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Compton Scattering In & Compton scattering experiment, the incident photon has an enery E The kinetic energy of the recoil electron Calculate the scattering ang...

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Compton Scattering In & Compton scattering experiment, the incident photon has an enery E The kinetic energy of the recoil electron Calculate the scattering angle of the photon (in ocerces)Take E = 66 keV and Ke = 2 kev40.71134.450.7176.00

Compton Scattering In & Compton scattering experiment, the incident photon has an enery E The kinetic energy of the recoil electron Calculate the scattering angle of the photon (in ocerces) Take E = 66 keV and Ke = 2 kev 40.71 134.45 0.71 76.00



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In the Compton scattering event illustrated in Figure $3.24,$ the scattered photon has an energy of $120 \mathrm{keV}$ and the recoiling electron has an energy of $40 \mathrm{keV}$. Find $(a)$ the wavelength of the incident photon, (b) the angle $\theta$ at which the photon is scattered, and (c) the recoil angle $\phi$ of the electron.

Hey, I don't First, we have to find the webs and Xander, which is a C over E and putting the value of E 0.1 MTV. We find the website to be 1.242 times 10 to the minus 11 meter now Lambda Prime. It was Lambda plus Age over M E C. That's one plus Basanta for Tarek was 60 degree. We find them. The prime equals 1.364 times 10 to the minus 11. Later, now E prime, it was eight. CEO. A Lambda Prime equals 0.146 MTV. This party is just jammed up, which is 0.1 toe to Pakistan to the negative 11 Major on the recoil kind of energy is given by cake was a CEO a Lambda Times. There's a damned over them down, divided by one plus Georgia Vanda over Lambda on that will come out as zero point double zero 894 MTV Who the recoil angle for the electron fee equals co tangent. Universe Janet upset over to times one. Does you over M E. C. Squared on putting those values in well defined the recall energy for the sequel Angle Photo Electron Toby Fight Board One fall

In the sensor size we have, ah, folding that scatters off the Lateran at an angle. Fada equal sue 17.4 degrees and the electorate is scattered at a speed of 2000 180 kilometers per second. And in question A. We want to find what is the wavelength London of the incoming full. In order to do that, we're gonna need the wailing shift between the incoming Fulton and the and the scattered folding and the kinetic energy of the election. So first, let's let's calculate the Lunda. And that's just according to contents formula age over him. See, one man is the cold sign off data. So this is 2.43 big commuters. That's just a chill room. See times one minus coal. Sign off 17.4 and this is 0.11 p committee. This is the Lunder, and I'm gonna highlighted in blue here because it's important. Also, we we need to complete the Connect Energon vets MV squared over two. So the mass of the electron is 9.1 times 10 to the minus 31 kilograms. V is 2.18 times 10 to the sixth meters per second. All this where? Divided by two. So this is 21 points. 62 time. Stand to the miners. 19 jewels. So if I divide this quantity here by 1.6 times 10 to the miners, 19th jewels were left in a vote and I'm just converting units here. This is equal to 13.51 electoral votes and again highlighting this and we are in a position to calculate Linda. And in order to do that, I'm gonna use conservation of energy. So the energy of of the incoming folding is equal to the kinetic energy of the electron, plus the energy of the scattered folding and the energy of the incoming Fulton is age see over lumber. This is K plus a c over the the wavelength off the outgoing folding off the scattered folding. And that is Lunda. Plus, don't under Okay, So from here we have that k equals a C. Times one over. Lunda minus one over. Linda, First Delta Lunda So ok equals a C. London closed out the Lunda minus Lunda divided by Well, I'm the Times, Linda. Plus that the Lunda So K equals a C. Delco Lunda over Lunda times Linda plus doubt the Linda. So multiply both sides by London Times Linda Ah, place that I love that we have. Okay, Linda Square plus k daughter Lunda times London is equal to H C, the hotel under. And so we have K Linda Square, Close data Linda K Lunda Miners a c the hotel under equals zero. So we can solve this equation for London using Bhaskar. So for that, we have a Linda equals minus de Lunda. Okay, plus or minus dealing the key. All the squares with this still on the battle in the square K square minus four times. Okay, times minus age. See the beloved. So we have Ah, plus sign and age. See Delta Lumber divided by tu que so I can factor off the K And we have lung, uh, equal Su minus Noto Lunda plus or minus. Don't ah love the squared Plus for age seed out Lunda over K. They've got about two and I can also simplify this further by again, factoring off but this time without hunger. So you have that turned over to times minus one plus or minus the square root of one plus for age. See over. I'm sorry for HC. Yeah, over K. That number. Okay, um, so now I noticed that this the cake square root is bigger than one. So for that reason, the only positive solution for Lunda is the one with the post sign. So this is gonna be, ah, the calendar over to minus one. Plus, that's the only solution that matters. One plus four age. See over key Delta Lambda. Okay. And now I can substitute all the numbers. We were ready, calculated. So London is gonna be I don't know, London. And that's Ah, 0.11 Pick a meters. That's just one point one. Uh, times 10 to the minus 13 meters. Actually, I'm gonna put it in an animator's. Okay, so this is 1.1 time sense of the minus four in the meters times. Ah. Divided by two. Of course times one minus one. Plus the square root of one plus four times a ch cities 1240. Electoral votes in the meters divided like K. Ah. And that's just 13 0.51 electoral votes. Times that the Lunda and that's 1.1 times 10 to the minus four and the meters. And now we can perform this calculation here, and we get that Lunda is equal to zero point. What? 01 millimeters. Okay, so this is the answer to question eight. And now we can move on to question be and in question be we arrest. What is the angle? Let me draw again. The diagram. So here we have the folding. Here we have the scattered, uh, fold. And down here we have the electric. Okay, which is SEB's, uh, 17.4. This is this angle here. We want to calculate this the angle and we with which the the electron is scattered. Eso we're gonna use the conservation of momentum that tells us that the moment it in the wider action uh, the initial momentum for the white in the wider afternoon zero. And the final momentum is the momentum of the scattered folding, which is age over Linda Place, about a London and a plus. The momentum in the momentum of the elector. And that's just MV sorry here way also have the This is the moment. All of the Fulton times, the the sign off 17.4 eight minus. Okay. At the moment, um, off the electron in the in the y direction that m v times the co sign off. Seven off the angle. Five that we want to calculate. Okay. I'm sorry. This is not the call sign. It's the sign times the sine of the angle. Phi. So having the sine of the angle Phi is h over Lunda plus Delta Lambda M V. Sign off 17 went four, and this is equal to and I can calculate 6.63 times sent the minus 34 usual second times the sign of 17.4 divided by, ah, lumber posed at the London. So, Linda is, uh, 1.1 time standard of minus four, uh, millimeters Start since the minus instead of ready, like this, 100 been right, like 10 to the minus 10 meters. Plus, Dr Lundell, which is 1.1 times 10 to the minus 13 meters times the mass of the electron. That's 9.1 time Stan to the minus 31 kilograms times a speed, and that's 2.18 times 10 to the sixth. This is in kilograms meters second or second. So carry out the calculation we have that The sign of Fader is 0.9 88. Ah, and hopefully fires the ark sign of 0.9 88 and this is 81 degrees. So this here is the scattering angle off the election.

