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visit MIT OpenCourseWare at ocw.mit.edu. MICHAEL SHORT: OK. I think things have been
getting pretty derivy 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 we're 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 that's emitting things
in all directions. Let's go with the
stuff from yesterday. Let's say it's a
cobalt 60 source. It's now 0.52 microcurie. 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? A 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. AUDIENCE: [INAUDIBLE] r cubed. MICHAEL SHORT: Close. It's, let's say, the
measured activity would be proportional
to 1 over r squared. Who knows where this comes from? I'll move the source a bit
away to lessen the beeping. Yeah. AUDIENCE: Well, the flux
of particles coming out is just [INAUDIBLE] over the
surface area of [INAUDIBLE] and the [INAUDIBLE]
is 4 pi r squared. MICHAEL SHORT: Yeah, exactly. If you were to draw
a hypothetical sphere around the source right
here, then you've got, let's say, 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, width W-- would be just L times
W. And actually, what Chris mentioned as
the solid angle subtended by this detector right here-- in other words, at a
certain distance r away, how much of this sphere-- how much does 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 we'll
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 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 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 do you think the
width of this Geiger counter is in meters? AUDIENCE: A centimeter MICHAEL SHORT: A centimeter. 0.01. We're going to have to change
our axes so we can actually see the graph. So instead of looking all the
way out 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 the source that's the radius of the distance
between the source and the detector,
how much of that sphere's area does
the detector take up? This approximate
formula-- the blue curve-- is a pretty good
approximation of the red curve until you get really, really
close to 5 centimeters away, or about this
distance right here. Does anyone know why this
formula would break down? What happens as r goes to 0? What happens to our solid
angle or our approximation for our solid angle? AUDIENCE: Goes to Infinity MICHAEL SHORT: It goes
to infinity, right? Can a detector actually
take up infinity area on, well, anything? Never mind that unit sphere. Not quite. If you were to take this
detector and bring the radius down to 0 so that the
source and the detector, if not counting for the
thickness of the plastic, were right upside each other, if
that solid angle went to, well, infinity , then the count
should go to infinity, and it does not compute. Does anyone know how many-- first of all, who here has
heard of solid angle before? So a little more
than half of you. 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 steradians-- steradians-- with a full sphere
taking up 4pi steradians. Interestingly
enough, 4pi is also the surface area of a unit
sphere with radius of 1. So that's where this comes from. If something were to completely
cover a unit sphere-- like, if you were to, let's say,
encase a light source in tin foil completely, and say,
how much of that solid angle does the tin foil encase? It would be 4pi
steradians, regardless of the size of the sphere or 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 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 with 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 sphere is the detector subtending? AUDIENCE: 2pi MICHAEL SHORT: 2pi--
half the sphere. Because let's say this
whole side of the source is completely obscured by the
detector and this whole side is free to move. And if you look really closely,
yep, at 0, the correct formula does give you 2pi steradians. Which is to say that half the
gamma rays leaving the 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
going to 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 banana. So there's a reason
I've been using potassium 40 as 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 intaking a fair bit of
radioactive potassium, which is a positron
emitter, and also it does electron capture
and all that fun stuff. So today, what we're
going to 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 in here 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 one of
the homework problems as a motivating example. You guys, did anyone notice
the extra credit problem on the homework? Let's start talking about
how we'd go about that. That should motivate
the rest of the day. So I'll pull up that
problem set, number 4-- 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 smokables themselves. And so I was thinking, there's
no better concentrated source of smoking radioactivity
than a smoke shop. There's one out at [INAUDIBLE]
at the end of the T. There's probably some
closer to campus. But I know there's a whole
bunch that are T 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. AUDIENCE: You know you have to
