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 today we launched into radioactive decay and so this is you know kind of what makes us us in this field right now that you've learned the general q equation we're going to look at some very simple specific cases and specifically all the different things that can come flying out of nuclei and the orbiting electrons around them first I'd like to try and develop a generalized decayed diagram what are all the different ways that nuclei can decay and I had written one of these up to show on the slides and my one-year-old son fixed it with a bunch of markers and crayons so I think we're gonna have to redo this from scratch so let's say you had a generalized unstable nucleus over here and we're gonna start drawing a generalize decay diagram you'll see decay diagrams well much like these I've already shown you a couple of these like these decay diagrams for uranium-235 as soon as I clone my screen so you can see it there are a couple of axes that aren't drawn on these decay diagrams that'll help you interpret them and the first one the imaginary y axis is an order of increasing energy and the second imaginary y axis is Z atomic number so this will help you determine how we read these and how to actually write them now what are some of the different ways you've heard of things that can radioactively decay or that you might have read from the reading this yellow mout alpha decay so in alpha decay what actually happens let's say that we had a parent nucleus with atomic number Z and mass number a what does it change into anyone know what an alpha particle consists of yeah a helium nucleus so let's just say helium well this will be a 4 and a 2 and there's going to be some daughter nucleus we don't know what with Z minus 2 protons and a minus for total nucleons so if we were to describe alpha decay on a decay diagram where would we write the final state of this alpha decay new alpha decayed daughter nucleus to the left or to the right I know it's like 9 a.m. but someone just shout it out you'd have to raise your hand to the left yep something that's decreasing in Z and also decreasing in energy we would draw an alpha decay like this to the left so let's say this would be something more stable with a Z - to make that clear and then a minus 4 what are some other ways things can decay I heard a whisper beta decay so what happens in usually by beta decay we're referring to beta minus decay which would be the emission of an electron from the nucleus again the differ what's the difference what's the physical difference between a beta particle and an electron nothing what's the nomenclature difference the beta comes from the nucleus otherwise when they come out they're kind of indistinguishable so what happens in beta decay let's say we have the same parent nucleus starting with Z a we know it emits an electron with no mass and what else this is just a matter of conservation of things here yep there is an anti-neutrino which has pretty close to no mass and no charge and what about this daughter nucleus how many protons and total nucleons would it have yeah should have one more proton and how many more total nucleons the same yep like that and so how would we draw a beta decay on this generalized diagram to the left or to the right to the right it's increasing in Z I haven't defined any scale so let's just say that's a change of 0 that's 1 that's 2 and that's plus 1 that's plus 2 hopefully we won't get to today so a beta decay would proceed thusly so you'd have some other stable nucleus with Z plus 1 and mass number 8 what are some other decays you might have heard of before electron capture so in electron capture what actually happens start with the same parent nucleus in this case the nucleus actually captures an electron from one of the inner orbitals and so that in effect like neutralizes a proton right in terms of charge so what do we end up with yep so we'd have some daughter nucleus if it neutralizes a proton we'd have one fewer protons and then how many total nucleons the same yep there we go and so if we were to draw electron capture on this map we would have one fewer proton so we could have some sort of decay by electron capture anything else what other particles can be emitted from a nucleus yeah positrons so let's get this list going up yeah so if we start off with a parent Z and a we know we emit a positron which is the antimatter equivalent of an electron so same general characteristics except opposite charge in this case we'll give it a zero protons and zero neutrons and we end up with well the same daughter nucleus so we could say that this precedes by positron creation or electron capture it's the same process or the same ending state but can you have positrons in any possible decay we actually went over this once anyone remember yeah so you're saying your head no we'll get back into that you're right so we'll put a little box around this because you have to have a certain amount of energy in order to create the positron and what else what about the the easiest one what else can be emitted from a nucleus I heard a couple things neutrons so certainly if you emit a neutron there are some very unstable nuclei like helium five which exists for what ten to the minus twenty six seconds or something that could have been a neutron if we start off with Z an a then we'll start off with a neutron and a daughter with the same Z and a minus one total so what would that look like on a decay chain you don't usually see this but we're draw it anyway it would go straight down right so it'll be some other nucleus so the same Z but an a minus one and it could decay by Neutron emission yeah that totally happens if you look at the very very right edge