the following content is provided under a Creative Commons license your support will help MIT OpenCourseWare continue to offer high quality educational resources for free to make a donation or to view additional materials from hundreds of MIT courses visit MIT opencourseware at ocw.mit.edu and to try something out a little real I took a detector that you all have as well my cell phone and this morning I went down with EHS to one of the very radioactive cobalt-60 sources a 10 mil aqui resource if you note the source that we were playing around here was as one micro Curie so this was a 10,000 times stronger source and was actually able to show the difference between a background count of my phone you shouldn't see much going on except for that one malfunctioning pixel because not much is going on and when I put the phone over the source itself things look a little different you guys see all that digital noise or snow in the video every one of those white flashes that you see is a gamma interaction with the semiconductor in the cell phone camera with one or more pixels in your CCD or charge-coupled device or your CMOS detector whichever one it happens to be so I thought this was pretty cool you can actually use your cell phone as a radiation detector and we're gonna understand why and what sort of radiation it could detect by virtue of its size and its composition today anyone ever try this before you have probably more intense than this if you were making neutrons right now awesome okay cool so let's just first figure out well where is this radiation coming from this is the link between the first part of the course and what we're gonna be doing over the next month as we've seen from the decay diagrams and I think I've harped on potassium-40 as an example for a reason it can undergo electron capture or positron release and if it undergoes electron capture by this likely route it gives off a one point four six one MeV gamma ray as the only possible transition here it also undergoes beta decay which you don't want to forget about if you're calculating the activity of potassium-40 but today we're gonna be focusing on what does this gamma ray actually do when it encounters matter or what are they uh possible things that can happen I'm going to introduce them conceptually today and we're gonna go through the math of the cross sections and the energetics more tomorrow so I'm doing a context first theory second kind of approach there's three main things that gamma rays will do in matter depending on their energy and the actual matter itself there's one called the photoelectric effect where a gamma ray simply ejects an electron from the nucleus so let's say we've got our potassium-40 atom have a bunch of electron shells I'm not going to draw all the electrons but I'll draw a few inner and outer ones here one of the things that the gamma ray can do is just eject that electron havecome firing out and the energy balance for that isn't that hard because this gamma has some energy e gamma this electron had some binding energy E binding and the kinetic energy let's call it T of the electron is simply the gamma ray n minus the binding energy back out it's just however much energy it takes to remove that electron that's what it takes and so you end up with if we go back to our banana spectrum what we call a photo peak or a photoelectric emission peak right here if you trace down this it's awfully close to 1469 ke V or 1.46 what was it one point four six one MeV it won't be exactly at that energy because it does take a little bit of energy to remove that electron anyone have a guess on what order of magnitude that might be yeah KETV all the way down to Evy so this photo peak will typically be extremely close but not exactly equal to the energy of the gamma ray coming out for most detectors that don't have that good resolution you can pretty much assume they'll be in the same channel or the same energy bin because your detector will have some sort of resolution it may have a thousand 24 or 2048 channels that span the full energy range and you might not be able to tell the difference between 14 60 MeV or 41.46 MeV and that - a few easy potassium in particular has quite a small work function then we'll get into why that is in a second the next thing it can do is what's called Compton scattering in the general case which is means that there's an electron here a gamma ray comes in with a gamma and then it bounces off with some energy E prime gamma and then the electron goes off with some other kinetic energy then the last one is what's called pair production just like in the QED equation if you have anything related to positrons you have to first create them so pair production doesn't happen below about 1.0 to 2 MeV and it happens with increasing probability as the energy of the photon goes up kind of like in radioactive decay there's a lot of parallels here is you can make a photo you can make an electron-positron pair at 1.0 to 2 MeV is just not very likely and it's an what we're gonna find out tomorrow is why the most likely photon effect is shown in these different regions anyone have any idea why do you think the photoelectric effect would be most likely at low energies and high Z you just had to give an intuitive guess yeah Luke that's right so that that explains the low-energy idea so that it doesn't take very much in fact does anyone know what the minimum energy you need to make the photoelectric effect happen well what is what's what's a typical order of magnitude for binding energy of the lowest or the the outermost electron shell or the lowest bound electron mm-hmm yeah that's called the work function anyone know an order of magnitude guess what it is it's in the single Eevee range in some cases it can even be slightly lower and that