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 okay I think things have been getting pretty derp IV lately so I wanted to shift gears to something a little bit more practical so I started alluding to this hypothetical radiation source I might have right here and things like if you have a source of known activity which we calculated yesterday and you have a detector of unknown efficiency how do you know what the efficiency is how do you know what let's say your dose distance relationship is and how do you calculate all this stuff so let's take the general situation that were starting to work out let's say we have a Geiger counter right here that's our GM tube and we have a point source it's emitting things in all directions let's go with this stuff from yesterday let's say it's a cobalt-60 source right that was it's now zero point five two micro Curie the question is how many counts do you expect in this detector when it's a certain distance away so I've actually laser cut out a little Geiger counter jig from a previous class and you guys can all do this too who here has been to the IDC before couple the International Design Center so they've got a laser cutter that you can sign up to use which is where I did this and it's set to just take a Geiger counter and put your sources at some fixed distance away so you can discover the dose distance relationship with things speaking of does anybody know what the relationship is between dose and distance or measured activity and distance yeah Luke close it's let's say the measured activity would be proportional to one of the 1 over R squared now who knows where this comes from I'll move the source a bit away to lessen the beeping yeah yeah exactly if you were to draw hypothetical sphere around this source right here then you've got a let's say you've got a detector that's roughly rectangular with a fixed area let's say it's got a half length L and a half width W then the area I'm sorry let's just say length L which W the area would be just L times W and actually what's what Chris mentioned as the solid angle subtended by this detector right here as in other words at a certain distance R away how much of this sphere how much of the area of this sphere does this detector take up in other words how many of these gamma rays are going to go in a different direction than the detector versus how many will actually enter the detector and a simple formula for the solid angle is just the surface area of whatever you've got over R squared it's kind of a it's a pretty good approximation to the solid angle of something for very long distances and it's probably the one that you'll see in the reading but I wanted to show you the actual formula in this case for a rectangle solid angle comparison good that's up there so on the let's say on the x axis right here this would be distance from the source to the detector in meters and I've said that we've got some sort of a detector that is 2.5 by 10 meters in size that's an enormous detector let's actually switch it to the units right here so this is roughly 10 centimeters long so let's change our length to 0.1 and what's you think the width of this Geiger counter is in meters centimeter 0.01 we're gonna have to change our axes so we can actually see the graph so instead of looking all the way up to 15 meters away let's look one meter away maybe less this whole thing is probably 50 centimeters and we'll take a look there and what we notice is that except for extremely short distances this approximate formula for the solid angle or in other words if I were to draw a sphere around this source that's the radius of the distance between the source and the detector how much of that spheres area does the Ted Tector take up this actual formulas approximate formula the blue curve is a pretty good approximation of the red curve until you get really really close to like five centimeters away or about this distance right here so anyone know why this formula would break down what happens as R goes to zero what happens to our solid angle or our approximation for our solid angle goes to infinity right Kenneth detector actually take up infinity area on anything never mind that unit sphere not quite if you were to take this detector and bring the radius down to zero so that the source and the detector if not counting for the thickness of the plastic were right up side each other if that solid angle went to will infinity then the count should go to infinity and does not compute does anyone know how many first of all who's here has heard of solid angle before so a little more than half of you so solid angle is kind of the that's getting clicky I'm going to turn that off solid angle is kind of the analog to regular old angle except in 3d so instead of looking at things in radians this has the unit of what's called ster radians d radians with a full sphere taking up for pi ster radians interestingly enough for pi is also the surface area of a unit sphere with radius of one so that's where this comes from if something were to completely cover a unit sphere like if you were to let's say in case a light source in tin foil completely and say how much of that solid angle does the tin foil in case it would be 4 pi ster radians regardless of the size of the sphere how much tin foil you had to use so this pretty simple formula isn't the best approximation for it and I'm not going to go through the derivation because like I said today is going to be of a more practical nature there is a more complex and rigorous formula for the solid angle of something let's say in this case a rectangle of length L and width W from a certain distance R or in this case on our graph X away from the sphere and you can actually see that red curve right there once you get to a few centimeters away it's pretty close anyone want to guess what the maximum value of the red curve is if I take this source and slam it right up next to the detector how much of the detector is I'm sorry how much of that sphere the detector subtending to PI half the sphere because it's this let's say this whole side of the source is completely obscured by the Tector and this whole side is free to move and if you look really closely yep at zero the correct formula does give you 2 pi sir radians which is to say that half the gamma rays leaving this source would enter the detector I didn't say anything about get counted yet that's where the detector efficiency comes in and that's something we're gonna be measuring today which is why I have my big bag of burnt bananas these are the ashes of roughly 50 pounds of bananas charred to a crisp at about 250 Fahrenheit for 12 hours in most of the dorms and a couple of the frat houses so last year I had the students everyone take home about 50 pounds of bananas or 50 bananas I forget which one it was a lot and we did some distributed labor so everybody peeled the bananas put them in the oven baked them separated off the tin foil baked off as much water and sugar as possible to concentrate the potassium-40 in the bananas so there's a reason I've been using potassium-40 has a lot of examples in this class because you're full of it that's pretty much the short answer of it if you eat bananas which I think most of you guys do you're in taking a fair bit of radioactive potassium which is a positron emitter and also does electron capture and all that fun stuff so today what we're gonna be doing is calculating the activity of one banana but that's kind of a very difficult thing to do so anyone know how radioactive one banana actually is in any units at all whatever it is it's very very very very little one banana contains a minuscule but measurable amount of radioactivity and one of the ways to boost your confidence on any sort of radiation measurement is to boost your signal strength or to boost your counting time and because I don't want to count for the next seven years we've concentrated the ashes of 50 pounds of bananas and he to boost your signal strength which is going to boost your count rate which is the intro I want to give to statistics certainty and counting so let's take the one of the homework problems as a motivating example you guys does anyone notice the extra credit problem on the homework let's start talking about how we go about that that should motivate the rest of the day so I'll pull up that problem set number four which by the way is due Thursday not Tuesday because we have no class on Tuesday that was a surprise to me but whatever I'll still be here we don't get holidays just you guys so bonus question go do this so we all know that smoking is a major source of radioactivity and if you think about it it's not just the smoke that contains those radiation particles it's got to