of the table of nuclides let's go back to the home page for that and look at the super Neutron rich like helium ten who's ever heard of this right doesn't even say let's say two neutrons so this is so unstable that it just immediately spits out two neutrons so yeah these things happen you won't tend to see this decay in textbooks because it only happens for exceptionally unstable nuclei but yeah that's true it does happen what else could happen remember we've been talking about yeah right it could be gammas and so I'll make one little extra piece here for a gamma decay which is nothing more than a photon emitted from the nucleus we start off with a parent Z and a and this becomes well what should I even write daughter nucleus I see some people shaking their heads no why not yep yep so very close you have the same atom so let's say the same parent with the same number of protons same number of total nucleons and I'll just correct that to say one of its nuclei is at a lower energy state but otherwise everything is completely correct so why don't we put a little star here to say that that was at an excited state just like electrons can be promoted to outer shells pick up a little bit of energy so can nucleon so can protons and neutrons and this is so going to be a subject of well great discussion in 22:02 for now all you have to know is that nucleons like electrons can occupy higher energy states and when they fall down to lower energy state they can release that energy in the form of a gamma ray so you could also have let's say squiggly line gamma decay to something stable and so this right here would be the generalized decay diagram anyone ever heard of one isotope that undergoes all these possible decay mechanisms glad no one's saying anything because neither have I there's one that comes close actually if you look at no that's not this part I want to show you I want to show you the big one if you look at potassium-40 the nuclide we've probably talked about the most so far it covers most of the space of this generalized a.k diagram and there was a question that came through at least I think or non-anonymous email what is it that makes these even even versus odd-odd nuclei less or more stable anytime you have an odd odd nucleus both the number of protons the number of neutrons these nuclear shells are not fully occupied and they're not that stable compared to an even even nucleus that has an even number of Z and an even number of n just kind of like electrons these things tend to travel in pairs and not fully occupied energy levels will be less stable potassium-40 happens to be one of those odd-odd nuclei that is relatively unstable and it can go either way either you can lose a proton or you can gain a proton by competing mechanisms like positron or electron capture or beta emission so this one I like a lot because it gives you almost every possible decay with the exception of alpha decay and spontaneous Neutron emission it's not that unstable and you know only one really missing from here I found what I think is the simplest to K diagram ever just prozium 151 there's only one thing it can do is it can decay via alpha decay to its ground state I want to point out a few of the features of these decay diagrams so you know what to look for up here is the parent nucleus down there's the daughter nucleus and these energies are not absolute they're relative to the ground state of whatever the daughter nucleus is so this is a simple example who helps show you that Galilean 147 doesn't have a binding energy of zero this is relative to the ground state of Gadd 147 and that will tell you that the Q value for this reaction is 4.1 796 MeV these things are usually listed in MeV unless said otherwise you also might notice a pattern that most alpha particles tend to come out around 4 MeV or larger the answer to y is going to be given in 2202 yep these percentages tell you the probability that each decay will happen these are usually measured because it can be let's say let's say things get quantum and difficult in terms of calculating these and our knowledge of wave functions of well higher and higher a or Z nuclei gets a little less time a little more tenuous so a lot of these would be measured you can look at the number of alpha particles of each energy that you observe and then you get the average probabilities for this one it's simple there's a hundred percent probability that this is the only thing that exists the other things to note the half-life will be given up here in this case at seventeen point nine minutes so relatively long half-life compared to helium five and we'll be going over what half-life is and what they are on Friday and then the last thing are the spin states of the initial and final nuclei which we will not cover in this class but you will cover in 22:02 so don't worry about those now but do know that when you need to go find the spin states of the initial and final nuclei to see if certain transitions are allowed this is where you're going to go any questions on what you see here on how to read these decay diagrams okay then let's move on to some the simplest of them which in the table can look the most complicated so here you can see that there's a whole bunch of different probabilities for different alpha decay nuclear this is one of those more complex examples where the easiest thing to do is just measure see how many alphas you get at each energy and this will give you the approximate probabilities that each decay happens and you'll notice here that the final energy states for each of these alphas is not necessarily zero this will tell you what they are relative to the ground state of in this case thorium 231 so you can emit an alpha from from any combination of