be 21 to go into a smoke shop? MICHAEL SHORT: Are you serious? But you have to be 18 to smoke. AUDIENCE: Yeah. It's a Cambridge, Boston law. MICHAEL SHORT: Interesting. We may have to leave
the city for this one. [LAUGHTER] What about Somerville? I think-- AUDIENCE: It's still--
you're not allowed to go into there either. It's all of Massachusetts now. MICHAEL SHORT: Wow. AUDIENCE: So [INAUDIBLE] [INTERPOSING VOICES] AUDIENCE: [INAUDIBLE]
you can buy them. It's still late-stage. It's like town-to-town. Most of the Boston area is 21. But once you leave Boston-- MICHAEL SHORT: It varies. AUDIENCE: Yeah. MICHAEL SHORT: Yeah. I don't think it is where
I'm-- from Swampscott, I don't think it's 21. But that's kind of up
on the commuter rails. You don't want to
go to Swampscott. At any rate, I would
think that, OK, 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 this stuff about binomial, Poisson, 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 radiation is in the room-- there we go-- to get enough
of a count right going on. As 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 value is actually right. So the two things that
you could do to decrease this standard deviation-- you could increase
your counting time. Why is there a C on top? That doesn't look right. It actually is OK. 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 counts
we have 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 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 going to 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, 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. It's just the gross count
rate minus the background-- let's keep the
symbols the same-- count rate. Does anyone know how to
quantify the uncertainty of this net count rate? Do you just add the two? 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. There is no correlation between
when one particle leaves and the next particles
going to leave. And because it's a
truly random process, these errors in the background
rate and the gross 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 overestimate 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, 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. It kind of looks like the
magnitude of a vector, doesn't it? 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 we don't
have any typos, so I'll just keep the notes with me-- so you'd need the background
count over the background time 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 problem set-- how long do you have to
count in the smoke shop to be 95% percent sure? So let's say your count
rate's 5% 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% confident of our count rate plus or minus 5% error? That's the main
question for today. Does anyone know how we'd start? Anyone get to the reading today? I see some smiles. OK. We'll start from scratch, then. All right, So who here has
heard of a normal distribution before? A lot of 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-- to limits of plus
or minus 1 sigma or one standard deviation,
1 sigma gives you about 68% confidence in your result.
Yeah, I 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've filled in 68% 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%. And then so on, and
so on, and so on. There's actually societies
called 6 sigma societies. And the way that they
get their name is we're so confident of
things we can predict them to 6 sigma, which is some
99 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 thusly-- let's say in order to be 95%
confident, in other words, 2 sigma, that our counting rate is
within 5% of the actual value, in other words, plus
or minus 5% error, we put our error
percentage here, and our true net
count rate there. So this part right here
tells us the 95% confidence. This part right here
is our 5% error. And 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, it depends on what the
information we're 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 this, it 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, I 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 and
our gross counting time, because it's 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
count rate is 5% 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 in everything we can. So 0.05 C n equals 2 sigma. And there's our
sigma expression, which I'll rewrite right here. So we have see C b
over t b squared plus C g over t g squared. What's next? How do we relate t g and C g? Well, let's start with
the easy stuff, right? What can we cancel, or
square, or whatever? Just somebody yell it out. AUDIENCE: Do we have
numbers for these counts? MICHAEL SHORT: 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 going to sit here with the 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 C g, you can tell him this is my
approximate t g, at which point he or she will say
yes or no, depending on how they're feeling. So why don't we just
start, divide by 2, right? Divide by 2. 0.025. We can square both sides. And there's a C n there. Square both sides, and
we end up with 0.000625 C n squared equals C b
