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Basic Physics III Lecture 21

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below so you remember that 2 days ago we started our discussion of modern physics the rock body radiation and photoelectric effect and
Einstein had this series that light is actually consisting of particles were America he explained the photoelectric effect by stating that these energy of photons of light particle we plank quantum times the frequency and therefore is to look these liberated electron kinetic energy memory is affected by the frequency of the life not not so much by the intensity which would be the prediction of the wait for you and therefore if it drops of EU kinetic energy of electrons as a function of the frequency of the photon the light particles when they lost certain frequencies no our plans are liberated all that list a cruel and demand of energy that is necessary to inject France fondly are potential in which there inside out and then after that you get a linear relationship this isn't Greenland list the
experiments therefore that quantum mechanics it's stock let's look at some
examples that's calculated the energy of Luo photon meaning of photons that corresponds to a new light although followed a wavelength of 459 only a mail and back and so since we knowledge that the energy of the photon given by the plant quantum times frequency firstly defined the frequency but not at the frequencies the speed of light derided by that and therefore the energy is plant quantum tons to a speed of light divided by around we can calculate what is the product of punk quantum and speed of light and come up with this number but they can also directed look up the product of this so that I am going to use as a product of HC these numbers either in units of Beulah of other world's and 1 Chung Altus at 1 . 6 times standard minus 19 Juilliard is the energy of Solectron receives In the potential of our 1 way or another ellipsis nothing but the air on that charge 1 . 6 times 10 to the minus 19 to multiplied 1 if would this number of these units where we can get the June the photon has simply by dividing this constant fire 450 not only to us and we come up with a 4 . 4 4 times 10 to minus 19 for 1 photon of wavelength 415 on or in units of I would try reviews the other the 1 . 2 4 0 Our Michael divided by the . 4 5 Michael needle wavelength and that gives us 2 . 7 6 time so if we have a visible light with the energy of photon is a few hours from who there's also estimate harmony photons emitted In your typical Hot 100 what like all every 2nd and for that calculation we assume that ball hasn't efficiency of about 3 per cent meaning that 97 per cent of the energy goes and by heat radiation just as we have done with the black body radiation and only 3 % goes into visible light and we will also assume some some average wavelength of 590 lead for a 1st observed that a really energy that is used up every 2nd or 3rd coming from the vault lobbyists 100 watts 1 2nd of 100 visual and since we have a 97 % In efficiency or fish that means only if we Jules although those 100 rules actually goes into visible light so now we make the assumption that the alliance has a wavelength of roughly 500 not only and therefore 1 photon has the energy off 1 . 9 8 6 per cent of the minors and part divided by fire on times 10 to the minus 9 meters that gives us a boat 4 times 10 to the minus 19 if and if you divide freed jeweled to by air by the four-time centers minus 19 visual forget about 7 . 5 times 10 18 vote on a quite a few photons In the single 100 I like there was
some technological applications off the photoelectric effect these days the most Vermont are somewhat obsolete for example the so-called electric by offering still have sewerage films that you could encode the soundtrack of movies next we these images actually use a small light source to lead the writers are about of the sound track and then measure year resulting current the photos Of course as semiconductor photo buyers will render the high-voltage Chu and by now everything is encoded digitally and you may have chosen the layout of this class who to Mount Carmel special relativity there are we cannot voided completely so I was like differences between classical mechanics and dispersal of classical mechanics the master of Paul goal is a constant and the momentum this constant terms loss and became adept at kinetic energy for particle the product of one-half the master of the velocity square using the rental momentum equals must have Rossotti this also means that kinetic energy use the more momentum squared divided by the time she can multiply both Award of the nominee times of the energy is just Connecticut Energy when there's no are potential and particles can any velocity and any announced use of bingo equals 0 Lindner special relativity and the most famous of their visits former answers that apparently equals the last time the speed of light gray however in this case the every is as a dynamic must meaning that it is not a constant it depends on the speed of the particles so define arrest last and 0 which is the master Walsh and the more you speed up the the particle the bigger last World Cup and then add variously Einstein energy momentum relations which says that the energy Scalia the rest last times the speed of light square Ferrero plus the momentum squared times and of costs because of this relation this must be cold will be dynamic must times the speed of light and the whole thing the cost and objects square a leave momentum as defined just hours in classical mechanics only the the dynamic must still rent arrested dynamic mass