be the cigarettes cigars and other smokable --zz themselves and so I was thinking there's no better concentrated source of smoking radioactivity than a smoke shop there's one out of a alewife at the end of the teeth is probably of some closer to campus but I know there's a whole bunch that are tea accessible and so I was thinking it'd be neat for us to find out how radioactive is it to work in a smoke shop because there's all these radon decay oh yeah you actually know are you serious but you got to be 18 to smoke interesting we may have to leave the city for this what about Somerville [Music] berries yeah I don't think it is where I'm from Swampscott I don't think it's uh I don't think it's 21 but that's kind of up on the commuter rail so you don't to go to Swampscott at any rate I would think that okay it's probably a fairly radioactive place to work but the question is how long would you actually have to bring a detector in and count in order to be sure that there's any sort of measurable difference and so without deriving all of the stuff about binomial poison and normal statistics I'll say that's in the reading for today I want to show you some practical uses and applications of this stuff let's say you were to measure some count rate in some experiment and we'll put this in units of counts per minute which would be the number of counts divided by the counting time that's about as simple as it gets from Poisson statistics you can say that the standard deviation of that count rate is actually just the square root of the count rate divided by time and that's kind of the simple thing right here but usually in these sorts of experiments if you want to know how much more radioactive is one place than another you have to take a background count so if I wanted to know how much activity that source was giving off there is lots of background radiation that we'll be going over in about a month I would have to sit here for quite a while and wait for the slow clicks of whatever background radiations in the room there we go to cause to get enough of a count rate going on you can imagine the slower the count rate the less certain you can be that the number that you're measuring is actually accurate so the idea here is that this standard deviation is a measure of confidence that your values actually right so the two things that you can do let's yeah the two things you can do to decrease this standard deviation you could increase your counting time right those looks like why is there a C on top that doesn't look right it actually is okay yeah yeah there we go so by Counting for longer you can decrease your standard deviation this is going to take forever it actually takes about 67 minutes because we've already done this calculation to get a 95% confidence on 5% uncertainty for this sort of background count I mean how many concept we had so far like 12 14 yeah not very many then you've got to be able to subtract that count rate from whatever your source actually is and the way that you actually measure this is pretty straightforward the May the way that you do error subtraction is not as straightforward so let's say we're going to separate these two experiments into a background experiment which we're actually going to do in an hour when we want to count these banana ashes we're gonna have to put we're gonna have to count radiation coming from the detector itself which will account for cosmic rays contamination in the detector whatever else might have been spilled in there from previous samples and we're also going to take some sort of gross count rate background which will be our background plus the net count rate of our actual source and that's what we're going for so the net count rate is pretty easy just the gross count rate minus the background let's keep the symbols the same minus the background count rate does anyone know how to quantify the uncertainty of this net count rate you just add the two anyone well in this case we have to account for the fact that radiation emission from anything is a truly random process so it's actually random you there is no correlation between when one particle leaves and the next particle is going to leave and because it's a truly random process these errors in the background rate and the growth rate could add together or could subtract from each other in other words one might be a little higher than it should be one might be a little lower than it should be if you just add together the two standard deviations you actually always get an over estimate of the true error because you're not accounting for the fact that these two experiments may have partially canceling errors so in this case this that would be your worst case scenario which is not your most likely scenario what you actually want is to do what's called uncertainty in quadrature where you actually add up the sum of the square roots of those errors kind of looks like the magnitude of a vector doesn't it kind of looks exactly like the magnitude of a vector so in this way you're accounting for the fact that more error in each experiment does increase the error on whatever net experiment you're doing but not linearly because sometimes you have partially canceling errors and with enough statistics if you count for long enough or you count enough counts then these things on average are going to add in quadrature which will come out to and I want to make sure you don't have any typos so I'll just keep the notes with me so you need the background count over the background x squared plus those there we go and so now I'd like to pose a question to you the same one that's here in the in the what is it and the problem set how long do you have to count in the smoke shop to be 95% sure that let's say your counter eights 5 percent uncertain and we're going to spend the rest of today's class taking apart that statement and getting at what it should be so again what we want to say is how do you know that we're 95 percent confident of our count rate plus or minus five percent error that's the main question for today does anyone know how we'd start anyone get to the reading today see some smiles okay we'll start from scratch then all right so who's here has heard of a normal distribution before Wrigley LA to you guys great the idea here is that with enough counting statistics this very rare event binomial distribution approaches a normal distribution where you can say if you measure a certain count rate let's say this would be your mean count rate and if you measure some other count rate to limits of plus or minus 1 Sigma or one standard deviation 1 Sigma gives you about 68% confidence in your result confident ya spelled it right the reason for that is that if you go plus or minus 1 Sigma away from your true average right here you filled in 68 percent of the area under this normal distribution similarly if you go plus 2 Sigma or minus 2 Sigma it's around 95% confident 3 Sigma is getting towards 99 point what was the number again I think it's 6 maybe it's more like 98.5 percent and then so on and so on and so on there's actually society is called Six Sigma societies and the way that they get their name is we're so confident of things we can predict them to Six Sigma which is some ninety-nine point a large number of nines percentage of the area under a normal distribution so if I ask you how long do you have to count to be 95% confident in your result you have to give an answer that will relate two times this standard deviation and now we know the formula for standard deviation of this net counting experiment so we can formulate our equation dust Li let's say in order to be 95% confident in other words - Sigma that our counting rate is within five percent of the actual value in other words plus or minus five percent error we put our error percentage here and our true net count rate there so this part right here tells us the 95 percent confidence this part right here is our five percent error that part right there is our count rate so then we can substitute in our expression for Sigma our uncertainty in quadrature and find out things like well depends on what the information were given is let's say before you go to the smoke shop you take your Geiger counter and for an extremely long time you count the background counts somewhere so let's say in this problem the known quantities we know our background count rate because you can do that at your leisure at home and when I did to this that came out to about 25 counts per minute and known is the background counting time and when I did this to get within 95% confidence of 5% error had to do this for 67 minutes and now all that's left is we want to relate our net count rate and our gross counting time or our gross