that were talking about visible light so like green light even yellow light can eject electrons via the photoelectric effect and then the reason that goes more likely with higher and higher Z we'll get into that when we look at the different cross-sections of interaction payer production is much more likely at higher energies because at higher energy you're more likely to create a positron and in addition pair production happens when a photon interacts with either the electron cloud or the nucleus there and that gets more and more likely let's say the denser the electron cloud is or the higher charge there is on the nucleus so first the simplest one the photoelectric effect this is actually what Einstein won the Nobel Prize for not equals MC squared which has been the bane of our all existence for the last month that's not what he got the Nobel Prize for it was demonstration of the photoelectric effect where if you start firing photons of an energy time Planck's constant times its frequency and then the next page I'll give you a quick photon math primer in case you don't know what those quantities are there will be no photoelectric emission until you hit that work function yeah like like Julia was saying that lowest bound electron energy and then the emission will simply go up and so this was demonstrated by applying a voltage to two different plates two different metal plates and then sending in light via this window and seeing when the current actually became nonzero so the way you detect photoelectric emission is if you've got electrons boiling off of one surface to the other that's the movement of charge and that's a current and so you can measure a current with an ammeter that's it actually is that simple but very elegant experiment back to the 1910s or 1920s and as a quick primer on photon quantity so you know what all of these different symbols mean the photon energy we give as Planck's constant times its frequency and I'll give you Planck's constant right here for reference I do recommend that you guys try checking out all the units to make sure that they work out because if you ever forget is that you know H times nu or is it HC over lambda you can always check the units of your expression to make sure they come out to an energy which an SI units is what joules and then how about in these sorts of things the most reduced SI units is what evey is another unit of energy similar to the Joule like one point six times ten to the minus 19 joules but what about in meters kilograms seconds other SI units yep kilogram meter squared per second squared indeed third meter squared per second squared yeah so just make sure that just make sure you remember that because if you're just looking for Jewel's you don't remember what a Joule is it's gonna make unit balance kind of hard and also we can describe the momentum or P of the photon as Planck's constant over lambda its wavelength this is going to get real important when I ask you guys to do a derivation much like the Q equation one that we were doing before but instead of me just doing it at the board and you copying it down I want you guys to try working through it and it's going to be another energy and momentum conservation thing just like before and this way you'll know what the energy is and you'll know what the momentum is so now on to this work function what is it actually there's a great paper by Michelson I did not look up whether this is the Michelson of Michelson interferometry but I wouldn't be surprised I'm gonna check into that but I did dig out this paper that actually shows the different patterns in the work functions of different elements so what do you guys notice in terms of patterns here first of all which elements are all the way to the left or have the lowest work function the what the group one metals like sodium lithium potassium why do you think that is they've got 1 electron in their outermost shell so looks like my potassium picture is not quite accurate I'm gonna draw another shell and put 1 lone electron in that for accuracy and so that electron is extremely unbound that's the same reason that these elements are so chemically reactive they want to ditch that electron to have a filled outer shell so you may also expect the work function of noble gases to be extremely high I don't know if any are plotted here but you do see the next row over like barium strontium calcium magnesium has a slightly higher work function and as you move this way through the periodic table to the left until you hit the transition metal craziness it follows a pretty regular pattern and so you can have a good guess of what the work function of something will be depending on at Z and depending on which wrote what is it which column it's in in the periodic table now can anyone tell me why do you think that work functions tend to increase with decreasing Z yeah indeed yep exactly for smaller Z that first you know that first or second shell is a hell of a lot closer to the nucleus even though it has a lower total charge in the nucleus it's much more tightly bound being much closer so like the outermost electron and cesium is quite far away and does not feel as much Coulomb attraction yeah good point so now into Compton scattering I'd say though the most difficult conceptually to understand the energetics but the kinematics or what actually physically happens should look strikingly similar to what we've spent the last month on instead of two particles colliding it's a photon colliding with an electron then e1 remember what we read in that first day of class with the Chadwick paper when he said hey maybe this quantum of energy is done in a process analogous to Compton scattering well this is Compton scattering his analogous process was maybe an electron hits a proton and something