Given their scattering. And girl for photo is 17.4 degree requires speed off. Electron is to 180 kilometer per second. Um, we can use this classical formula for electron as it speeds is very low. And the speeds, um, the relative mystic effects are not prominent, so they kind of take energy off. The recall electron is, um if half and it we square. That is half AM S 9.1 into 10 to devour minus 31 in 22.18 and 2 10 to the power six square that is equal to 21. 62 inches to 10 to department in 19 Jews. K F s Sorry, K is equal toe h f minus. Jeff, not is Etsy upon lambda minus eight C upon lambda dish is a okay. They called to 21.62 into 10 to the power minus 19. Um, Linda and a Lambda Desh are the way evenings off incident and scattered photon. So, um, one upon Lambda my in this one upon Lambda Dash is a girl toe 21.62 into 10 to the par minus 19 18 c there is equal to 1.8 16 to 10 to the power seven. So one upon them them and is one upon them. Daddy, she is a good look. 10 it says in returned to the first seventies equation one also Lambda Dish Minister Um, there is a good of age one AM a say multiply Golan minus course. 17 point full. There is a whole tour. The dash minus lambda is a canto 0.0 do for three into 10 30. Power nine into one minus course, 17.4 Linda Dash minus lambda, minus 1.11 into 10 to the power minus 13 plus Lambda equation, too. Or Bangladesh is the world's 1.11 in 10 to the par minus starting plus member. That is when, upon Lambda minus one of 11.11 into 10 to the par minus 13 plus lambda the call to 1.8 They've been to 10 to the power seven. So by calculating this, we get Lambda is equal to 1.314 important to the par minus stand meters. Um, second, the sister Wei blank off the incident. Four time. Second is, um um the kind of tech energy off the required electron is Okay. Cool toe. Eight C multiplied by one upon lambda minus on upon Lambda Desh. We have, um okay. The girl to 13 point 46 left, and the rest in energy of the electron is. Then I she half electron. Their 0.51 month. Really total energy is equal to mm. The electron is a good long are point by 11 plus 13.46 into 10 to the power minus six. That is one farm was the good little 10.51101 train. Yeah. No. The recoil momentum for electron is he is half one upon see square minus m a square. Say to the bar food. Uh huh. There is a good A 0.0 physics for right for us. See? First get the photon paid ashes. H Dasha. Proceed. ASHA Ponsi e g dash upon. See? That is a goto each upon h dash that is 6.63 Tend to depart minus 34 upon 1.11 into tend to depart minus starting 30 birth. Linda that is a girl toe. There a 0.1 toe. No, but see, we have this scattering angle of photo on the 17.4 picked up off. So sorry. Yes, it could do. Get doing. Yeah. Angle off electron. Then be a sign. Phi. Is it going to be the sine theta Fine five physical toe be touch upon B A ST Peter, that is. Girls do. So you're blind, you know that? 50 point, you know, one toe, one little 10.0 play 64 time data. So five is a girl. Five is a girl toe 90 degree That is the, um, angle through which the electron

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.


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