times velocity and if we learned that Oh this equation get and zeros see where families that divided about the speed of light squared equals and the whole thing square off with dynamic last equals the arrest last time and at times the speed of light divided by the square root of the speed of light gray minus the velocities and usually is put in this fall the dynamic announces the arrest last divided by the square root of this fact we can edit energy is the the energy minus the rest energy in the air the and to get the rest frame of public and that has I'm not a forwarding consequences there too if you have a rest mustard is bigger than 0 that particles of cannot reach the speed of light they have to be slower than the speed of light and the reason for that is that there may become seat and the denominator becomes Euro and the dynamic mass becomes infinite so requires an infinite amount of energy to accelerate bigger than 0 arrest last Cardinal the speed of light if this rest now zeroed then have pardon can't be slower than the speed of light they always have trouble forever at the speed of light and can see that in the following way and the Einstein relation between energy earned momentum this term falls out because rest and that means that the energy equals the momentum times the speed of light and if people are gave the momentum equals vast times velocity we arrived at the conclusion of the velocity has to be the speed of light so such particles it cannot dominant 1 particle apparently already know that has that quality of photons of passed by definition animal the the speed of light so
we have the following photons properties it has no rest since there wasn't the speed of light and it's energy it's given by the media John Heard quantum times frequencies or off we can also say quantum divided by 2 called H all times and the frequency on a kinetic energy and energy of the same thing because there's no arrest last and the momentum is just given by the energy divided by the speed of light and therefore since we know that the energy use each Times f or each following under seat a baguette that momentum the photon this plant quantum divided by the wavelength or age times a wave case and photons have all the usual particle interactions including collisions and collide photons particles however unlike other particles photons can't be slowed down if there was ever a duty they dressed shift in frequency still will with the speed of light we can build a little simulation of provisions off of times electrons so you we have a photon coming in and we have transiting sitting addressed initial the photon goes end and it collides With the ELECTRONIC becomes a full-time with a slightly longer wavelength or smaller frequency and then they this morning we can now look what happens when you change the
angle of the U. scattering the the photon so if I make the angle worries small that the photons goes almost in the same direction as the stop then it has a very little changed and uh and wavelength and you can see that on the bottom graph he would chose this this line you can see how the wavelength changes so this is a scale and not only does and you have the original photon wavelengths and this position we have shifted on and off castaway gets longer since the frequency becomes smaller since photon rules as an engine and also see what happens if you go total shorter wavelength and it doesn't affect me as shift in harmony not only does change when undergo scam
that's actually air calculate this collision process but before we do that let's 1st look again at our example that we can cut with the light and see how much momentum is actually absorbed by a piece of paper when if you focus all photons from 101 light onto it and we know that the momentum of 1 photon again assume are not only those divided by land closes Planck constant divided by fire not only those that we get 1 . 3 3 times 10 to the minus 27 kilograms 2nd and that means since we have 7 . 5 times 10 to the 18 photons that the total momentum clients for every 2nd this tender the 1 is 8 over meters per 2nd so that every 2nd that means that the force which still run meters a 2nd career as 10 to the minus 8 In other words a light bulb exerts a force of 10 to remind you that if you focus all all of its photons on some object and every can also look the efficiency of faultless centers for serious molecules like a full molecule in plants capture the energy of the sunlight and changes see O'Toole who I useful carbohydrates and begins to grow up and it requires about 9 for this transformation that take place and the the reverse process will resume burned wood 40 releases 4 . 9 from of molecules consume so if we still 617 not only as a typical wavelength since chlorophyll absorption somewhere between 650 not only the German on Arnold then we can calculate how efficient these photos centers so again we calculate the energy of 1 photon so its 1 . 2 4 0 public tumbled Michael readers divided by wavelength which is . 6 7 Michael so this gives us 1 . 8 5 tumbled for the energy of 1 photon since we know that photosynthesis requires 9 photons multiply that by 9 and we get the total energy solar energy is needed a 16 . 7 and a female form the ratio of 4 . 9 0 Trumbull games are the year product molecule or with a 16 . 