count rate in our gross counting time because it's like the same thing so this is actually how you decide how long you have to sit in the smoke shop to count in order to satisfy what we asked for 95% confidence that your counter eight is five percent error so let's start substituting this out that's not mine so we can get rid of that so we'll take that expression and substitute it everything we can so 0.05 CN equals to Sigma and there's our Sigma expression it's all rewrite right here so we have C V over T V squared + cg / TG squared okay what's next how do we relate TG and CG well let's start with the easy stuff right what can we cancel or square or whatever just somebody yell it out yep so we have numbers for C B and T B but not C G and T G we have not yet answered the question when you go into the smoke shop and talk to the owner and he says fine you're gonna sit here with a radiation detector how long do you have to be here looking all weird you want to have an answer and so if you get some initial estimate of CG you can tell him this is my approximate T G at which point he or she you'll say yes or no depending on how they're feeling so why don't we just start / - right / - 0.025 we can square both sides and there's a CN there square both sides we end up with 0.006 - 5 CN squared equals CB / T V squared plus C G / TG squared there's lots of ways to go about it I want to make sure I do the efficient one oh I'm sorry those aren't Squared's because those are already our standard deviations had the square root in them there we go that's more like it okay what's next we got too many variables yeah we're going isn't there still a what because in this case the standard deviation is the square root of the count rate over the time so the standard deviation squared is just count rate over time was there in Perley or expression we have to correct yup that's where it came from that's right that's not because that's right there we go good good tracing out that okay now that everything is corrected here what's next we got too many variables yeah not quite because there's a count rate in here so the units of standard deviation if this is square root of count rate over time which is the same as number of counts times time over time right yeah because again account rate is I'm sorry is a number over - uh where'd it go yeah number over x squared that doesn't sound right though let's see hold on I think although the standard deviations got to have the same units as the count rate itself because they're they're additive right because they usually expressed some count rate plus or minus either Sigma or two Sigma's that they've got to have the same count rate so standard deviations are expressed in counts per minute if your counts are expressed in counts per in it okay cool so you got too many variables but it's easy to get rid of one of them either CN or CG do you have a question great okay so you're gonna say the same thing that I was gonna do cool so we'll take out our CN and we'll stick in a CG minus CB okay and we're trying to isolate T G as a function of CG or vice versa there's a lot of C G's and not a lot of T geez so let's just keep the TG on its own so we'll have 0.000 six-to-five cg minus CB squared and I'm going to subtract CB over TB from both sides minus CB over TB equals cg / TG and do I have to go through the rest of the math with you guys think at this point we've got it pretty much solved we divide everything by CG flip it over and you end up with actually I've already written out the expression which I want to show you guys here back to smoke shop counting time so I want to show you some of the implications of this expression that number right there is just a more exact part a bit of to Sigma instead of 0.05 and let's see yeah instead of 0.05 we had something much much closer so what I want us to look at is this graph right here we've got a nice relation now between the count rate in counts per minute and the require was of the gross count rate and the required counting time to get to that five percent uncertainty well there's a couple of interesting bits about this equation what are some of the features you notice yeah yes if the count rate is extremely low it's going to take an infinite amount of time you're actually right on some levels so if we have that expression right there so let me just actually get it all the way out so we can see because I want to show you some of the math related implications for this so if we had our counting time is what do we have CG over 0.0 let's say 2 5 CG minus CB squared minus CB over TB at what point is this equation undefined yes that's right for the condition so like Sean said for the condition where 0.025 CG minus CB let's just call it C net squared minus equals CB over TB this equations actually undefined which means that if your CB and TV let's say if the uncertainty whoops stepped on the cord if your uncertainty from your background counting great experiment is such that you can never get the total uncertainty down to let's say five percent error with 95 percent confidence you can't actually run that experiment because these uncertainties are added in quadrature if you're trying to reduce Sigma down to a value below that already how can you do that you can't have a negative standard deviation right so what this actually means is that when you're designing this experiment even if you count for 67 minutes at 25 counts per minute like we can now out in the air that might not be enough to discern the activity of the smoke shop or the source or whatever you happen to be looking at to 95 percent confidence within 5 percent error and so let's actually look at that on the graph if we keep on scrolling up just by adding stuff to the y-axis eventually we see that it gets all straight and right here at about 49 counts a minute suspiciously close to the background counts you'll never actually be able to get within this confidence and error interval so there's always some trade-offs you can make in your experiment let's see there it is so the sometimes do you necessarily have to be 95% confident of your result depends on what you're doing or do you necessarily have to get within 5% error that's probably the one you can start to sacrifice the first so usually you want to be confident of whatever result you're saying and be confident that you're giving acceptable bounce so you can remain at 95% confidence which means where that heart go yeah over here which means keep your to Sigma but you can then increase your allowable percent error so if you can't get within 5% error and I believe the homework doesn't actually say that for a reason yeah we don't tell you whatever to choose but we do say try to get to 95% confidence so then the question is for a reasonable counting time how what - what error can you get within 95% confidence the more air you allow the shorter time you have to account for and I want to show you graphically how some of that stuff interplays at each other let's say you were to increase your counting time which we can do here with this slider so for the same background counting rate if you increase the counting time what happens to the uncertainty on your background experiment does it go up down or nothing it's gonna go down yeah count for longer the uncertainty goes down I'm gonna have to change the bounds here to something more reasonable so we were at 67 minutes and now notice as you increase your counting time even though you haven't changed the counting rate it then takes less time to distinguish whatever your source is so let's say count for less time in the background you have to count for more time in the experiment until it just kind of explodes count for more time in the background you have to count for less time in the experiment in order to get to the uncertainty in confidence you want to get to so like if you doubled your background count time from 67 minutes to 134 then you can measure count rates as low as 42 counts per minute growths so when you start going into the smoke shop you can let's say count for a few minutes get some very crude estimate of the counting rate and then decide how long you have to let your background accumulate so you can distinguish the activity in the smoke shop - within some confidence in some error yes it's definitely location dependent so we will get into background counts and sources of background radiation in about a month but to give you a quick flash-forward depends on your elevation to say how much of the atmospheres protect you from cosmic rays definitely depends on location so in New Hampshire the background counts quite a bit higher because there's a lot of granite deposits and granite can be upwards of 52 parts per million uranium um