over t b squared plus C g over t g 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. Because our standard deviations
had the square root in them. There we go. That's more like it. What's next? We've got too many variables. Yeah? AUDIENCE: I think there's still
a square value [INAUDIBLE] MICHAEL SHORT: Isn't
there still a what? AUDIENCE: Isn't
there a square value still under the [INAUDIBLE]? MICHAEL SHORT:
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
overtime time. Was there an earlier
expression we have to correct? Yep. [LAUGHTER] That's where it came from. That's right. That's not. Because that's right. There we go. Good. Good, tracing out that. OK. Now that everything is
corrected here, what's next? We've got too many variables. Yeah? AUDIENCE: [INAUDIBLE]
the standard deviation have units of [INAUDIBLE]? MICHAEL SHORT: 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? AUDIENCE: OK. MICHAEL SHORT: Yeah. Because again, a count
rate is a number over-- where'd it go. AUDIENCE: Number
over time squared. MICHAEL SHORT: Yeah. Number over time squared. That doesn't sound right though. Let's see. Hold on a sec. Although the standard
deviation has got to have the same units
as the count rate itself, because they're additive, right? Because they usually express
some count rate plus or minus either sigma or 2
sigma, so 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 minute. OK, cool. So we've got too many
variables, but it's easy to get rid of one of
them, either C n or C g. Do you a question? AUDIENCE: No, I was just
going to say [INAUDIBLE].. MICHAEL SHORT: Great. So you were going to
say the same thing that I was going to do. Cool. So we'll take out our C n, and
we'll stick in a C g minus C b. And we're trying to isolate t
g as a function of C g or vice versa. There's a lot of C
g's and not a lot of t g's, so let's just
keep the t g on its own. So we'll have 0.000625
C g minus C b squared. Then I'm going to subtract C
b over t b from both sides. Minus C b over t b
equals C g over t g. And do I have to go through the
rest the math with you guys? I think, at this point, we've
got it pretty much solved. We divide everything
by C g, 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 2 Sigma. 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 and counts per minute-- and it was the gross count
rate and the required counting time to get to that
5% uncertainty. Well, there's a couple
of interesting bits about this equation. What are some of the
features you notice? Yeah. AUDIENCE: The count rate is
extremely low for [INAUDIBLE].. MICHAEL SHORT: Yes. If the count rate
is extremely low, it's going to take an
infinite amount of time. You're absolutely
right on some level. 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-- what do we have-- C g over 0.025 C g minus C b
squared, minus C b over t b, at what point is this
equation undefined? Yeah, Sean. AUDIENCE: [INAUDIBLE]
question [INAUDIBLE],, using the second one
after the [INAUDIBLE].. MICHAEL SHORT: That's right. So like Sean said,
for the condition where 0.025 C g
minus C b-- let's just call it C net squared
minus equals C b over t b, this equation is
actually undefined. Which means that if
your C b and t b-- let's say if the uncertainty from
your background counting rate experiment is such
that you can never get the total
uncertainty down to let's say 5% error with
95% 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%
confidence within 5% 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 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 first. So usually, you want to
be confident of whatever result you're saying and
be confident that you're giving acceptable bounds. So you can remain at 95%
confidence, which means-- where did part go-- which means keep your 2 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
what error to choose. But we do say try to
get a 95% confidence. So then the question is,
for a reasonable counting time, to what error can you
get within 95% confidence? The more error you allow,
the shorter time you have to count for. And I want to show you
graphically how some of that stuff interplay with each other. Let's say you were to
increase your counting time, which we can do
here with a 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? AUDIENCE: It goes down. MICHAEL SHORT: It's
going to go down. Yeah. Count for longer-- the
uncertainty goes down. I'm going to 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 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 and confidence you want to get to. So 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 gross. So when you start going into the
smoke shop, you can, let's say, count for a few minutes and
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 to within some confidence
and some error. Yes. AUDIENCE: So does the background
in the case of the smoke shop just the area right
outside of it? Instead of the inside? MICHAEL SHORT: 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, it depends on your elevation to