7 from both was required to manufacture then efficiencies is about 30 per cent of the citizens the world it wasn't so let's now calculate the was still operating photons with our chancellor show the jobless in which they Compton effect which is what services called isn't an elastic and that means that both momentum and energy is conserved could and for the momentum we have 2 components wiring in the direction of the incident photon and 1 that is perpendicular to the incident so let's assume that this scattered 4 Tom and makes some angle with the incident direction and that ELECTRONIC which is initially addressed makes angle fado so if you look at these component off the moment of them initially of cause recently have the momentum of the incident photon all after you have the yellow from momentum triumph after the collision times the of component disappointing along the x erection plus be ecstatic photon times cosigned 5 so we can solve this for Pete prime cosine fade and there this then we looked at the Y component and the Y component there was no white component before the collisions allege that should be no white component after the provision so that means that prime-time Society of of which is the outlook from our white must equal we be equal and opposite at told be why component of the scattered photons purchased and are prime signed 5 so what since we have those toe equation Peter favor and P Prime science data can scrambles operations and add them up and then get a cheap crimes Scalia because signs with fate of schools and that equals 1 so this is the Y component of this part square X 4 . com from the x component to multiply assault was and we get a term was calls on square find and termed the p gamma square this 1 and the mixed this means since we have from the other component already won the sides of fine rain collect those terms hero and recognize this we have momentum of the Stabat so we get a bit of momentum square off the outlook on after the collision it is the sum of these gather photon momentum Graham 1st dissident photo momentum both photons miss this uh mixed so we remember that result and just copy it on to the next page so we
can make this a little bit nicer expressing some of those tormentor script and a slightly different way we observe that the binomial formula give us this expression she gum up Prime minus gamma equals gum up Times Square 1st minus the mix and we can therefore expressed this summer by the difference in the area of photon momentum squared plus tow times Our product of the photon moment this into hero than we get a momentum of these Allah after the collision as the difference aware of the photo moment of plus about this mixture which depends on who you are discovering and all of this is coming just from all our momentum conservation knowledge you losing energy conservation so our 1st of all of the photon energy before the collision he gamma and divided by the speed of light and you get initial momentum p down and the ELECTRONIC energies initially since the Thomas the rest just rest mass of times the speed of light square for divide by the speed of light and the rest of the old and the speed of light then that after the collusion by Getty galosh prime and dividing by the speed of light gives me a R P gum Prime and the ELECTRONIC energy and values can the Einstein relations so our Einstein Willie China which I get after the collision and chest my way of better noting that its photon so it's gum my has no particularly as just a symbol for the sins are particle physicist I think of a photons a guy Murray's it's just a notation this that I could have written for so since the energy is concert that means that initial energy of photons and electrons must be he called final MMG our for and if I sold this for each trying and divide by the speed of light this and I recovered here the momentum of the initial photon momentum off these scallops and had the rest mass would from now if square the whole thing I can use the Einstein relation on the left hand side just this 1 and on the right hand side just multiply out with all-male formed a difference in mementos Graham plus a mixed term plus the rest momentum and I get this relation for the momentum of the sky the electron after the quotas that already have a relation for that comes from momentum conservation justice for him the rise on the previous page so I can set those 2 things equal in the 1st term is identical that councils about the effect of cancels so I'm just left with this term equal equally that and now from multiplying the nervy junk constant and divided by tool memento the photon and a rest mass of the Ehrlich on the speed of light than I did this term goes away and he H P gum up prime barred are both looking down on time but this is just a wavelength of the scattered photons and then there for the next term I get although he Guyana but that is just the initial photon and on the side both of gum on Bugama prime go away and I just I'm left with a 12 times one-liners cos I'm fine so in other words the result is that these wavelength the photon shifts by a constant amount because all of these are constant nature of this is the best players of the electron the speed of light and plant so the shift in the wavelength just controlled by the scattering angle and nothing else so therefore I've been on open various angles and 0 degrees there's no shifted on and then at 45 degrees there are some shift at 90 degrees as a bigger share and the biggest ship that shifty will observe a 180 degrees which sometimes called Baxter furthermore weekend gives us expression of Constance of nature of the mainland because before our call but Compton wavelength of our strong because as the way so the Compton wavelength Thomas H. over NBC's and nephew rugged mountain meaning from 11 Kuala some of the speed of light square the mask and therefore plants constant using this expression than I get 4 . 4 2 7 and pickle meters for the Compton wavelength and therefore our since we ever since had this expression Havel or Compton shift of wavelength show there is a Compton wavelength of electron times 1 minus goes on Compton scattering has some complications if you use gamma-rays instead of honor X-rays gamma-rays had even shorter wavelengths X-rays and it can produce gum with radioactive sources and the number of scattered photons of a proportional to leave not what I would consider all wrong total intuitive and therefore it is proportional to the density of electrons in a particular material and you can do is be calm gathering to scan the density of bones of the density of electrons ought to be proportional to the density of all material and you can't do that to diagnose bone diseases sometimes the onset of such diseases accompanied by a change in the bone density but has some