happens which is not actually what happens and in this case you have a a photon with energy H nu and momentum H nu / C striking an electron with rest mass M of electron C squared or 0.5 1 1 MeV and afterwards the photon leaves at some angle theta and the electron leaves at some angle fee so we are I'm going to show you guys some of the Compton scattering energetics relations like what is the wavelength shift which means that if this photon comes in with a certain wavelength lambda and it gives some of its energy to the electron it comes out at a different wavelength it's going to be lower or higher wavelength do you think I heard a bit of both so who says lower so lower wavelength let's go back to the photon formula with a lower wavelength result in a lower or a higher photon energy okay so in a Compton scatter you start off with an electron kind of at rest they're definitely not actually at rest but compared to the energy of the photon there are at rest enough and then you give some of that energy to the electron that Energy's got to go down and because these two quantities here are constants the wavelength has got to increase and hopefully this makes intuitive sense the photon does what we call a red shift it shifts closer to the red end of the visible spectrum than the blue end and as you guys know the high-energy light in the visible spectrum hits towards the ultraviolet that's what tans you or gives you skin cancer red light or infrared light doesn't do much of anything at all and so this is that on the extreme scale where when we say redshift we don't necessarily mean the photon is visible but we do mean that it's shifting to a lower a lower energy or a higher wavelength and so this wavelength shift is always going to be well is it going to be positive or negative is what so you say the wavelength shift is gonna be positive which would mean an increase in wavelength there you go yep cuz it's got to be it's got to lose energy so I'm not going to go through the derivation of these because I want you guys to go through the derivation but we're going to do it in the exact same way and I'll help kind of kick you off where in this case what are the three quantities we can conserve and like every physics everywhere mass energy and momentum the trick here is what is the mass of the photon massless so we've got energy and momentum and we've got let's say some wavelength shift to determine which is some change in energy and we've got two angles to deal with that's three unknowns we need three equations so we know that our initial energy coming in is going to be H nu plus approximately zero becomes H nu bar and the kinetic energy of the electron so that's our energy conservation relation and then what do we do about the momenta what do we do last time exactly split it up into X&Y momentum so the X momentum of the photon so I'll just label this as energy put the X momentum of the photon is H nu over C and there was no X momentum of the electron to begin with so then we're going to say this has outgoing momentum H nu prime over C times cosine theta plus whatever the electron momentum is let's say M electron V or root 2m electron t electron cosine fee and then how about the Y momentum what's the Y momentum of the system at the beginning yep nothing for the Photon nothing for the electron and at the end we've got H nu over C sine theta minus because it's in the negative y direction momentum of the electron sine fee I'm gonna stop my part of the derivation there cuz I don't want to steal away your whole homework problem but you're going to start it out exactly in the same way as we were doing kinematics of two particle collisions because what is a particle about a wave they're all the same thing it's modern physics and then here's an interesting bit here this maximum wavelength shift if you want to figure out what is the well let's say what is what's called we call it the Compton wavelength so if you were to decide what is the maximum wavelength shift where would that be at what angle hmm did you have a question or did you say what was it what was the question oh okay sure is what is that angle PI over 2 because at that point cosine cosine of PI over 2 equals 0 yep and so then you get this interesting result no matter what the incoming energy of the photon is you get this zero point 2 3 8 MeV shift and that's actually gonna help explain to jump back to our banana spectrum what the distance is between our photo peak which is our photoelectric peak which is pretty close to the energy of the photon and this part right here which we call the Compton edge which would mean the maximum scattered energy of that photon in this case or no I'm sorry that would be the maximum energy imparted to the electron almost misspoke there and no matter what this energy the photon is that distance right there that's the Compton wavelength interesting quirk of physics huh because in the end all that matters is if the angle is all the same everything else cancels out and you just get a bunch of constants I jump back to there so now we'll take another look at our detector spectrum and start identifying some of these Peaks if you notice this point 2 3 8 MeV looks just like what it does on the graph so this is the kind of cool thing like you guys threw some bananas in a detector last week we got a spectrum yesterday morning and how well timed it was we're actually going to start explaining it today there's a whole lot more going on in this banana spectrum part of what we'll be explaining tomorrow is why do you get this kind of bowl shape this Compton Bowl and it turns out that there's a is a different probability of scattering at every different angle or what we call a differential cross-section a D theta over D Omega because the probability of that photon