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Question

Predict/Calculate Consider two different photons that scatter through an angle of $180^{\circ}$ from a free electron. One is a visible-light photon with $\lambda=520 \mathrm{nm},$ the other is an $\mathrm{X}$ -ray photon
with $\lambda=0.030 \mathrm{nm}$ . (a) Which (if either) photon experiences the greater change in wavelength as a result of the scattering? Explain.
(b) Which photon experiences the greater percentage change
in wavelength? Explain. (c) Calculate the percentage change in
wavelength of each photon.

Zulfiqar Ali · Accepted Answer

part, eh? We know they did. Change in Waveland is a cold too Itch divided by mass of electron times the speed of flight into one minus Call Sign Tita here today Is this sketch in on though, And this agreement it is clear date changing Devlin Onley depends on the scattering angle Peter. Changing javelin only depends on Peeta discovering angle Rest of the quantities are constants. It is a plan constant massive electron is constant, Speed of light is constant and one is a constant. So the only factor the determines change in battle. And is Peter the scheduling angle And therefore the change in Valent is the same for the board for dawns So the change in Dublin the change in Babil int is the same for bought for dawns. All right, now let&#x27;s sold part B Well, for both of photons, changing Redland is the same. Ah, change in Babel int eyes the same is the Sam. No keeping this point in mind. Let&#x27;s calculate our percentage change in travel and four, uh, the visible for Tom so or send each change person did change in development in the babble int in the prevalent off visible visible light foot on. Well, to calculate the person teach change in babbling Oh, visible light food on, uh, we divide changing, prevalent, divided by the reverend off the visible light which is 500 20 nanometers. And this changing babbling is also Indiana meters multiply by 100 and this gives us zero point 19 times, uh, lender zero point 19 times. Ah, change in Babel int so 0.19 times changing, babbling and similarly percentage change in the lab. Lint off. Uh, X ray foot on is given by let&#x27;s do it here. So percent age change percent a change in the travelin and, uh, vab lint off X ray foot on X ray for John, this is equal to change in gavlin divided by the babble and off X ray photo on which is a 0.0 tree zero nanometers. Uh, Nana meters multiplied by 100. And this gives us 3.3. Multiply it by 10 to the power tree. Time&#x27;s changing babbling hence X ray foot on experiences. Greater percentage change in Babylon. Excellent. Put on his smaller frequency, then the visible light for dawn and changing babbling for both the photons eyes the same. Therefore, extra foot on experiences greater person teach change here. X ray Patan X ray foot on expediency ese expedience ese crater percent be change greater or sent each greater percent each change. No. Let&#x27;s, uh, sold Bart see and Peter equals 1 80 degrees. We have changing. Devlin is equal to two times It&#x27;s divided by Amoss off electron times the speed of light, and this gives us two multiplied by 6.63 multiplied by 10 to the power minus 34. Divided by Massif Electron is 9.1. Multiply returned to the barber minus 27. Multiply the speed off light, which is three. Multiply 10 to the power it and solving this changing Web glint comes out to be four point 86 multiplied by 10 to the power minus drug meters. Now for let&#x27;s calculate for visible light foot on for visible for visible light foot on for a visible light for tar. So first of all, we calculate, uh, person big change for visible light foot on time. It can be done by dividing 4.86 Multiply. We tend to the power minus 12 which is a changing babbling divided by the rabble end off visible light, went on sequel to 5 20 Multiply. We tend to the powered minus line leaders multiplied by 100 and this gives US 9.3. Multiply every 10 to the power minus for percent and similarly, for X ray for dawn for X ray, put on percentage change in battle in is 4.86 Multiply. They tend to the collar minus 12 divided by, um, the violent off extra foot on which is zero point zero tree. Zero multiply. I tend to the bar minus line, multiply by, uh, one Andre, and this gives us 16 point 2%.