radium Conway granite in particular named after Conway New Hampshire is pretty rich in radium or where you're from oh there you go okay yeah it's also neat you can use you can use background counts as a radiation altima tur one of my graduate students actually built a Geiger counter interface to an Arduino where you could actually tell what the height you were flying at is by the amount of background radiation increase so certainly it's going to depend where you are right but you want to make sure that you're in an area to answer Shawn's question representative of where the smoke shop is so you can't go into the reactor and drop this in the core and say I'm doing a background count that's not enough that's not a valid experiment so yeah you'd want to be I don't know same block right that would be pretty good and then go in there and see can you measure any sort of increase get a crude estimate of your CG your gross count rate use this formula right here to estimate how much time you'd have to wait so for example let's shrink our y-axis down a little and be more optimistic than we probably should let's say you go in there and you get a count rate of a hundred counts per minute that would that would surprise me you'd only have to count for an extra 28 minutes to nail that net count rate with 95% confidence to five percent error let's say now what happens if we increase the allowable percent error so let's say 10 percent error would be acceptable we just take that number double it then all of a sudden you don't have to count for nearly as long so again at five percent error which means 0.25 here at a hundred counts per min you'd have to count for well about 30 minutes if you're willing to accept 10 percent error that goes down to 7 minutes and 18 seconds so do you guys see the general interplay between confidence percent error counting time and counting rate who hears built an NSA Geiger counter before awesome so this is definitely a try it at home kids kind of thing if you want to find out is something radioactive this is what you can actually use to find out answer the question is it discernibly radioactive to within some limit of error or limit of confidence that's what we're gonna be doing here with a much much much more sensitive detector so the only thing missing from our complete picture of going from the activity of a source which we've shown you how to count to dealing with the solid angle which is just a simple formula to dealing with statistics and uncertainty is now the efficiency of this detector out of the number of radiation quanta or whatever that enter the detector how many interact and how many leave out the other side that's what we're gonna be spending most of the next month on when we do ion photon electron and neutron interactions with matter so we'll find out what's the probability per unit length that each one undergo that interaction what kind of interactions do they undergo and then we'll complete this actual picture so you can take a source of let's say unknown activity put in a known distance away from a known detector with a known efficiency and back out what the activity of that source is with accuracy that's what you're going to start doing on this homework as well for the banana lab well the only thing you don't know is the activity of this bag of bananas but we're going to give you all the information like the efficiency of the detector and the geometry of the detector and you're going to be able to measure the number of potassium-40 counts that the detector picks up so by taking let's see for us we have some space left we had a little bit here so by taking that number of counts and dividing by let's say the efficiency of the detector where that efficiency is going to range from zero to one probably much closer to zero and also dividing by let's say your solid angle over 4pi to account for how many of the emitted potassium-40 gamma rays actually get into the detector and dividing by two gamma rays per disintegration I think that's what we had last time or was that cobalt-60 yeah we've been using cobalt-60 as an example so remember we had two gamma rays emitted per cobalt-60 disintegration on average then you can get to the actual activity of the source once you know the activity of this bag of bananas you can then divide by either the mass of one banana or the number of bananas or whatever to get the final answer that's we're gonna spend the rest of today doing so since it's getting on 505 of do you guys have any questions about what we cover today or what we're about to go do [Music] not necessarily let's say you were to encase your detector in an infinite medium of radiation material right then you could subtract every single gamma-ray your solid angle would be four pi so if your solid angle is four pi then that would equal ish the area over r-squared of your thing but this is actually not that good of an approximation when you put a source very very up close to a detector so there are actual formulas for solid angle where the the real formula for solid angle you actually end up having to do a surface integral of the sine let's say the which accounts for the fact that the object that you have might be lets say tilted towards or away from the detector times some differential D theta D was it D Phi D theta of this unit sphere so you'll have to integrate to say how many of these little D 5 D Thetas are actually subtended by your detector and the value of that actual surface integral gives you the real solid angle that's the super simple x1 if you just know the area of something and you know that you're kind of far away but again whenever possible use the exact formula so any other questions yeah Shawn the two gammas / cobalt-60 this one that accounts for the fact that if you remember the decay diagram for cobalt-60 how does that decay by beta emission it goes to one energy level and it tends to go down by two Danna gamma decays to nickel 60 so each time it gives off a gamma ray to one level and a gamma ray to another level so in this case one Becker l of cobalt 60 would give off two gamma rays per second so if you are measuring a number of counts of each count one gamma ray was responsible you have to then divide by the number of gamma rays per disintegration on average in order to get the actual activity of that source so member activity is measured in disintegrations not in number of gamma rays emitted that's the difference here dose you'd actually care about how many gamma rays you absorb but activity is how many atoms are disintegrating per second yeah yeah the units of cobalt-60 oh this would be like atoms of cobalt-60 and those gamma rays would be gammas per atom so in this case it's like - sorry - gamma rays per atom of cobalt-60 disintegrating or better yet per disintegration so you've got to know what material you're looking at in order to know how many gammas are how many betas or more that you're gonna get per disintegration who hears heard of this uncertainty and quadrature before this couple folks okay yeah the idea here is that again if you just add the arrows up you're probably over estimating the error and selling yourself short cool that case if there's no questions let's go do this so follow me to the counting lab okay so this is my counting lab these are three high purity germanium detectors have you explained high purity germanium detectors okay have you explained any detectors okay well here down in here there's a little high purity germanium crystal with a couple thousand volts across it when a gamma ray goes into it make some electron hole pairs nod when I say electron hole pairs okay good and basically you get more hole electron hole pairs the more energy of the gamma you have so you collect the current from that and you know you get a little pulse of current and the height of the pulse tells you how many hole pairs you had and then back it up to what the energy of your gamma was that works fine if you collect all of the gamma energy you don't always quite do that but anyway so that's how the United are y'all can scoop shop if there's not a whole lot to see in there but it's worth a look I mean there's not you can't really see the crystal there's just a aluminum cylinder in there the black part is just a carbon fiber window because you don't want to cut off the low-energy gammas so it's got a really thin carbon fiber window on it what's with the hundreds of pounds of copper on the side there's not a hundreds of pounds of copper on this side these guys are LED which does two things it shields the detectors from the activity out here from you guys from the activities coming out of here because sometimes I'm counting very low activity samples and it also if I'm counting something