scattering off in any direction is not equal but if you know what direction the photons scatter is often you know what energy it has or you know what sort of energy it gives to the electron because that's a one-to-one relation and that's why you end up with this very smooth almost cosine ish looking kind of curve and you guys will actually get to derive that yourselves so then on to the wavelength and energy shift by looking at the electron recoil energy and this wavelength shift from that you can actually get some sort of an energy shift you can arrive at what is the recoil energy of that electron and so here's one of the topics that's usually hard for folks to understand but I want to stress it right now when you send gamma rays into a detector draw an imaginary detector in fact let's draw the real one that we used in our banana counting experiment so we had these copper walls we had our bag of bananas and we had our high purity germanium detector let's say we had a good shield on top and then a good shield on the bottom that right there is our active detector and this banana is sending off gamma rays into that detector the way a detector works is not by counting the energy of the gamma ray directly it can't actually do that in this germanium detector you've got a huge voltage applied across it think what Mike Ames actually said was the one we used was about 2,000 volts what happens here is let's say I'll actually need three colors for this let's say a gamma ray comes in that's our gamma ray and interacts in the detector that gamma ray will redshift let me get a redder color because that'll be like physically accurate that gamma ray is going to hit an electron go off at a different angle and redshift or get lower in wavelength meanwhile that electron that it hit actually goes flying off and in the other direction we're gonna call it a hole a defect missing one electron of some sort in this semiconductor normally if there was no voltage applied here these two would just find each other and annihilate and you would have nothing so much to count but by applying a gigantic voltage let's say this voltage was really plus and this voltage was really minus this electron keeps on moving and this hole keeps on moving to the electrodes instead of recombining in the detector they're actually then sent through where they're counted in some sort of ammeter or some sort of energy pulse counter and what we're actually measuring is the recoil spectrum of the electrons that the photons make you're not directly measuring photon energy you're measuring the electron effects part of that is because chances are photons just go through everything this is why I wasn't so worried this morning standing with my face over a 10 military cobalt source because while I was getting billions of gammas per second flying through my brain most of those billions just flew out the other side it's literally in one ear out the other and so most of these gammas if they interact at all will escape again the electrons however because they're charged and very low mass have a very low range in the detector so chances are the electrons that are made are gonna stay there unless you happen to make one like right here at that surface a few atoms and it escapes that almost never happens so forget that and this was last year a huge source of confusion to say why are we seeing some of the other peaks that I'll be explaining in like five or ten minutes or why aren't we seeing 0.23 8 MeV peak because what you're seeing here is a photon losing that it's energy minus 0.23 8 MeV in its maximum energy transfer which is given to that electron then what actually happens next is this electron slams into a bunch of other ones and that slams into a bunch of other ones until all the energy is lost in the detector and all of those electrons get sucked into the electrode by this very high voltage and then the way you count the energy of an interaction is by how many electrons you get in a certain little amount of time and so that's why for example for the photo peak that's this kind of simplest reaction a gamma goes in a really high electron comes out it smashes into tons of other electrons imparting all of its kinetic energy in the detector which is all summed up in a nanosecond or however long we collect for and then we say that we saw an energy blip containing about 14 60 ke v of energy it all came from that first gamma and then it was all given to that first photo peak electron which then slammed into a whole bunch of others and they slammed into a bunch of others there's this what's called this ionization cascade where a whole bunch of electrons make a whole bunch more until all of them have too little energy to ionize anything else and then they're just collected so that's what we mean by a pulse in a detector it's not exactly an intuitive concept because it's not like the gamma goes in and we just count its energy there's more things that physically happen in here but it's important for you guys to know especially when we start to look at pair production you guys remember some of this stuff from the positron annihilation spectroscopy well the way we actually know that positron annihilation spectroscopy or pas works is by measuring photons or their eventual electron recoils that can only be possible from this process so as a quick review let's say you had a positron source like sodium 22 which naturally undergoes radioactive decay and forms a positron along with a gamma ray from a very short isomeric transition or I T then that positron bounces around in the material until it reaches an electron and once it hits that electron because the positron let's say the rest mass of the positron is the same as the rest mass of the electron which is 0.5 1 1 MeV once the two of these combine