diagnostic purposes so let's calculated example assume we have X-rays uh wavelength 0 . 1 4 9 on 140 people and we scatter them from overreaching slices of calm and the question is what will be the an wavelength of X-rays after scattering when they gather 0 degrees 90 degrees at 180 and so for the Compton formula at 1st just look at the scattering angle and one-liners cos signed as 0 degrees this one-liners want schools and 0 degrees 1 this gives us 0 part a four-part beat this 1 China's coast of 90 degrees and calls on 90 degrees 0 so 0 I mean get 1 and 4 parts seat we actually get one-liners minus 1 or 2 so now we can calculate the the Compton shift which is just the Compton wavelength times a these expressions of no calm shifted awful we get a Compton wavelength or 2 . 4 and because leaders upon me get twice the Compton wavelength of all of 4 . 8 5 people need for parts solar since we had originally 140 figure leaders as the wavelength and therefore this scatter wavelength is in part a again 140 people and personal shift and in Part B it's about 140 too pickle meters and in part see it is 145 people and now you see why you was gamma-rays this kind of measurement rather than expertise because all those mavens are relatively close but so you need a fairly high precision and measuring while if you'll have a say just a wavelength off just 10 people meters and the comp shift is far more Norwood for the shoulder the wavelength easier to detect finally Compton chip as the conscious doesn't change in in its size this independent of initial area for our small collection off photon interactions with can't and in this case photon survives it just has a long away then the photoelectric effect and in this case a photon is completely absorbed the old Thomas and if we don't have enough frequency or enough energy to actually ELECTRONIC we can still excited about this taste the photon is also managed absorb and Noella Thomas admitted however the excited atoms and candy excited after some time with mother of 4 and finally us yet another effect which is called their production which is shown me so we have a photon are coming in and out of nothing it creates ramallah Chinese miners and the positron traps and Bill Abby positron Andy ELECTRONIC called the pair positron isn't Solectron pairs all the same properties as an but the opposite shot a day that's why this process is called their production their production can only
happen in some material because you actually need under the clears to participate in action because otherwise it is impossible to conserve bills energy and momentum of the and pair production so you need the no peers to absorb some of the momentum for someone who is kind the opposite of their production is also possible so you have have a ELECTRONIC and positron colliding with each other and dual photons are limited and air electron and fire positrons destroyed so that is called on elation if the comment on the ELECTRONIC positron is small enough than before the I mean big can form of bond state which is called positron sort of looks like a like an after where the nucleus Of the outermost placed a deposit because of this this process the emulation process positrons and don't last long and in nature unless to isolate them from all the other just somewhat tricky do just 1 example of followed pair production so we can calculate what the minimum energy of photon has to be so that it can actually produce symbolic positron him and in this case we have we are not concerned with the momentum conservation just assumed that the nucleus takes care of it and we just look at energy conservation Olivet electron Moss's 511 Katie square and I just told you that the the positron has all the properties of aren't ELECTRONIC except that it has the opposite charge for the positron has also arrest 111 sees career and flooding meet price the rest energy of hour or 1 . 0 2 to any need to produce both electron and positron and that is the the energy that the photon has Kelly because 4 of its suppliers and so it became a calculate what wavelength that corresponds to are taking Our the plant constant and divide their energy get these resulted wavelength and its 1 . 2 1 times 10 to the minus 6 Micro meters or 1 . 2 1 so I this is the guy Murray range of electric expect so it requires a hot dog Maurais to produce electron-positron pair of X-rays on not energetic enough to do it yeah I've seen in the last few weeks there were a a lot of experimental evidence the letter mimetic plays and light on uh our wait for example looked at interference and diffraction reflection and all those effects that that depend on labeling phase in diets seems to pool their beyond any doubt that the electoral magnetism of light is away from home however know we have collected also of her impressive list of experiments that that show the prodigal nature of like a like a black body radiation and the photoelectric effect that can't scattering and the pair production actually is also difficult explained wave so how does this sit together and it doesn't really fit together yeah simply state that it does so say light has a dual nature it has some aspects of waves and it also has some aspects of particles and that is called the principle of complementarity if you wanna understand light then you have to take it into consideration both these partygoers most nature of the but it gets a little weird arose because in quantum mechanics matter also has fueled on other worlds every particle also has has a wave nature waivers particle each so this principle of complementarity refers to them for example
