne changing Valenti&#x27;s three point forward. Multiply my 10 to the power minus 12 meters. And then for Lambda equals, um lender equals 3.17 3.17 Multiply. We turned to the power minus 10 meters minus 10 meters and this can be regiones leather equals a 0.0 point 317 nanometers. Lambda equals Is it a point to a tree? 17 nanometers? So let&#x27;s old Barbie energy or photon is given by a Jeff, and I just can&#x27;t be written. Is each see divided by lambda? No. Let&#x27;s calculate energy of incident for dawn. Um, will calculate energy or incidental Dawn and Sid don&#x27;t foot on what on? Let&#x27;s plug in the values A equals 6.63 multiply by 10 to the power minus 34 multiplied by three. Multiply returned to the power it divided by, um lander is 0.317 months of life returned to the bar minus nine. And this gives us, um 62 point 74 Multiply by 10 to the power minus 17 jewels minus 17 jewels. No, let&#x27;s convert this into electron walls. Ah, 62.74 multiplied by 10 to the power minus 17 jewels. Uh uh. Hey is 62.7. Ford multiplied by 10 to the power minus 17. Divided by 1.6 multiplied by 10 to the power minus 19 minus 19 electron waas and this gives us, um, this gives us 39.2 39 points to multiply. Returned to the power to electron boards, and this can be region is 3.92 kilo electron balls. So energy of incident for dawn is 3.92 kilo electron vote. Now let&#x27;s calculate energy off. Scheduled for dawn energy off scattered, put on scattered energy of scattered put on well energy is given by etc. Divided by lend a prime. Let&#x27;s plug in the values, which is 6.63 Multiply with 10 to the power minus 34 multiplier e speed off light is three. Multiply. Return to the bar eight, divided by lender prime is 0.0 point 3 to 0, multiplied by 10 to the power minus nine. And this gives us e equals 62 point 62.16 multiplied by 10 to the power minus 17. Jules, let&#x27;s express this number in electron volts. Therefore equal 62.16 Multiply. We tend to the bar minus 17 divided by uh divided by 1.6 multiplied by 10 to the power minus 19. And this gives us Carty. And on eight 38 point it multiplied by are 10 to the power to electron world. On this can be written his three point it 3.88 kilo electron bald. So energy of scattered for dawn is 3.18 Killer electron world. No, let&#x27;s calculate the kind of dick energy off record Electron part. See? Well, we know they, um, gonna dig energy equals, um kinda tick energy equals R h c, divided by Linda Exceeded. Guided by lend a minus. Uh, let&#x27;s see, Divided by lender Prime So kinda thickeners e equals, etc. Divided by lambda is three point a nine to kill electron balls minus etc. Divided by lender prime is 3.8 kilo electron balls and therefore kinetic energy off record electron equals ah 0.4 killer electron volt. And this came The region is 40 electron volts

Ren Jie Tuieng · Answer

minus content scattering problem. You have an incoming X ray hitting a free electron that it&#x27;s at rest and it gets reflected back in D makes it same direction. The exact opposite direction A total scaring anger off 180 degrees. We are not given the original whistling A rather recommended scattered we think offers your points your trees, your millimeters notifying Wasti riffing off the initial incident 14 So we know that from the contents catering equation timeto right now. So you show we think this some top prying my next Linda supposed to h of m C one minus sign fight. So we&#x27;re sure to get the origin wavelength, which is just to be loved a prime minus each of them See minus sign fight. We don&#x27;t eco sci fi, no sign of 180 degrees. It&#x27;s ah, negative one. So, as a result, this becomes, if any off to So this is just two times off issue over and see you can actually fed it is quite easy, right? And Mr Kits, you tell you well, for about your points, your 781 NEDA Metis. Okay, so this is summer or is, you know, incident reflex not to find any momentum off the electron right after it moves off. You know that since this collision is a one dimensional collision, there is only one direction. Ah, what excess? For its momentum. So using conservation of momentum in this access, we should be fine, right? The evil mentality Electron. So initial total momentum is just from the original photo on just each over Lunda. The final momentum, yes, equals toe the momentum off the electron minus away even went, um off he in Ah, reflected four times, right, Because it&#x27;s moving in the opposite direction and we deem the direction do the right s positive. So we have to subject He went home to west. The left with the election would just be each when we&#x27;re under. Plus, when we&#x27;re trying in this case Ah, it&#x27;s quite it&#x27;s already co created for us. Aren&#x27;t really co creator the lambda to be so points? You&#x27;re 71. You know me, Tess. Then we have two points. Your eight trees. Oh, centimeters reflected in. Ah, just take note to put in the S i units. When doing the calculations in your co creator, I saw what place for a tent up all Nice night, and we should be able to get the momentum to be a boat. 1.65 Senate part minus two. Any treats, Tim Softy s I units not to find any kinetic energy off the electron since ah, election is Can we thought office non relativistic. You can. I know that it isn, or relativistic by. You can t change in the energy off the election with the amount of energy that is imparted by the full time. This is because, too see, over, uh, this is a zero points. You&#x27;re 71 jets about 93 7 if he which Ah, this disability energy imparted to the electron. And this is much less than rest energy off the electron, which is your 0.511 MTV. Therefore, we can safely say that it isn on a stick, and we can use the kid American question P square over to em to find t kinetic energy off the electron so O p. 1.65 stay part of the state tree square by two times t mess off. The electron should get 1.4 night said, oh, minus 16 juice

Problem

An X-ray photon scatters from a free electron at …

Problem 56 Hard Difficulty

An X-ray photon with a wavelength of 0.240 nm scatters from
a free electron at rest. The scattered photon moves at an angle of
$125^{\circ}$ relative to its incident direction. Find (a) the initial momentum and (b) the final momentum of the photon.

Answer

no answer available

Related Courses

Physics

Related Topics

Discussion

Top Physics 103 Educators

Christina K.

Andy C.

Marshall S.

Zachary M.

Physics 103 Courses

Wave Optics - Intro

Multiple Aperture Interference - Overview

Recommended Videos

Watch More Solved Questions in Chapter 30

Video Transcript

James S. Walker

Physics

Christina K.

Andy C.

Marshall S.

Zachary M.

Wave Optics - Intro

Multiple Aperture Interference - Overview

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

no answer available

Physics

Christina K.

Andy C.

Marshall S.

Zachary M.

Wave Optics - Intro

Multiple Aperture Interference - Overview

James S. WalkerPhysics

Christina K.

Andy C.

Marshall S.

Zachary M.

James S. Walker

Physics