nuclear shell levels inside this nucleus and you might end up with a new daughter nucleus whose protons or neutrons are in excited States and the way you remove those excited States is gamma decay like we talked about here so a lot of alpha decays are immediately followed by a chain of gamma decays or what we call I teased or isomeric transitions so you'll see a couple bits of notation for example you make here called gamma decay you may hear it called isomeric transition we'll try to give them all so that in the various readings you have you know what's what so notice here you can have with the probability still small that they didn't bother to draw it an alpha decay to 0.6 3 4 MeV and then any series of gammas from let's say from this state to that state and then from this state to one of those or one of those and then another one down there so an alpha decay may be followed by a whole bunch of gamma transitions or as few as none if you want to see what the Alpha energies are well let's head to the table of nuclides and look at uranium-235 so if we look up u-235 you can see that at alpha decays to thorium 231 and I'll show you the part of the table that I didn't show you in the slides which is then you've got a table of alpha decay energies as well as relative intensities and what's called a hindrance this stuff right here comes from the fact that different alpha decay energies can happen with different probabilities at different times so the half-life of a particular alpha decay can be slightly different and this is another one of those really kooky things where certain energy alpha transitions will happen a little more often initially then finally but we don't have to worry about that yet I just want you to know that's why the hindrance is there and so you can look from this table what's the probability that each of these alphas will come out and there's going to be some uncertainty associated with these this is going to usually be some sort of measurement uncertainty then you might also ask why is it that the highest energy alpha ray is not the same energy as the Q value so for this it's a greatly simplified application of the Q equation that we learned last time so for here what are the two equations that we need to conserve if we have a system consisting of we have our initial nuclei going into our final nuclei and they go off in equal and opposite directions if it's alpha decay then we have no little initial nucleus we just had a large initial nucleus at last at rest and afterwards you've got a small final nucleus which we know is the alpha particle and a large final nucleus which we'll call the daughter product and let's say this is the parent it's a much much simpler system than the general one we analyzed last week so what are the equations that will use to conserve to find out what's the energy of this alpha particle anyone same three answers as always yep yep mass energy and momentum I'm gonna lump these two together because they're kind of the same thing so let's just go with energy and momentum so what is the initial kinetic energy or let's say the initial kinetic energy of this parent nucleus we can assume to be zero what about the final kinetic energy of the system well there's only two particles there's going to be some kinetic energy of the alpha particle plus the recoiled kinetic energy because if the alpha goes in one direction the daughter nucleus has to go off in the other direction and the total energy comes out to Q this Q value you can get by conserving Nath's where we can say that the mass of the parent has to equal the mass of the Alpha plus the mass of the daughter plus Q so that's where we can get cute if we don't know it already luckily we know it already so there we've used mass there we've used energy and now what are the momentum of the initial and final states here anyone just shout it out what's the initial momentum of the parent nucleus zero equals what's the momentum of the Alpha and then remember that trick if we want to say p equals MV equals what more convenient form that contains the energy square root of 2m t so let's go with that so there'll be the square root of two mass of the Alpha kinetic energy of the Alpha minus the square root of two times the mass of the daughter times the kinetic energy of the daughter because these have to have equal and opposite momentum so all we have to do is move that one over here this makes that equation easy everything's got a square root of two we can square both sides and we end up with a pretty simple relation mass of the alpha times the kinetic energy of the Alpha is the mass of the daughter times the kinetic energy of the daughter we don't usually care about the kinetic energy of the recoil nucleus or the daughter because the range is so small that we usually don't get to measure it but we are trying to measure what are the actual alpha particle energies so that we can reconstruct oops this table down here so we can take our energy conservation equation and rearrange it to isolate TD the kinetic energy of the daughter and say TD equals Q minus T alpha substitute that in here and let's rewrite what we've got mass of the alpha T alpha equals mass of the daughter times Q minus T alpha if we multiply each term in here by M D we get M DQ minus M D T alpha then we can take all of the T alphas on one side so we'll just add T I add M DT alpha to each side so we have M alpha T alpha plus M DT alpha equals M DQ we can factor out the T alpha here and then we can divide each side by M alpha plus M daughter cancel out the MA plus M D and there we have the answer the kinetic energy alpha is just the Q value times the ratio of the daughter mass to the total mass this should look awfully familiar when we did this