Zulfiqar Ali · Answer

the changing of length Delta Lander equals Lend a prime minus Lambda Lambda Prime minus lambda equals bitch divided by empty lots of electron multiplied by C, which is speed of light into one minus co sign of Peter. Here, Peter Peter is the scattering angle. Peter is the scattering angle. All right, If Peter equals 90 degrees, then we have changing. Javelin equals ich divided by months of electron time. See into one minus course I know mine. Two degrees we&#x27;ll sign off minded agree Equal is equal to, um zero. Therefore, changing babbling equals itch divided by m e multiplying. I see so changing balance equals edge divided by months of electron times the speed of flight when Peter equals 90 degrees. If Peter is zero, then we have changing. Valent equals itch divided by changing Babylon equals each divided by Marcel Electron time see into one minus one Because go sign of serious one and changing Valent is equal to zero. Sure, uh, did for change in Babel int in crazies change in that lint in crazies increases. It&#x27;s the scattering angle in quizzes from zero to 90 degrees and it feed Isaac Walton 90 degrees. Frieda is equal to 90 degrees. Change in Babel in is a maximum is maximum, so change in Valent increases is ah, scattering angle are is the scattering angle increases increases. Now let&#x27;s sold part B well, the best explanation is explanation. Number one. There&#x27;s explanation number one, and it says that a lot of scattering angle means Ah, large shirt, A larger scattering angle. Frieda means, um, a large transfer of momentum, a larger transfer off, larger transfer of momentum momentum and thus a larger change in battle. That&#x27;s a larger changing balance. Uh, march here change and you&#x27;re babbling, Well, let me see the game. Uh, a larger scattering Ingle Peter means a lot of change in momentum. So large, uh, change in momentum and a lot changing momentum means a large is changing bat linked and grab lint off the foot down. Leant over the don&#x27;t

Yaqub Khan · Answer

and ultraviolet photon is absorbed by a fluorescent molecule with then Emmett&#x27;s blow for Jones. So we can write a relation for energy off ultraviolet for down that energy off ultraviolet for dawn. Physical, too. And our job first, immediate for dawn. Well, US energy off sicken, and we did Fordham here. We assume that none of the energy off absorb ultra wondered for down is he converted to other forms. So by this relation, it is a clear that energy off immediate for dawn. Immediate first for Donnie&#x27;s, less them energy off ultraviolet for dawn. Yes, well is energy off second, immediate for dawn, use a less than and our job ultraviolet for dawn ISS according to the religion, relent, physical toe, etc. Upon e here, lend eyes were lent offered on it is a Planck&#x27;s constant sees. It&#x27;s a pity of light and E&#x27;s energy, a photon. So the relation shows there where land and and as you are for done, are inversely proportion. So is energy off. First, immediate Ford on his list them energy off ultraviolet for dawn. Therefore, we&#x27;ll end off first. Immediate for dawn. Is it good or than we&#x27;ll end off ultraviolet or done. Yes, well is relent off. Second immediate for Don. Is Asa greater than Maryland? Off. I&#x27;ll travel it well done. So were lens off. Immediate for Don&#x27;s will be longer than the violent off ultraviolet for done now. In the second part, we help were let off. Ultraviolet for dawn is 2 54 No matter which is equal to 2 54 times tended a power minus nine meter. And it is also given that Weyland off one immediate for Adonis 4159 Momentum so we can write. It is for 15 times 10 to the power minus nine meter. And we want to calculate the violent off second immediate or don&#x27;t no. Again by using the relation energy off, I&#x27;ll travel it for tone is equal to energy off first, immediate for dawn. Well, US energy off second immediate for Don. No, By putting the values off energy here energy off our travel, It for Don is equal to SC upon Welland off ultraviolet for tone that is 2 54 No matter which is equal to energy, our first emitted for dawn that is etc. Upon its gallant here. Prevalent is 415 nanometer and and that job, second emitted for down that is SC upon its gallant Let Roland off this button is Linda do now by taking it&#x27;s see common from bottoms in the right hand side, he&#x27;ll be here, etc. A bung 2 54 No matter is it will do at sea into one upon 145 nanometer plus went upon Linda too. So by dividing both sides by S E S C and S E will be cancelled. So the hell one upon 2 54 no matter physical toe one upon 4159 A medal unless one upon Lambda Tau. So from here we have one upon them, not to physical toe. One upon to 54 nanometer minus one upon 415 No matter. No by taking the awesome off these two numbers. So we have all Sami&#x27;s 2 54 No matter Indo 41 five. So we have here for 15 nanometer minus through 54 nanometer. So in the next every hill Lambda Tau physical too 2 54 nanometer multiply 415 nanometer upon for one five. No matter minus 2 54 And murder So by computing the hell Lambda Tau equal to six 54.7 nanometer. So that is approximately called too 655 nanometer. So this turbulent are second, immediate for on thanks for watching.