they annihilate producing 2 5 1 1 ke V or 0.5 1 1 MeV photons and it's those photons at this exact energy all the time that really give it away because there's not many other processes that produce a huge amount of exactly that Photon now that we've talked a little bit about momentum and energy conservation does anybody know why you get what's called a blue shift or a red shift in positron annihilation spectroscopy I'll give you a hint it goes down to conserving the same things that we're doing all the time yeah Kristin your clothes I mean technically your clothes if you treat electrons as waves would you totally can the electrons themselves do have a nonzero momentum as they're flying about in the atom or around the nucleus and when a electron collides with a positron if that electron already has some momentum associated with it then the cell system of mass was not at rest it's moving at some small speed so this little minus Delta energy in plus Delta energy accounts for the initial momentum of the electron which means not only can you tell like from the lifetime how many electron looking defects there are but you can probe electron momentum by looking at the slight energy changes as positrons collide with electrons it's a really cool and powerful technique that uses only 2201 concepts to probe matter at its deepest level so what's happening on the atomic scale is let's say a photon made a positron and the positron bounces about what's called thermal ices or just slows down via collisions via other types of collisions that will go in too soon and then gets trapped in a defect which is a relatively electron poor place but it doesn't matter no electrons like you know in every space everywhere there's a probability that there's an electron in it in a defect not containing an atom that probability is lower but not zero and so by figuring out how long they last and when those 511 ke V gammas are emitted you can tell let's say what size defect that was but now let's talk about what happens to these 511 ke V gammas what evidence do we have that positron or pair production actually exists so before I reveal the labels can anyone tell me what on this graph suggests that positrons are happening and there's actually two things what do you think yeah that's right that's exactly right there's a peak at 5:11 ke V that they trace that up yeah I went went over yeah right there five-eleven ke V is it exactly 5 11 kV what do you guys think so forget the fact that it came from a positron let's say a 5-11 ke V gamma came in somewhere how would it then release electrons to be counted it then undergoes photoelectric emission so the actual energy of this would be 511 ke V minus the work function of the material this is one of those tricky questions that you might not even see it on the spectrum but I want you to physically understand what happens here it's not like 511 ke V positron photons magically get counted at 511 kV they then have to eject an electron somehow and for those electrons to be counted they have to interact in exactly the same way as all the other electrons there's no difference what else oh yeah good question [Music] that was my next question to you so let's think about this a little bit we'll start off with gammas being emitted in all directions from our bag of banana ashes now the question is where do these 511 ke V photons come from if the gamma ray interacts with the detector by any mechanism including pair production what are the possible things that could happen there's three different scenarios let's pick a 511 ke V color well first of all it might just undergo a pair production and it'll release to 511 ke V gammas let's see those are there are five 11 kV gammas and because their gammas and they interact with almost nothing they can get out so you might end up your energy that you detect in the detector might be the energy of your gamma ray -2 times 511 MeV this is what we refer to as double escape close the quotes like that so if this gamma ray right here came in at 14 60 ke V and the double escape peak if it undergoes pair production in the detector and both of those 5 11s escape because a lot of them do where would you expect there to be a double escape peak on this spectrum yeah let's say you add that - so we're at 14 60 minus 1.0 - - that comes out to about 450 ke V for 50 K easy right here not much going on is there you're not gonna see it in every detector especially the larger the detector is the less likely both of those photons are going to escape so this is where the concept of detector size can tell you whether or not you're going to see every peak that's physically happening so in this case the germanium detector is pretty big it's pretty expensive so chances are a lot of those 511 K V's even though they're are produced in pairs one of them didn't quite get out yeah Luke that's right dad yeah that's right why don't we write that down in steps for let's call this pair production in the detector so step one would be gamma emission step 2 would be electron positron creation step 3 would be annihilation no lotion in the detector and then step 4 would be somewhere between zero to two photons escape so we have actually three scenarios that could happen here for pair production inside the detector one of them we just described where a pair production happens you get anihilation in a very short time frame like tens of Pico seconds or hundreds of Pico seconds both the gammas get out that would have produced a 460k EVP which it might be there but I can't tell if that's a P curve if that's noise so we don't really know and chances are the reason that didn't happen is because the detector was big so an X next possibility what if one of those photons gets out and one of them doesn't it then interacts via compton