say how much of the atmosphere is protecting you
from cosmic rays. It definitely
depends on location. So in New Hampshire, the
background count's quite a bit higher, because there's a
lot of granite deposits, and granite can be upwards of
52 parts per million radium. Conway granite in
particular, named after Conway, New Hampshire,
is pretty rich in radium ore. Oh, is that where you're from? AUDIENCE: No. My last name is Conway. MICHAEL SHORT: Oh, there you go. OK. [LAUGHTER] Yeah. It's also neat. You can use background counts
as a radiation altimeter. 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 Sean'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 a valid experiment. So yeah, you'd want to be,
I don't know, same block. That would be a pretty good. And then go in there
and see, can you measure any sort
of increase, get a crude estimate of your C g-- 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 100 counts per minute. That would do 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 5% error. Let's say now, what
happens if we increase the allowable percent error? So let's say 10% error
would be acceptable. We just take that
number and double it. Then, all of a
sudden, you don't have to count for nearly as long. So again at 5% error,
which means a 0.25 here, at 100 counts per
minute, you'd have to count for about 30 minutes. If you're willing
to accept 10% error, it goes down to seven
minutes and 18 seconds. So do you guys see
the general interplay between confidence, percent
error, counting time, and counting rate? Who here is built an NSE
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 answer the question, is it discernibly radioactive
to within some limit of error or limit of confidence? That's what we're going to 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 we're going to 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 undergoes
an 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 it 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. 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
where 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 0 to 1,
probably much closer to 0, and also dividing by, let's
say, your solid angle over 4 pi to account for how many
of the emitted potassium 40 gamma rays actually
get into the detector and dividing by 2 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 what we're going to
spend the rest of today doing. So since it's getting
on five out of five of, do you guys have any questions
about what we covered today or what we're about to go do? AUDIENCE: You said
that for solid angle you wouldn't do this. MICHAEL SHORT: Yep. AUDIENCE: So for
solid angle, it's [INAUDIBLE] to the surface
area over y squared. And in this situation,
does solid angle over 4 pi mean that you can only have a
maximum of half of the sphere? MICHAEL SHORT: Not necessarily. Let's say you were to
encase your detector in an infinite medium
of radiation material. Then you could subtend 4 pi. So the idea here is that if
you captured every single gamma ray, your solid
angle would be 4 pi. So if your solid angle
is 4 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 real formula
for a solid angle, you actually end up
having to do a surface integral of the sine,
which accounts for the fact that the object that you
have might be, let's say, tilted towards or away
from the detector, times some differential d phi
d theta of this unit sphere. So you'll have to
integrate to say how many of these little d
phi 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 one 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, Sean. AUDIENCE: You said
that that expression is a true statement
[INAUDIBLE] per second, right? MICHAEL SHORT: The two
gammas per cobalt 60? This one? AUDIENCE: Yeah. MICHAEL SHORT: 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
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
becquerel of cobalt 60 would give off two
gamma rays per second. So if you're measuring a number
of counts, and 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. Because remember, 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. AUDIENCE: What units of
cobalt 60 [INAUDIBLE]?? MICHAEL SHORT: The
units of cobalt 60? AUDIENCE: It's just two gamma-- MICHAEL SHORT: 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 two
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 gamma or how many betas or
more that you're going to get per disintegration. Who here has heard of this
uncertainty in quadrature before? There's a couple folks. OK. Yeah. The idea here is that, again,
if you just add the errors up, you're probably
overestimating the error and selling yourself short. Cool. In that case, if there's no
questions, let's go do this. So follow me to
the counting lab. MICHAEL AMES: OK. So this is my counting lab. These are three high-purity
germanium detectors. Have you explained high-purity
germanium detectors? MICHAEL SHORT: No, we haven't. MICHAEL AMES: OK. Have you explained
any detectors? MICHAEL SHORT: Just
the Geiger counter we were playing