that has a lot of activity it shields us from that activity so it kind of goes both ways the reason there's copper is if you get a high-energy gamma ray into some lead it makes x-rays it makes it very nice 75k you guys know KTV good awesome you makes a really nice 75 ke V gamma x-ray that interferes with trying to count things around 75 k UV because we're getting all these x-rays coming out of lid so you line it with copper which makes a lower energy x-ray and filters out the light x-rays so anyway yeah so this is just these I've got two germanium detectors that one's also germanium it's a well detector so it's got a little one centimeter hole in it so if you can stick a sample like right in the germanium they're hooked up through in a little electronic box and go into the computer over there that does all a peak height analysis oh yeah liquid nitrogen Dewar thanks for pointing yeah you cool the electronics and the dent everything down so you cuts out the thermal noise because you're looking for really tiny little signals here so you cool everything down and that way it's not too noisy these guys are okay warming up it doesn't destroy the detector the old detectors you have to keep cold all the time and if they warmed up then they were just paper weights but so this is just the counting lab I've got an actual sample counting in here right now we'll take a look at the spectrum in a minute you're bananas we're gonna go here and see if we can yeah cuz it would be nice if I could close the lid oops almost well we'll smash this down I know here wouldn't you guys do this you smash that down till it fits in there although don't break the bag oh okay we'll get another bag it's okay it's just banana ash we'll find another bag it's okay you know I'm all about I'm all about making mistakes yeah yeah yeah just be a little more gentle we'll throw some duct tape on it and it'll be fine so you're looking for potassium-40 in your bananas correct where else do you think we got potassium-40 or do you think there's any other potassium-40 in the room Yeah right so when you do the banana count we frequently take a spectrum on this with the lead closed and we always see potassium-40 there's potassium-40 everywhere so after we get the count of the bananas we'll take a background count you'll want to subtract the two signals your so ahead of me okay um I think that's all but is this gonna fit now okay close enough I've got this thing I've got a whole bunch of little spacers if I'm counting something that's hot and by hot I mean radioactive hot I like you know I'll space it out a little further no that's fine we just got to close the lid and okay if I've got something that's very radioactive all just space it out away from the detector if you've got something that's really hot it just kind of swamps out the electronics there you go is there anything else I want to say in here no let's move this way this is the spectrum I'm collecting on MIT one right now I don't know how long has that been going half a day and less than that anyway so this is a sample of quartz that was irradiated next to the reactor you guys are going to do shorts in like a month did you bring your samples okay good anyway this is a sample of quartz that was irradiated in the same spot you guys are going to do your radiation sort of in the graphite region of the reactor the reason we're running it is the people who are looking at this quartz want to run it for 80 hours and we'd like to know if there are any impurities in it that'll cause grief meaning a lot of activity when it comes out so we went for a short period I think this ran six hours and it's just a little tiny piece and so I can look at the gamma spectrum coming out of this so you can see there's a whole mess of Peaks in here this one yes see that - see that little peak right there can you nod yeah okay so that's the full spectrum that's the peak that's a tungsten 1:87 peak so I did put up one little thing right behind you see that's the okay and have you all seen the chart of the nuclides this thing every day good I've got one of these on every wall in every lab in office and a little handbook yeah so the tungsten 1-86 activates into tungsten 187 so I mean if you've looked at the chart of the nuclides you can tell that there's all the sort of parameters you would need to calculate you know how much activation you'd get based on Neutron flux and time and cross the twenty-eight point 43 that's the abundance of that isotope you can see the Sigma Gamma 38 that's the cross section for thermal neutrons and so that's how likely you'll get from 186 to one-eighty-seven one-eighty-seven that's the half-life 23.9 hours so with all of that and underneath the 23.9 you've got what the gammas are 685 479 it's got a whole mess of gamma so that's a bunch of the gammas in here from that so you could knowing how big that peak is what the efficiency of the detector is for collecting that peak in that geometry it's the half-life the cross set you know that whole mess of parameters you could back calculate how much tungsten is in the sample so that's kind of how naa works which I assume you've explained okay there you go but that's not how I do anyway so right right no no no so there's there's two things you could do one of the things you could do is you take all those nuclear parameters and you calculate it just from the peak height the other way that everybody who does naa almost everybody who does naa is you run a standard material and if you guys chemists anything put your life you all took some chemistry at some point okay so you've run a standard which means a material that you know how much tungsten is in it or how much a whole mess of other things are so I run a bunch of different standards so along with this pizza piece of quartz I ran a standard irradiated it at the same time I'll count the quartz and then I'll count the standard and by comparing the peak heights and doing all the decay Corrections and the weight Corrections then I calculate how much tungsten is in my sample so I don't actually use the cross sections or the flux or any of that other stuff all of those parameters disappear notably the detector efficiency disappears out of the equation because that's the parameter that you usually to have the fuzziest idea about and so you get you reduce the uncertainty in your in your concentration by doing this sort of comparative method with a standard that all makes sense okay yeah so when we run shorts I guess in a month we'll take whatever your samples are I've had feedback about oh god you don't want to run that many samples but we'll figure out how many samples we'll run oh that's a lot of shorts yeah so I'll show you how the shorts get run so when we run your shorts we'll run your samples and we'll run standards and then you can do the comparative method or if you feel like it you can do the other method depending on what exercise you're gonna do the other method you don't want to do this standard method okay not practical well if the computer goes down you can't get any data anyway I can do the comparative one on an envelope anyway okay well we'll run standards or not depending on how you guys are feeling yeah so that's that oh right so let's count your bananas okay so this is detector two we did an energy calibration earlier today so yeah actually these are I've got a couple of little button sources have you seen the button sources yes so that's just a couple of cobalt-60 lines and a caesium-137 line down in here and I know where those energies are so that just gets used to calibrate the detectors there you go there they are they're kind of small there cuz my buttons are probably 30 years old yeah so anyway so we cleared that out and we just hit start and we're not gonna see anything for a while where are we anyway you are banana peak will end up out in here yeah so that's it'll take a while we're gonna let this count till Tuesday because why not I don't feel like coming in over the weekend and turning it off so so yeah so I mean this is just picking up all the gammas coming out of the bananas and everything else that happens to get through the lid and all the contamination on the inside of that and we just let it count and then you guys can calculate how much potassium-40 is in your ashes you'll need to do the background subtraction I will give ya I've got we collect background spectra you know once a month or so so I'll give you a background spectra I will provide the efficiency for this geometry which is pretty poorly defined because I've got a program that'll do that and I can't give you the program and it's the pain in the neck to run anyway if we've got a really well-defined geometry that's not a big bag usually I try