that we know that a 3rd of photon of round carries of momentum by age old man can turn this around and say the particle from she has a wavelength age he simply the same formula sold for around and their new leader body part of this terrorist and sort this is covered the body wavelength Bob particle momentum p and what it means is that you can actually old 0 diffraction portables look for example when they some crystal just like diffraction have a X-rays and crystal so that they may have some regular spaced Adams of scattering samples and incident Ehrlich from being than we can out of formulate diffraction criterion interference criteria review observed maxima and minima based on what angle of your and we can't let experimentally and created an image of diffraction emerged that looks similar diffraction images of expert as long as the particles of coherent however away from each of us well but so let's look at an example let's say they have about 200 grams 0 . 4 kilograms ball that is moving at a speed of 15 meters per 2nd what is really wavelength that ball and you lose these relationship between wavelength momentum and this is the from constant this time again and jewel seconds and divide by 0 . 2 kilograms times 50 meters per 2nd and get away with 2 . 2 1 times 10 to the minus 30 and this is such a small amount of that there's not even a prefix they invented for he fixes only go to 10 to the minus so it's a very rivers small wavelength and we will not be able to this actual observer easily the diffraction pattern of 200 ground ground ball on the other hand if you look at microscopic particles are just showed that you observe diffraction our let's assume that we have our chance there have been accelerated the electric potential difference of 100 kilowatts or 100 miles and calculated that to do that we again have to wear use relativistic formula so the rest of the hour from 511 KDD proceeds with means the rest and countries are on island and the ad the potential energy riches at 100 kilowatts times chunk of electron or 100 Katie so we get 611 energy of electron after goes through potential and we can calculate the momentum using the Einstein relations services the momentum square Our 112 thousand Medicaid Ferrero Austria under 35 need seat when took off those funds and now we can look at these corresponding wavelength simply a P all HC PC and other words I can divide 1 . 2 4 0 electron world Michael by 335 Katie and I get 3 . 7 Arab because I do that so this wavelength this hours small but not so different from that of gamma rays for example so in the pound we if only have a 100 world rather than our 100 killed that I can do about preceded the same way now the total energy is 511 . 1 case could do that but I can also use a classical formula of corresponding classical form simply the momentum squares twice times kinetic energy times a master and in both cases I get at 10 . 1 KTV perceived as the momentum of the electron it was the same relations give me 120 me epic of us so that is the U. X-ray range wavelengths so another loads to accelerate our from a reasonable potential differences between 100 Walter and 100 kilowatts and you get wavelengths that correspond to rule Daimler raised 6 4 4 as a further example we can actually calculate diffraction path let's say they have such a hundredfold of potential and accelerate or plants and let's save you observe maximum and the 1st maximum Crozet 24 degrees what is the separation a deal between Apple and told that since the energy of electrons Ismael we don't penetrate into the crystal like X-rays were so we simply look at the surface atoms and therefore we observe that there's a path length difference of the spacing times signed fatal for maximum that needs to be an integral and number of wavelength and therefore he gets that a peace sign there has to be equal to up to lumber and since know that traders 24 degrees baguette the lumber freedom but now that we know it's 120 of the previous example and therefore the A. 123 people leaders divided by a sign of the 24 degrees of 0 . 4 7 and that means that the spacing of atoms 300 tool that pickle so we can calculate that diffraction patterns from comes just like we did for X-rays diffraction gratings for life let me conclude said
yesterday and come all the talk about the nature of the electron next March
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Gammabestrahlung
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Tag
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Titel Basic Physics III Lecture 21
Serientitel Basic Physics III
Teil 21
Anzahl der Teile 27
Autor Smy, Michael
Lizenz CC-Namensnennung - Weitergabe unter gleichen Bedingungen 3.0 Unported:
Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nicht-kommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben.
DOI 10.5446/12957
Herausgeber University of California Irvine (UCI)
Erscheinungsjahr 2013
Sprache Englisch

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