in the frame of Neutron elastic scattering or any other reaction we had the same equation with just different notation so do you guys recognize this firmware we had t3 equals Q times M 4 over m 3 plus M 4 it's the exact same result just different notation last time we did it in the most complex way possible this time we started off with the simplest possible equations for alpha decay in the end it's the same q equation we just didn't bother what all the other terms and angles and things that we don't need so is everyone clear where this came from cool and that's why you're never going to see an alpha particle that's got the same energy as the initial minus the final energy because the recoil nucleus or the daughter nucleus takes away some of that kinetic energy in order to conserve the momentum of the system that was initially at rest another way to say this for those who like center of mass coordinates is the center of mass of this system was the parent nucleus it was at rest the center of mass of the final system has to remain at rest to conserve momentum but again I won't go into much into center of mass because I find it a little unintuitive I'll stick with a laboratory frame of reference so any questions before I move on alpha I think is the simplest case of radioactive decay and think now you know all you need to know about it yes they were not not MA and MD but TA and TD would change yep so in this case for a different alpha decays they'll have different Q values so the Q value of let's say this top alpha decay is this energy here four point six seven six MeV minus 0.63 four so use a different Q and you'll get different TAS and T DS yep so don't worry you'll get chances to try out these calculations on the homework well I'll actually ask you to verify some of these you know calculate some of these from this equation make sure you get the same values as the table any other questions on alpha decay before moving on to beta we're just going an order of the Greek alphabet so beta decay is a kind of funny one you don't tend to get a beta particle out at the energy of this Q value you actually end up getting a spectrum and this measured spectrum of different beta kinetic energies is what led to the thoughts that there must be something else carrying away some of that extra mass of some of that extra energy I say that like it's the same thing because yeah it totally is and this is what led to the thinking that there's got to be some other very difficult to detect particle so the theorists here we're saying if we take we know the initial and final energies from beta decay and we know that we get a spectrum of different beta energies and the probability of finding a beta particle at energy Q drops to like zero you'll almost never see it there's ought to be something else carrying away the energy so this idea of the neutrino or in this case the anti neutrino was proposed a long time before it was confirmed and finally we know why and one of the questions I want you to think about because it might be on an exam in exactly two weeks is if this is the relative number of electrons from beta decay as a function of energy what does the number of anti neutrinos versus energy look like in order to maintain conservation of energy so it's something I want you guys to think about but I'm not going to tell you what it is until the solutions for an exam in the meantime what another thing to note is that these beta decays can also be followed by any number of gamma transitions I've given you a simple one if you want to look up simple ones to test your knowledge go with the light elements they don't have that many nucleons and they won't have that many transitions for example if we pick a beta decay nucleus something simple let's go with lithium which typically has the stable isotopes are lithium six or lithium seven so do you think that higher or lower mass number lithium will tend to go by beta decay based on this generalized decay diagram it's what lower lower proton number well we got to stick with no number of protons because we need to remain lithium so in other words do you expect lithium four and lithium five or lithium eight lithium nine to go by beta decay the higher ones okay if you guys remember the math parabolas from a couple weeks ago we delineated where you'd expect beta decay in order to reduce the proton number and positron decay in order I'm sorry beta decay in order to increase the proton number so if you've got too many neutrons and not enough protons chances are beta decay will help equalize you out so that's a guess I haven't even tried this at home let's see let's see what happens with lithium eight oh look at that beta decay can also decay by beta plus two alpha which is another word for the nucleus just blows apart it's interesting too if you read Chadwicks paper again the way he described a beryllium nucleus is consisting of a neutron plus two alpha particles interesting huh lithium nine could decay by or let's say lithium eight what do we have beta plus 2 alpha yeah so Chadwick described any nucleus as consisting of these elementary ish particles that you could measure and in this case you kind of see a physical example when this nucleus blows apart it just becomes two alphas and a beta interesting but let's look at the beta decay two beryllium eight pretty simple you may ask why can't you have beta decay for directly from the highest energy to the ground state energy that is a 2202 question that I'll mention there are allowed and unallowable in and energy states so if you're wondering why isn't every line drawn in the case of really complex nuclei there aren't enough pixels on the screen sometimes but for the simple nuclei there are actually rules of selection to decide