to count sort of point sources so I've got an efficiency standard that I can use that I know what the disintegrations in that are at a lot of energies and I use that to do an efficiency calibration usually but I don't have an efficiency standard that's that big it's just a point source I think that's the practical naa from this end that all makes sense I want you guys to mad about him to nod yeah my dessert well time because we were just talking about this all week good deal for neutron activation that's kind of a real common part of the chart so there's the manganese iron cobalt nickel one of the things that you like what you like usually when you're doing naa is you want a nice thermal Neutron spectrum you know what thermal Neutron spectra means real slow neutrons and they'll just give you sort of an n gamma reaction so on that chart I earn fifty eight iron 59 that's a nice you know in gamma reaction and that's the one I use to analyze for iron if you're near the reactor you're also getting some fast neutrons which can give you an NP reaction so if you're looking on the chart there cobalt 59 if you get an NP reaction will also make the iron 59 and that's a pain in the neck because then because if you've got iron you've always got a little cobalt floating around you maybe need to do a correction so in practical terms when you're running naa you really want to have you want to avoid having all these fast reactions there's usually an energy threshold for the fast reactions like one MeV PV or so yeah okay right the place where we do the radiations is very thermal got a very low fast spectrum so I don't usually have to worry about that there's a couple of times I actually use the fast n P reaction if I want to measure nickel you can see nickel 58 an NP reaction to get your cobalt 58 and since there's not a good reaction and gamma from cobalt 57 cobalt 57 isn't around usually so that's how I measure nickel using an NP reaction and I need to put the rabbits in to where I've got a fast flux in the reactor which I got a couple of spots for that I try not to have to measure a nickel because it's pain in the neck but sometimes people want to know a nickel and we talked a little about you know what we've run in here four types of samples every night okay okay so back 15 20 25 years ago we did a ton of environmental samples in this lab we had a whole like three grad students myself included who did atmospheric particulate matter rain water snow we even did some fog collection which is kind of fun ice cores which are old particulate deposition and it was all for trace elements in those kind of environmental samples also lake sediments other analytical methods have gotten a lot better and so they've kind of caught up to naa and you don't need a reactor to run those so the environmental side of this is kind of quieted down a lot but it's still useful for a bunch of things and so that's you know I do some work here now I also work in the import group so that's a lot of my time rather than just this this lab practical things let's go take a look at a couple other labs you're not on wheels you don't have a Steadicam okay okay you got a question the weirdest thing I've been asked to count that's already activated or okay mm-hmm I don't know brain tissue fish samples that we actually did the fresh fish samples and you want to kind of homogenized those and we had this kind of titanium blender that you remember the bass-o-matic we had this titanium blender that we dropped the fish in and you hook completely homogenized the fish and then you took a little sample of it and freeze-dried it and then analyzed it for mercury Yeah right cuz I mean you guys saw the rabbits are only this big and the samples I want are only that big and so to get a representative fish you want to kind of make a fish smoothie and then take a sample out of that we did have a guy who came to me and was promising he we're gonna do this giant study using fingernails and toenails for nutritional analysis I mean he was working with a group that looks at zinc deficiencies and fingernails and toenails will give you a good record of how much zinc you've had over the last you know a week or month or whatever depends where you cut the nails and so I was going to get you know a couple hundred African children's toenails that didn't happen but I did analyze my own toenails well it's if you if you went to somebody who was a little suspicious of you asking for toenails is a lot easier than asking for a blood sample because people will give up toenails it's not a big deal you all have you ever seen the movie or read the book civil action about the Superfund site in Woburn it was a big old Superfund site and Woburn had arsenic and chromium contamination there used to be a lab I forget which building it was in that did a ton of research there one of the things we did and in this lab was we collected baby hair samples from people's scrapbooks so we had baby hair going back 50 60 years dated because everybody knew how old their kid was and they knew and we analyzed the hair samples for arsenic and chromium and then we plotted out where they were when the head sample was taken and how close they were to some contaminated Wells and because we did a fairly short of radiation after a while the activities died down we gave the samples back and so that was and we found that it didn't correlate with the well water or the time when the contamination was the worst which made people happy sort of in retrospect you know that the contamination from that area didn't get into the weld water so anyway that one of my samples and the hair is a pain in the neck to work with so I hope none of you give me hair samples I won't run them okay so let's go down the hall this way you all got to follow so this is I mean it's just a fine powder and it's fly-ash from a coal-fired power plant fly-ash means the ash that goes up the smokestack as opposed to bottom ash which is what falls down and so they collect whole you know hundreds of kilograms of fly ash just homogenize it sieve it send it out to all a lot of labs to analyze NIST is really good at this take all the data and so this is this ash is characterized for about twenty elements or so so when I run my samples if I were to run your samples with standards I'd run a little bit of this five six seven milligrams and I know what the the concentrations are on this and so that's how I do the comparative method and so I got you know this and they all look the same you know this is some soil from Montana next to a mine so it's nicely contaminated with some metals this is my IAEA mercury in hair standard but again it's just a little powder and this is kind of what everybody uses for standards and you just kind of have a whole collection of them and depending on what elements you're looking for you try to mix and match them so you get cover what you want without having to run five or six off my hot lab or one of my hot labs you guys last week or whatever it was I came by so this is the rabbit those of you who weren't there these are I call these these are called rabbits because it's the little thing that runs through the pneumatic tube you guys are doing parable nips later today yeah when you're sitting at the control panel there's a button I think it's to the left and it says insert rabbit and that's what this is referring to for longer radiations there's a spot in the basement in the reactor where they can get these and they send them into the radiation location for shorter radiations like what you guys are going to be doing in a month I send them in from here that's okay you just don't want to bump into that thing yeah so this is one end of the pneumatic system and so I can put a couple of samples in here I stick it in that little tube there call a control room and say okay turn a bunch of knobs and switches and whatnot and it goes shook and in about 15 seconds it's next to the rillette neck to the core of the reactor in the graphite I usually run shorts I'll usually irradiated for about 10 minutes we usually let the sample sit in the reactor for a little while so the very short half-life stuff decays away and then it comes back out here and the whole thing just kind of shoots out there and bounces into here and then pop open the rabbit and in that hood pull the samples out I usually try to repackage the samples so this is partly why I asked for stuff that's kind of one or two good solid pieces because then I can take it out of whatever it was radiated in put it in a clean bag or vial and that way we don't have to do a blank subtraction for the sample that makes sense because otherwise if I take like a little vial in or radiate it and then count it I'll also have whatever