scattering or photoelectric effect or any of the possible mechanisms then you'll end up with an energy counted equal to energy of the gamma minus only one of those things getting out and we call that single escape at what energy would that single escape peak be oh it would be that pink people be at the energy of the gamma 1460 -5 11 kV so roughly 900 kV or so there we go there it is that's the second bit of evidence that there is pear production going on not only do you have a peak at 5:11 kv which we have not explained yet but you also have the single escape peak which is the energy of your gamma minus 1 escape from a 5-11 ke V photon photon yeah yes I mean it what I escaped I mean it escapes the detector and is no longer counted so it might go and dropped somewhere else but your detector doesn't know it so what's the third scenario that could happen what if zero of these photons escape what energy will you count exactly so all that's going to happen is it's going to look like the photoelectric effect in reality you'll have slightly slightly lower energy because you have three work functions to subtract off from the three photons doing stuff but I would count that as correct it's gonna look just like the photoelectric effect first you get that energy minus one point o2 2 MeV and then both of those 511 ke V photons interact in the detector by probably photoelectric emission and you just get another count at this channel right here now the last question I want to ask you guys where did this peak come from under what circumstance would the detector just count 511 ke V I'll give you a hint there's a reason I drew gammas going off in every direction yep so most of the gamers don't hit the detector but let's say you had a gamma that went into anything else like the copper shielding and it underwent pair production and one of those gammas made it to the detector I'm sorry one of those photons made it to the detector that's actually where these things are coming from because most of those gammas are not heading towards the detector this is a very small solid angle but surrounding the rest of the detector is this really dense copper and these high-energy gammas in this relatively high Z material undergoes a lot of pair production so it's firing out 511 ke V photons in all directions and some of those enter the detector when nothing else enters the detector and that's why you get this 511 ke V peak right here so we haven't explained every peak on this graph does anybody have any ideas where what's that about or that or those yeah could be cosmic rays that's probably what's contributing to a lot of the noise here as well as thermal noise in the detector but what else haven't we accounted for now to bring this a little more into reality we ran an experiment where we burned bananas we didn't put a potassium-40 certified source in we put bananas in what else could be going on other isotopes that's right but you can identify them quite easily one by checking to see where you expect the photo peak so just from the decay diagram you'll expect to see some interactions or photoelectric effect interactions at these transition levels luckily you know they're not due to potassium because potassium Zone Li got one of them in addition you should see some very similar features so if you have a photo peak here you would expect to see another compton edge 0.23 8 MeV away and it's kind of hard to tell if it's going on because that's a rather weak photo peak and you would expect then for the high-energy gammas to see another single escape peak maybe right there and add to the 511 ke V peak because those are all the same so when you take the spectrum of a real thing and you have two deconvolution stitch ooh --nt interactions it's important to know what all these possible interactions are so that you can take them apart and say start off with a photo peak which should tell you what elements are there and then you can subtract off the expected amount of compton scattering the expected amount of single escape peak and then see what's left over what other isotopes may there be that you haven't accounted for yet so the last thing I want us to try as a mental exercise is to draw to spectra let's say this will be energy versus intensity and for this I want you to imagine that you're at first your detector is very small and then I want you to imagine that your detector is very large and I'm gonna keep this visible so you can have this as a mental model if we had just one isotope potassium-40 what do you think the spectra would look like for an extremely small detector and for an extremely large detector so where do we start that's right and it will there be any difference between the two probably not so a small detector maybe a large detectors going to have I don't know a larger intensity but for the same type of detector you're gonna have pretty much the same thing what's next compton edge so there's going to be some energy that compton scattering is going to start out and then it's going to proceed up the slee is there gonna be any real effect of the detector size probably not because as soon as you release that compton electron that electron slams into all the other ones and nanometers or microns of material and all the energy is collected what's the real difference going to be that's right so though a 5-11 peak and the other associated ones so for a really really small detector we have the possibility for a double escape peak a single escape peak and just more photo peak what's the most likely scenario double escape so if we go down here let's say if this difference is 1.0 to 2 MeV you would expect a larger double escape peak and what would you expect your single escape peak to be significantly smaller so let's say this difference right here is 5 11 kV how