around with today. MICHAEL AMES: OK. 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, it makes some electron hole pairs. Nod when I say
electron hole pairs. OK, good. And basically, you get more
electron hole pairs the more energy of the gamma you have. So you collect the
current from that, and 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 or your gamma was. That works fine if you collect
all of the gamma energy. You don't always quite do that. Anyway, so that's how-- You all can scooch up. There's not a whole
lot to see in there. MICHAEL SHORT:
It's worth a look. If you've never seen it. MICHAEL AMES: It's worth a look. You can't really
see the crystal. There's just an aluminum
cylinder in there. The black part is just
a carbon fiber window, because you don't want to
cut off the low energy gamma. So it's got a really thin
carbon fiber window on it. MICHAEL SHORT: What's with
the hundreds of pounds of copper around the side? MICHAEL AMES: What's with
the hundreds of pounds of copper on the side? There's not hundreds of
pounds of copper on the side. These guys are lead. MICHAEL SHORT: Ah-hah! MICHAEL AMES: 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. And it makes a
very nice 75 keV-- do you guys know keV? Good. MICHAEL SHORT:
We've done x-rays. MICHAEL AMES: Awesome. So it's a really,
really nice 75 keV x-ray that interferes with
trying to count things around 75 keV, because you're
getting all these x-rays coming out of lead. So you line it
with copper, which makes a lower energy x-ray and
filters out the lead x-rays. So anyway, so this is I've
got two germanium detectors. That ones also germanium,
but it's a well detector. So it's got a little
one-centimeter hole in so you can stick a sample
right in the germanium. They're hooked up through
a little electronic box and go into the computer
over there that does all the peak height analysis. Oh, yeah, liquid
nitrogen [INAUDIBLE].. Thanks for pointing. Yeah, you cool the electronics
and everything down so it 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 OK warming up. It doesn't destroy the detector. The old detectors you had
to keep cold all the time. And if they warmed up, then
they were just paperweights. 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. Your bananas are
going to go here. And let's see if we
can smash it down. Yeah. Because it would be nice
if I can close the lid. Oops. MICHAEL SHORT: Well, almost. MICHAEL AMES: Almost. Well, smash this down. Here, one you guys do this. Here, you. Smash that down until
it fits in there. Although, don't break the bag. Oh! OK, we'll get another bag. AUDIENCE: Oh, did I break it? MICHAEL AMES: It's OK. It's just banana ash. We'll find another bag. It's OK. You know, I'm all
about making mistakes. AUDIENCE: [INAUDIBLE] MICHAEL AMES: 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? AUDIENCE: In us. MICHAEL AMES: Yeah, right. So when you do the banana
count, we frequently take a spectrum on this
with the lid 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. MICHAEL SHORT: We just
did 15 minutes ago. MICHAEL AMES: You're
so ahead of me. OK, I think that's all-- Is this going to fit now? AUDIENCE: [INAUDIBLE] MICHAEL AMES: OK. 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'll space it out
a little further. AUDIENCE: Need a
little more smashing? MICHAEL AMES: No, that's fine. We just got to close the lid. And if I've got something
that's very radioactive, I'll 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. MICHAEL SHORT: We did just go
for a solid angle too, today. MICHAEL AMES: 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 1. Right now, I don't know--
how long has that been going? Half a day-- 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? MICHAEL SHORT:
We're getting them. MICHAEL AMES: OK, good. Anyway, this is a
sample of quartz that was irradiated in the
same spot you guys are going to do your irradiation,
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 run it 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-- you see that? You see that lovely,
little peak right there? Can you all see that? Nod. Yeah, OK. So that's the full spectrum. That's the peak. That's a tungsten 187 peak. So I did put up one little
thing right behind you. Have you all seen the
chart of the nuclides? This thing? MICHAEL SHORT: Every day. MICHAEL AMES: 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 186
activates into tungsten 187. So 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
how much activation you'd get based on neutron
flux, and time, and cross. The 28.43, 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 187. 187, that's the half-life-- 23.9 hours. So with all of that-- oh, and underneath
the 23.9, you've got what the gammas are-- 685, 479. it's got a whole mess of gammas. So that's a bunch of the
gammas in here for that. So you could, knowing
how big that peak is, what the efficiency of the
detector is for collecting that peak in that geometry, the
half-life, the cross set-- that whole mess of parameters-- back-calculate how much
tungsten is in the sample. So that's kind of