elements are in the vial on the thing for when I'm running standards and this is when you won't if we're not running standards you don't have to worry about this that powdered standard stuff I'd never get that out of a bag because you'd never get all of it out and I'd have contamination everywhere if ice cutting open those bags so I do have to do a bag correction for those so when I do in a radiation I always radiate a few just empty bags and then you do a correction for those because the bags of God aluminum and antimony and a bunch of things in them yeah and so then like I take a couple of samples I throw them in a lead pig so I got a whole bunch of these floating around and I run it down the hall and throw it on a detector and we count it when are we doing shorts I'll radiate two samples at a time because I have two detectors what I used to have four detectors I ran four samples at a time so you irradiated repackage it count it while that sample those pair of samples are counting you come down here you are radiate the next two so that you know you're just kind of always radiating and counting I usually do a ten minute of radiation for shorts I'll do it fairly quick count five minutes right after I get the sample down there and that's looking for stuff with half lights sort of under 10 minutes the shortest half life I look for is for aluminum it's two and a quarter minutes but things usually have a lot of aluminum in them so I see if I see aluminum pretty well for shorts I'll count all the way up to about sodium which is almost fifteen hour half-life longer stuff I'll do a longer radiation account there's a little overlap on my shorts and Long's that helps me do QA on things and if I run two standards I'll check you know the concentrations from one standards the other there's another little q8 thing I don't know what else we got questions it's pretty straightforward yeah what do we got oh yeah yeah okay yeah there was a lot of archeology that did you know naa got used for that a lot I don't think we ever did it here Fred Frye who's a professor retired now from EOBs Earth atmospheric and Planetary he did a lot of geological samples and yeah there's I forget where it was it they did all the archaeology one of the things na is really good for is rare earth elements which are hard to measure by other methods I mean I didn't get very low limits on that and by picking out various rare earths and the ratios you can help identify where things are from in the world if you give me a little tiny piece of it I mean you know I mean the well see that's the rabbit so it's definitely got to fit in there the thing I really like yeah excuse me where's my vials yeah I used to have some smaller ones up here but so you know that's should definitely fit in one of those like to see that guy my usual description of what size sample I like is if it's a piece that you would pick up with a pair of tweezers so not too small to pick up with you know to be able to find so no powders but you know and you could maybe get it with your fingers but 20 milligrams 50 milligrams 100 milligrams is just in the right ballpark nope doesn't matter but we'll look at what comes in and yeah I might veto some things or not we'll see well we got bricks everywhere so when I when I get the sample out of there I do the repackaging in here and so this is just shielding between the samples I'm working on and myself I don't have my toe simony on now but I usually I've got the symmetry and a ring badge and then it kind of comes over here and I do the this is where the heat sealer is so I can I you know heat seal it here and then I'll have a pig over here oh yeah these are just painted lead bricks and you know these have been here longer than I have so and you don't sometimes things just are somewhere and you never move them yeah these they think older than me too so this lab has been doing any a she's I don't know since the 70s I think so anybody else the full-size bricks this like that size 2 inches by 4 inches by 8 inches weighs about 25 pounds there's usually a bunch of them floating around that one's not quite full-size you know they're heavy they're lit okay when people ask me because I work in the reactor as well they say is there anything dangerous in the reactor the dangerous thing is dropping wet bricks on your feet that's why I've got steel toast if I miss the toe yeah probably break my I don't want to think about it and they move much bigger things in the reactor when you if you toward the reactor yet yeah so I mean there's that giant crane there and they move you know five tonne pieces of shielding and that's the other dangerous thing and there's dropping really big things we've never dropped anything that big I think somebody dropped a steel plate on their foot once that was about the worst of it you know like four foot half inch steel boom yeah okay good yeah you know when people trip and fall off ladders and it's the usual industrial accidents okay good yeah yeah I mean I've broken a few but not not here sure and I'll see you guys in a month or something and have fun running the reactor oh good day folks you guys are here to do an experiment on the reactor it's in two parts the first part is raising reactor power the first is raising reactor power using a low earth absorber called a regulating rod and then the second part will be lowering reactor power using a high worth absorber and the high worth absorber things would move much faster and we don't want to run into a chance of you accidentally going too high so that's why we use the low worth absorber on the way up and a high worth absorber on the way down okay and I just want to show you the controls with me today is Tim to actually do this experiment we need to licensed people in here one that least has a senior reactor operator both Tim and I are both senior licenses so that we have that covered the only way you can actually do these manipulations are if you're in my training program on the training supervisor for the facility or you're in a program that needs you to actually operate the reactor and the program you guys are in fits that definition okay so I just want to show you some of the controls of the reactor first we have our shin blade controller this basically moves one of six shim blades at a time the one that's selected has a slide on it and we can change which one selected with the shim blade selector switch this switch here is a regulating rod this one will allow you to move the regulating rod up and down our blades are fixed speed meaning they can only move at a at the exact same rate at all times moving the shim blade in upward direction or the regulator rod in upward direction take underhand grip and pull up or twist upwards until it stops we get just a little bit doesn't move anything you have to move all the way until it stops and then the absorber will move in the outward direction if you want the blade to stop just release it it's spring-loaded and will go back to the neutral position and stop moving if you want to drive something in the inward position take an overhand grip and twist downwards and that will drive the absorber in once again let go it'll snap back up and stop the motion of the blade while the regulating rod the experiment we're doing is basically changing rack of power by half a megawatt and we're currently at 500 kilowatts we're gonna bring it bring the reactor up to one megawatt and then bring it back down to 500 kilowatts so before we can do this you have to log into our log book as a trainee on console we'll show you the proper way to make the entries as you make those entries you'll go ahead and then do the actual movement itself okay so the first one is going to be using a regulating rod to move the rack for power up what's the reactive power we have about nine different instruments that tell us what the reactive power is at all times but the ones we're going to be paying attention to our channel 7 and channel 9 these two channels are what we use to basically tell us what the reactive power is channel 7 is what we control our automatic control act if you watch the regulating rod you'll see it move up and down on its own that's because it's changing power based on what it sees channel 7 is doing so if channel 7 sees that the power level is going too low it'll cause a regular rod to drive outwards to increase the amount of neutrons making the rack part of the world channel 9 is a linear power channel and it basically tells us what the power level is based on our chart that we create so it's not showing you megawatts or kilowatts or anything like that it's showing you a current coming from a chamber and that current is then converted into megawatts and so forth so right now