about for a large detector quite the opposite you might expect a tiny or even non-existent double escape peak maybe a large or single escape peak but most of the time you're just going to add on to your photo peak depending on the resolution of the detector because in this case for a small detector if you have an interaction inside that volume chances are most of those 5 11s get out for a large detector chances are most of them stay in and undergo their own Compton scattering or photo peak reactions so let's say that all these detectors will also have a 511 ke V we'll just mark that off let's just give them the same height what else are we missing if this is an ideal scenario with no noise well what are those five what can those five eleven ke V photons do can they make peer production of their own no they're not high enough energy in fact they're half the required energy can they undergo photoelectric effect sure that's probably where we're getting those five Elevens can they undergo Compton scattering why not there's no minimum energy to scatter so what you're going to end up with then is 238 kV away you should have another little confident at a distance of 238 KETV away from the 511 kV now in reality you probably won't see it cuz you're gonna have other x-rays you'll have bremsstrahlung which we'll talk about tomorrow which is that breaking radiation you'll have background radiation and it might be hard to see but technically it should be there because any photon of any energy is going to have that same sort of Compton edge shape the shape changes just a little bit depending on the energy of the photon but you're always gonna have an edge you're always gonna have some sort of a bowl just how big the edge is compared to the bowl well we'll get to that tomorrow so it's a little after 505 of I think this is a good place to stop because it's the full conceptual explanation of the ways that photons can interact with matter so I want to ask you guys if you have any questions based on what we've done today yep yep that's right so the electron and the positron annihilate turning their mass into energy since the rest mass of each of those is 5 11 kV the photons come off at 511 KB yep good question the positron is not a whole so like here where we were talking about an electron hole pair a hole would be lets say an atom with a missing electron a positron is a particle itself of antimatter that has the same mass but the opposite charge as the electron and so every particle has got its antimatter component like there are antiprotons and antineutrons that if they find their regular matter selves do annihilate yep so a small detector would see double escape because at first let's say a gamma ray interacts and undergoes pair production and so it's going to let's say create an electron-positron pair and it's going to give them a whole lot of extra energy so they're gonna knock around and ionize things and that's going to count up to the made-out energy at a gamma minus 1 MeV then when they annihilate if it's a small detector chances are those gammas just get out we're gonna be going over why soon when we get into mass attenuation coefficients or cross sections or interaction probabilities but as the energy of a gamma goes up that's interaction probability goes way down and this is a fairly high energy photon compared to like the easier ke V x-rays that you tend to see so chances are these these photons get made from annihilation but they don't stay in the detector then the bigger the detector is the more mass there is in the way and more the more likely they get counted but all of this happens well at the speed of light leads the photon part and so it's so fast that the detector picks it up as that sum of all the different processes of energy in one time interval this is like I said this is the harder stuff because it's not direct it's a multi-step process with different possibilities but it's important to know where the single and double escape come from where the five 11s come from which is outside the detector yeah had a question ionization cascade exactly yeah so like if a 511 ke V photon enters the detector the detector does not know until an electron interaction happens so most of the photons that entered this detector leave the detector that's why if he actually look at the banana stuff which I'll pull up right now at the efficiency check out those values their efficiencies in the realm of 10 to the minus 4 or 10 to the minus 3 which is to say that out of every thousand or 10,000 photons that enter the detector one of them undergoes an electron interaction and the other 9999 just goes screaming on through and the detector does not know where that they're they're the way that Mike Ames got these efficiencies is by putting a source of known activity in calculating how many gammas that detector should have picked up and dividing and taking that divided by the number that it actually picked up and so that way you know how many gammas really went in and how many gammas it saw and that's how you get the detector efficiency and you will have to account for this when you do this on the homework problem so the only quantities you're gonna need is how many gamers did it get what's the efficiency and then back that out so you'll have to calculate the activity of the bananas and then figure out how much a banana weighs and then you should know be able to calculate the radioactivity of one banana in Curie's or beccarose or micro carries it's all it's all good it's a good question so it's three of so I want to let you guys go but I'll see you again tomorrow when we'll review a little bit of this stuff and we'll get into more of the math of the cross sections and why Compton scattering and pair production take up the energies that they do you