Guilherme Barros · Answer

if this exercise we have a full term scattering off in electric at an angle of 90 degrees and the electric it&#x27;s scattered at an angle of 20 degrees. So the exercise asked us to justify the claim that these information that were given to us are enough to calculate the wavelength Linda, prime of the Scattered Fulton. Okay, so we can drop three equations from the the scenario that&#x27;s in the figure. So the for the two first once come from conservation of momentum, and they are the conservation will mean the X coordinate. And that&#x27;s gonna be the moment, um, the month off the incident fold, which I&#x27;m gonna call p gamma. And that&#x27;s equal to ah, the momentum of the electric in the X coordinate. And that&#x27;s P e ah, times call sign off 20. So he is the magnitude of the momentum of the election. I am. I&#x27;m I&#x27;m just gonna subject to things here. So p gamma The momentum of the fulton is the age over Lunda and P E is m times e. M is the mass of the election. Time is a cool sign of 20. Uh, we have another equation in the y axis, Um, where the initial we went on zero the total nation moment. And this is equal to the momentum of the photon in the scattered folding. And that&#x27;s P Goma prime minus p times sign of 20 PM A prime is London Over is H over on the crime minus M v Sign of 20. So we have that age over. Lunda is equal to M. V. Signed 20 and we also have 1/3 equation that comes from the company&#x27;s quick scattering That love the prime is equal to Lunda plus h over M C. Times one mine is the co sign of the scared, a scattering angle that I&#x27;m calling Fi. And since here the scattering angle is 90. Madeleine, the prime is able to Lunda plus age over M. C. So notice that we have three equations. I&#x27;m just gonna highlight them here at the this 1st 1 Then we have the 2nd 1 here. And then we have the 3rd 1 and also notice that we have three variables in these equations. We have Linda, Prime, Lunda and V. All the other quantities are No. I am, uh, the cold sign of 20 the sign of 20. So since we have three equations in three variables, uh, to find out, then this is solvable than the These system of equations is solvable, and we can find ah, the value off Linda prime in question be were asked to splice it. Lee, calculate the value of LEM the for prime. So for that, I&#x27;m gonna use first these two equations here that come from the conservation of momentum. So the 1st 1 is that h over. Lunda is equal to M v. Cole. Sign of Fada. The second is age over. Loved. The prime is envy. Times the sign of Fada. Okay, so if I divide the second equation by the 1st 1 we have, um Lunda Overland The prime is equal to the tensions off Fada. Okay, so you have Lunda equals love the prime tensions of Fada. Okay, but we don&#x27;t already have another equation linking London and Linda Prime. And that&#x27;s continous formula up here. And I&#x27;m gonna use this. What? We want to find Islam the prime. So I&#x27;m gonna isolate Lunda in this formula here. So in the Compton formally had the Lunda equals on the prime minors age over him see? So from from the equation that&#x27;s highlighted in blue have that limb the prime minus age over him. C equals limb, the prime times 10 Jin&#x27;s off Fada which in this case, data I&#x27;m just reminding you of today&#x27;s 20 degrees. So I&#x27;m the prime times one minus. Tensions of Fada is equal to age over m c. So on the prime is age over. I m c uh, times one over my over one, minus tension of failure. And I we can substitute the numbers so long The prime is 2.43. Pick a meters that&#x27;s age over him, See, divided by one minus attention off 20 twenties. The angle Ah, the scattering angle of the electorate. So on the prime is you go to 3.80 to pick a meters, Okay. And this is the wavelength of the scattered Fulton