we're at 500 kilowatts 8.5 micro amps on this channel and that's 8.5 micro amps equals 500 kilowatts you're gonna be bringing the rapper up to 1 megawatt and since it's a linear it'll be double that so 17.1 now you want to be careful when you raise reactive power so when you start to add power to the reactor by raising the regulating rod you don't want to bring it you don't want to keep raising it until you reach your value because you have to actually stop the power increase as well so we have two rules that we have to follow one at the power level or at we have period there at the period the reactor period is the amount of time it takes you out to power to increase at the power level we're at we're not allowed to go shorter than a hundred second period okay so here is one of three period meters one here one here which is selectable between two different meters so as you're pulling up the regulating rod one of the things you have to watch is to make sure that the reactor period doesn't go shorter than 100 second period if it does you have to stop following blades the other thing we have to watch for is to make sure that the power level Channel nine doesn't exceed where you're going to not only not exceed but we also want to make sure that you can actually control the reactor it's called feasibility of control and what that means is when you get to about 80 percent of the power level you're going to since we're going up to one megawatt that's about 800 kilowatts you want to be able to drive the absorber in and hold the absorber in you'll buy the regulating rod inwards and watch that channel nine value it'll slow until it actually starts to go down again once it reaches that value and you see it going down you now know that you could control the reactor and keep it from going away rack power increasing continuously so what we're going to do is have you when you reach 80% of the power level you're going to which happens to be 800 kilowatts you're going to start increasing or lengthening a period by driving the absorber back in the regulating rod and you'll keep holding it in on you see the number not only stop increasing but actually go down a little bit as soon as you see it go down a little bit let go the regulating rod you haven't stopped the power at this time you just increased how or you decrease how fast it's going up and then the power level still go up but a much slower rate than it was before and once it reaches the power level you want to stop at the one megawatt keep driving the regulating rod in to hold it at that power level once you're at that power level you're going to make an entry in the log book that basically says you made it to the power level you're going to and then we'll go down in power so once again you make an entry in the log book that says I'm going to lower reactor power to 500 kilowatts and then this time we'll use a shim blade the shim blade is worth a lot more than a regulating rod about ten times the shim blade excuse me of the regulating rod so things will happen much faster so you'll be able to drive this in and rack power will change much faster than before same thing as you get closer to the power level you start at 500 kilowatts you don't want to under shoot and go too low so at around 600 kilowatts or so start driving a shim blade out to slow down how quickly the power levels going down okay and once you get back to the place where you started at we'll use a regular rod regulating rod to fine tune it to keep the rack of power where we want to be there'll be another logbook entry and your time round console will be completed okay so with us today we actually have to MIT soon so our actually my training program and they've actually done a lot of these manipulations already Sarah let's go I'll take I'll take those so normally we sit and watch if at any time you don't feel comfortable doing something let us know we'll ask you just to take your hands off the console and we'll take care of doing whatever is necessary to keep the reactor safe but be aware we're a factor of 10 lower than where we would automatically scram at so it'd be very difficult for you to get to someplace where it would cause a problem without us being able to stop it okay so our normal I don't know if you want to move or anything but we the supervisor normally sits like kind of right in your way so that they can keep an eye on what's happening okay you can go ahead and make the announcement that your that were starting power manipulations and then the last verse to make announcing that we're done with our manipulations right now the reactors on auto control and when we do these manipulations the reactor opera is going to take manual control that'll cause an alarm to come in and this only happened for the first time so one of the things she's going to do after she makes our logbook entry no we'll do that at the end is she'll take manual control the reactor and alarm will come in on console and she'll answer it and that should be the only time you hear this alarm because we'll leave it on manual control until the final participant has done their manipulations okay now she's pulling up the Reg rod all the way you see the Reg rod number going up the period is getting shorter it's no longer at infinity it's going closer to a hundred second and channel seven and channel nine are increasing in value another way you can see it is we have a display on in front of the operator those three displays two of them are just for evaluation only we don't actually use those to control the reactor they're based on a system that haven't been approved yet but we're testing them to see how well they work so you can see that the power level on the far left is going up the middle one is showing what the actual power level we saw a 500 kilowatts sorry up to 630 kilowatts and increasing and the period that was at an infinity is now around 160 seconds so she's watching until she sees the 800 kilowatt value here on channel 7 channel 9 and she started to drive in the regular rod so she's slowing down how quick the power increases bowing and you see the period lengthening it's no longer at 150 160 seconds it's going closer to infinity again so she's proving that she could stop the reactor power if she continued driving in this regulating rod No she's closing in on the one megawatt one of the things the note is that when she started the wrecker I was around Oh 300 oh three ten and she's almost right back to there when you raised reactive power you basically open up a valve and let more neutrons in and when you get to the place where you want to be you basically close that valve again so you basically add reactivity and then stop that reactivity in addition by bringing the absorbers back to about where they started from now okay one megawatt go ahead and make your logbook entry so once again she has experience she's been doing startups and power manipulations for a while when the rest of you sit down here will guide you through those the logbook entries that she's making uh so forth yeah 30.6 yep so one of the things that could change the reactor is xenon it's a poison that built into the reactor while we operate poison in that it absorbs neutrons not leading the fission and it has to make ways of being made in two ways of having removed one is direct from fission and the other is decay that's the way it's produced the way it goes away is basically absorbing a neutron and decaying to another isotope and okay yep his blade sucks and what happens is when we lower reactive power the way we remove most of the xenon from Verna basically the neutrons being absorbed by the by the fission process the the fact that we don't have the reactor at a very high power means that the amount of xenon in the core isn't being removed so we actually start the power would actually want to go down on the tunnel so you would have to do a lot or regions and for a while that's a very large amount of reactivity that has to be compensated for for this experiment though we actually shut down the reactor yesterday and we started up early this morning so it's not a big factor as it normally would be after doing one of these blowing reactor power now I think we'd be able to get at least one more person so once again she's long reactor power you can see on the period meter she's at a negative period and the reactor power is decreasing she's almost at 500 kilowatts she's uh driving the absorber out again to slow down how quickly the power levels going down and when she's done the shin blade will end up about at the same point where started to thirteen point four two inches out of the bottom of the core we closed cops say what the regarding you two 30.8 okay and that's the end of the exercise