when you can make this transition but a lot of beta decays will usually be something like a beta decay followed by a gamma so let's see a couple of well-known examples for example carbon-14 this is the basis behind carbon dating one of those rare instances when you have a beta decay directly to the ground state it's about as simple as it gets and because the half-life is 5730 years it's really useful for dating when did an organism or a piece of material die on the timescale of let's say 10 to tens of thousands of years once you've gone past a few half-lives and there's very little carbon-14 left there aren't a lot of decays left and your counting statistics get crappy and it gets harder and harder to carbon-date things the basis behind this is that all living organisms that are in taking an exhaling carbon by some means remain an isotopic equilibrium with the carbon surrounding them and while most carbon is co2 and sand food and whatever is carbon-12 you're going to have a little bit of carbon-14 production from the upper atmosphere this is usually a cosmic ray phenomenon which we'll get into when we get into cosmic rays the moment you die you stop in taking carbon and the little bit of carbon-14 in the cloth and the food and your body whatever starts to decay naturally with a very regular decay curve and so this is the whole basis behind carbon dating and in the next pset you'll actually see how this was used to debunk the Shroud of Turin or the supposed burial cloth of Jesus of Nazareth because the carbon dating data just didn't check out as much as people really wanted to feel like we found it no science that's the answer no another well-known one we've talked about before is molybdenum-99 decaying to technetium-99 metastable notice how here any number of beta decays and any cascade of very fast gamma transitions they almost all end right here at this state of about C there's two numbers written over each other but it's about a hundred and forty ke V or 0.14 MeV this transition from this state to the ground state is a slow transition so you can actually build up technetium-99 in what's called series decay which were going to cover on Friday and then you can use these 140 ke V gamma rays to do medical imaging so when you get a medical imaging procedure done chances are this is how it's done you get Molly 99 out of a reactor or an accelerator Technic a toda that chemically isolate the technetium-99 metastable which lasts on the order of six days or so very quickly get it to someone inject it an image where do the gamma rays go or what are the gamma rays come from one last notable one is responsible for a lot of well problems when folks go urban exploring an old dentists offices nowadays they have electrostatic x-ray machines at dentists offices but back in the day you could get a little button of cobalt-60 which would emit two very characteristic gamma rays in addition to its beta decays so normally what happens is cobalt-60 decays quickly to an excited state and gives off two gamma rays an accession succession which would be used for imaging problem is that's a radioactive cobalt source and if you don't know what it is and you're like oh cool what's this blue thing I think I'll put it in my pocket and keep it that has been responsible for some injuries from some folks that didn't know any better then how do you detect the neutrinos we talked about the theoretical reason why they exist let's actually see how they're measured there's a hollowed-out salt mine of some sort called kamiokande in Japan it's a humongous Hall in the ground filled with water for a reason and lined with tens of thousands of highly sensitive photo tubes that can pick up tiny tiny amounts of light the reason for this is because neutrinos as you saw in problem set 1 are always traveling near the speed of light in a vacuum so if the speed of light in a vacuum let's call that one and the velocity of the neutrino wasn't it something like 0.999 C or something like that it was pretty high the speed of light and water is significantly less than the speed of light in a vacuum when you have a material or a particle that goes faster than the speed of light in the medium that it's traveling in then you can produce what's called Cherenkov radiation which I think I've mentioned once before it's kind of like a sonic boom in that you get a conical shock wave of energy radiated from that particle that tells you which direction it's coming from but instead of a sound wave you get light and this whole detector is designed to look at the ellipses of Cherenkov radiation released by neutrinos and antineutrinos so what happens is if a neutrino happens to interact with the water here it produces Cherenkov radiation lighting up a ring of these detectors so you can tell it's energy and you can tell where it came from so if you let's say cone correlate a supernova or some sort of crazy galactic whatever with a slight burst of neutrinos then you've got a pretty significant astronomical event it also led to my favorite BBC headline ever particle physics telescope explodes you'd see this on like fox news or something no this was the BBC what happened here is one of these 30,000 or so tubes was slightly defective couldn't hold the pressure and it burst and the resulting sound shockwave from one photo - bursting blew up about 11,000 of them so yeah the particle physics telescope kind of did explode they did rebuild it and it's still going it was an expensive repair cuz all eleven thousand three hundred something tubes had to be rebuilt and if you noticed there was a guy on a boat there how do you install them well you float on a boat quietly and put the photo tubes in and raise the water level and float to another part of the Tector