Mayukh Banik · Answer

Yeah, creating energy of the required electron will be given by half. A mass of the electron velocity of the electron squared equals half times 9.1 times 10 to the negative. 31 times velocity is two point 2.18 times 10 to the six squared. So we have kinetic energy equals 21 point six to transcend to the negative. 19 Jews. Yeah. Now kind of big energy. Ease a C times one of our lambda minus one over Lambda Pride. So we find one of a lambda minus one was on the prime equals 21.62 times 10 to the negative. 19 divided by eight c. It was 1.86 times 10 to the seven. Also, we have Lambda Prime minus lambda. It was eight. Over F E C. Times one minus course Sign the angle of the scattering, which is 70.4 degree. So this comes out as age of what NBC is 0.243 times 10 to the minus. Nine times one Might s co sign 17.4 degree equals 1.11 times 10 to the negative 13 you know. So we have Lambda Prime minus lambda. It was 1.11 times 10 to the negative. 13 meter and one over Lambda, minus one over them. The prime. It was 1.86 dying stand to the seven meter. So solving days we find Lambda equals 1.1 04 But I am staying to the minus 10.

Bruce Edelman · Answer

Okay, So you&#x27;re in chapter 37. Probably 30. This problem says X rays of wavelength lambda equals 0.12 Nana leaders are scattered from carbon. What is the expected Compton wavelengths shift for photons detected at angles 60 90 and 180 degrees. Okay, so for a here, so a is doing 60 degrees now, First of all, we&#x27;ve confined the Compton wavering shift using equation 37 6 e such that the final minus, the initial waving or Delta Lambda equals H over mass of the electron times. See, time&#x27;s one minus coast by. Okay, So if we&#x27;re trying to find the wavelength shift, then that&#x27;s just dealt a Dr Linda here. Then we could easily find that. Okay, So what we can also write, as in terms of the company, so is the same thing. Is Delta Liam to the equals lame to see the Compton weaklings, which is just this here turns one minus coast by. Neither are constants. We can plug that end. The company we think here becomes 2.43 times 10 to the negative. Three nanometers, one minus coast by. Okay, so now that we have this All we have to do is find what the wavering shift ISS. So don&#x27;t go. Lambda for 60 degrees s equals 2.43 times 10 to the negative. Three animators was one minus co sign of 60 degrees. Well, that&#x27;s just easy enough to do 1.22 times 10 to the negative. Three centimeters. That&#x27;s our answer. Pray Part B wants us to do the same thing just for 90 degrees. So don&#x27;t the Lambda 90 bigger use here is 2.43 terms. 10 inmate of three Nana meters. I was born minus coasts of 90 degrees. Well, coast of 90 degrees is zero. So it&#x27;s just the company wiggling cool. And lastly, part C wants to do the same thing at 180 degrees. Well, don&#x27;t blame the 1 80 here. It&#x27;s gonna be 2.43 I agree. One minus coast 1 80 which is negative one. So this becomes too. Or double the company. Waveland. 4.86 Thompson and you three nanometers. And that&#x27;s everything. Answers for a baby. Don&#x27;t see me, um, boxes and better. Here go

Problem

An X-ray photon with a wavelength of 0.240 nm sca…

Problem 55 Hard Difficulty

Answer

a) same
b) $X-$ ray photon
c) 16$\%$

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James S. Walker

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Wave Optics - Intro

Multiple Aperture Interference - Overview

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a) sameb) $X-$ ray photon c) 16$\%$

Physics

Farnaz M.

Zachary M.

Aspen F.

Jared E.

Wave Optics - Intro

Multiple Aperture Interference - Overview

James S. WalkerPhysics

Farnaz M.

Zachary M.

Aspen F.

Jared E.

a) same
b) $X-$ ray photon
c) 16$\%$

James S. Walker

Physics