quietly and continue installing the photo tubes until you're done yeah you don't ya don't sneeze so ya favorite BBC headline ever thanks again science for a positron decay okay we've got about 10 minutes left for positron decay this is the energy that you need in order to make a positron it is approximately exactly double the MER rest mass of an electron and the question usually comes up well a positron has a rest mass energy of 0.5 1 1 MeV why do you need double that to make the positron because in order to conserve the charge of the system you have to shed an orbital electron so the system has got to be able to lose two electrons in the process of one positively charged and one negatively charged and so that's why the q for positron decay is just gonna be remember the symbols the excess mass here excess mass of the parent - SS mass of the daughter - two times the rest mass of the electrons squared to refresh your memories a bit find some empty space the excess mass is nothing more than the mass - the horrible approximation of the mass so the excess mass and the real mass are directly related and these are things that you can look up just to remind you guys that excess mass and mass and binding energy and kinetic energy are all related again by the Q equation it's probably the last time I'll say it cuz I think that's about a hundred by my count positrons can be used for some pretty awesome things and I will in the last five minutes of show I want to show you some work done by Professor Brian Werth at the University of Tennessee Knoxville on positron annihilation spectroscopy using antimatter to probe matter and find out what sort of defects exist and as a nuclear material scientist I'd be well terrible if I didn't inject a little bit of materials and how we use nuclear stuff in 2201 in order to probe that thing so the way that positron annihilation spectroscopy works is that well matters mostly empty space and in a in a regular crystal lattice where the atoms are arranged in a very regular array let's say these atoms have their orbital electrons the empty space between is also arranged in a very regular array and positrons annihilated electrons to produce well we'll find out in a second but we're in matter would they want to live or where were they last longer not near an atom but near the space in between so you can map out the empty spaces in matter in a regular crystal and calculate an average positron lifetime if you were to fire a positron into this matter how long would it sit and bounce around before colliding with an electron and releasing that extra rest mass energy it turns out if you have crystalline defects but positrons tend to last a little longer there's a little more empty space which is to say there are more places with a slightly less probability of finding an electron and so they last longer and you can measure the lifetime of positrons as they before they enter the material and then how long before they produce their characteristic destruction gamma rays so if you think about it you have a positron coming in with a rest mass 0.51 one MeV and it collides with an electron from some orbital nucleus that has the same rest mass the positron and the electron annihilate sending off gamma rays in opposite directions where the energy of this gamma is the same thing point five one one MeV so you can tell when a positron was destroyed because you instantly get a half MeV gamma ray or actually you get two half MeV gamma rays then the question is how do you tell its lifetime let's go back to something that I didn't quite point out but I want to show you now is this positron decay is immediately followed by a one point two seven MeV gamma ray which is in pas or positron annihilation spectroscopy we call this the birth gamma ray this gamma ray is emitted the instant this nucleus is born and the positron takes a little bit of time to get destroyed so you actually look at the difference in time between sensing the 1.27 MeV gamma ray and the 0.5 one 1 MeV annihilation photons and that is measured in let's say hundreds of Pico seconds with resolution of around 5 Pico seconds and you can then tell from the lifetime at how many survived what sort of atomic defects might exist in the material so if you want to count the number of missing atoms or vacancies in a material which is extremely important to those of us in radiation damage you can do so with positron annihilation spectroscopy so I think I wanted to show you a little bit about how this works you start off by making a radioactive salt sandwich you take some sodium chloride specifically of the isotope sodium 22 which is giving off positrons all the time and you sandwich that radioactive jelly between the two slices of bread better known as your sample that way you catch every positron that gets out so you don't lose half of them to one side you've got two detectors on either side waiting so that that's there's some probability that the photons emitted are going to go in the direction of the detectors so you miss most of the signal but so what whenever you actually sense a 1.27 MeV gamma ray followed by to 511 K V's here then you know you've had a positron annihilation event and you can actually count the time between when those things happened and you can see the number of counts and get the average positron lifetime from finding out how many counts you get every five Pico seconds for example there's something to note about these counting spectra anybody know why they're so smooth up here and then they're so delineating down here anyone have an idea you're gonna see this a lot in 2209 when you actually count beta particles or alpha particles and you're counting statistics get a little crappier this is a log scale of counts or in this case counts per 5 Pico seconds 10 to the 0 is better known as 1 so you're looking at one count or two or three you're looking at the discrete events you can't have one-and-a-half counts so you're gonna see this kind of thing quite a lot when you're trying to count very rare events and if you're down in that down in the weeds like this let's just say your statistics aren't that good but since this is a logarithmic scale 10 to the fourth is better known as 10,000 that's enough to get good statistics and fit a nice curve to this positron lifetime thing this is what one of them actually looks like and you can kind of tell right there's the big inside there is where all the positrons are coming out so that's probably lead shielding here's two detectors on either side and here's another detector to detect that 1.27 mev birth gamma-ray so if you get those three events happening all in the right time you've got a positive event that you can count and last thing I'll mention is you can actually use this like I said to gut not just a number of vacancies but the number of different size defects you might have two or three missing atoms next to each other which will have different positron lifetimes and you can actually count the number of each of these to get the diameter or the size of these atomic defects and this is one of the ways of confirming our models of radiation damage which is like all I do that's half of our group if you want to read anything more about positron annihilation spectroscopy all the stuff in these slides were from these references which you can look up easily on the MIT libraries we have access to everything because that's MIT we just buy everything there is so I'd encourage you to look here if you want to see more details on how this works and why it works so because it's exactly ten of tenna or five of five of I want to open it up to any questions on alpha decay beta decay positron decay or the decay diagrams that we've developed today yes what is the most dangerous kind of decay to be exposed to so in this case you'd want to say the energy of the particle is held constant and the number of those particles is held constant and actually we're going to answer this question when we get to medical and biological effects but let's do a little flash board now let's assume if you want to see which one of these decays is most dangerous we'll have to say constant constant energy of decay constant activity and what else can we hold constant well constant you let's say the same number of particles end up hitting you that depends on whether they're inside or outside your body if you were to ingest material then alphas would be your worst because alpha particles are massive and charged nuclei which means they interact very strong with matter around them so if you ingest them and they end up incorporating into your cells where they can just get next to DNA they can just blast it apart however an alpha source of equal strength held in your hand would do nothing the dead skin cells are enough to stop alpha particles and we're gonna find out exactly why when we look at the range and stopping power of different particles and matter from the outside alphas won't really get through your skin betas might get through a little bit of your skin but not much gamma rays will mostly go right through you it's neutrons that are the real killers says neutrons are heavy but uncharged so they interact kind of strongly when they do hit they pack a wallop and they do a lot of damage and they're mean free path and you is on the order of 10 centimeters so a neutron source from the outside can do a lot of damage from the outside the alphas and the beta's would be stopped by your skin and clothes the gamma rays almost all of them will go right through you and you guys will actually have to do this calculation to find out how many gamma rays would you absorb from a gamma ray emission and how many go right through you the hint is most of them get out so there's a there's an exam question we used to ask in 2201 that I was asked during the first exam is you've got four cookies an alpha emitter a beta emitter a gamma emitter and a neutron emitter of constant energy and activity you must do one of the following you have to hold one in your hand at arm's length you have to put one in your pocket you have to eat one and you have to give one to a friend what do you do and why anyone have an idea pop quiz yeah that's right I can tell this is the West because when I asked a group of Singaporean students the same question they would eat the neutron to save the friend because of Confucian ethics yeah I doesn't fly here your answer is correct because this is America what would you do with the other three eat the gamma because most of the gammas will just get to the friend right what about the Alpha and the beta yep hold the beta at arm's length because there's another aspect of shielding betas that we'll get into when betas stop in material they produce some low energy x-rays called bremsstrahlung so you'd want to get those far from you and the Alpha in your pocket we'll just be absorbed by the pocket yeah so that's the right question so you're not gonna see that on the exam but good news is you've pretty much got the right answer because this is America probably time for one more question if anyone has one cool if not then I want to remind you Amelia we'll see you on Thursday so do come to class Thursday I'm gonna change the syllabus to reflect that and we'll have two hours of class on Friday to get through decay and activity in half-life followed by an hour of recitation so I will see you guys Friday and we'll see what mood I'm in depending on how the nano caliber entry goes could be a fun measurement you