how NAA works, which I assume you've explained. MICHAEL SHORT: We have. MICHAEL AMES: OK. MICHAEL SHORT:
Actually, the whole idea behind doing those
short NAA activations is these guys are
going to calculate what's in their samples. MICHAEL AMES: There you go. MICHAEL SHORT: Once
we get the date. MICHAEL AMES: But
that's not how I do NAA. MICHAEL SHORT: [INAUDIBLE] We're
doing a simplified version. MICHAEL AMES: Right, right. No, no, no. So there's two things
that 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. Any of you guys chemists
at any point in your life? You all took some
chemistry at some point? OK. So you've run a standard,
which means a material that 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
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 have the funniest idea about. And so you reduce
the uncertainty in your concentration by doing
this sort of comparative method with a standard. That all make sense? OK. 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. MICHAEL SHORT: It's
one per person. [INAUDIBLE] MICHAEL AMES: That's
a lot of shorts. MICHAEL SHORT: In pairs, right? MICHAEL AMES: 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-- MICHAEL SHORT: The other method. MICHAEL AMES: You're going
to do the other method. You don't want to do
the standard method? MICHAEL SHORT: Oh, no, no no. We're drilling comprehension,
not [INAUDIBLE].. MICHAEL AMES: Not practical? Oh. MICHAEL SHORT: What happens
if the computer break down? MICHAEL AMES: Well, if
the computer goes down, you can't get any data anyway. MICHAEL SHORT: Oh, [INAUDIBLE]. MICHAEL AMES: I can do the
comparative one on an envelope. Anyway-- well, we'll run
standards or not, depending on how you guys are feeling. So that's that. Oh, right. Let's count your bananas. So this is detector 2. We did an energy
calibration earlier today. So actually, I've got a couple
of little button sources. Have you seen the
button sources? Yeah. So that's just a couple of
cobalt 60 lines and a cesium 137 line down in here. And I know where
those energies are, so that just gets used to
calibrate the detectors. MICHAEL SHORT: We were playing
around one of those cobalt 60 buttons today in class. MICHAEL AMES: There you go. MICHAEL SHORT: We mentioned the
two gammas per disintegration, and there they are. MICHAEL AMES: There they are. They're kind of small there
because my buttons are probably 30 years old. MICHAEL SHORT: Oh, I
got some fresh ones. MICHAEL AMES: Yeah. So anyway, we cleared that out. And we just hit Start. And we're not going to
see anything a while. Where are we? Oh here. 14-- anyway, your banana
peak will end up out in here. So it'll take a while. We're going to let this
count until Tuesday. Because, why not? And I don't feel like
coming in over the weekend and turning it off. So yeah. So this is just picking up
all the gammas coming out of the bananas, and
everything else that happens to get through
the [INAUDIBLE],, 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 you-- MICHAEL SHORT: Do you
have background spectra? MICHAEL AMES: Yeah. We collect background
spectra 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 a 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. And I think that's
the practical NAA. From this end, did
that all makes sense? I want you guys to
nod, not him to nod. Yeah. MICHAEL SHORT: Do you guys
have any questions for Mike on what you've just heard? Well-timed, because we were
just talking about this stuff all week. MICHAEL AMES: 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-- what you'd 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,
iron 58 to iron 59, that's a nice n 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 n p reaction. So if you're looking
on the chart there, cobalt 59, if you
get an n p reaction, will also make the iron 59. And that's a pain in the neck,
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 avoid having
all these fast reactions. There's usually an
energy threshold for the fast reactions,
like 1 meV or so. MICHAEL SHORT: Sound familiar
from the cube equation? MICHAEL AMES: Yeah, OK. Right. The place where we do the
irradiations is very thermal. It's 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 n p reaction
will get cobalt 58. And since there's
not a good reaction n gamma from cobalt 57, cobalt
57 isn't around usually. So that's how I measure
nickel, using n p reaction. And I need to put the
rabbits into where I've got a fast flux in the reactor. Which, well, they've got a
couple of spots for that. I try not to have
to measure nickel, because it's pain in the neck. But sometimes people
want to know nickel. And we talked a
little about what we've run in here
for types of samples. MICHAEL SHORT: Well,
why don't you tell us? MICHAEL AMES: OK, OK. So back 15, 20, 25
years ago, we did a ton of environmental
samples in this lab. We had a whole 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 has kind of quieted down a lot. But it's still useful
for a bunch of things. And so I do some work here now. I also work in the NCORE group. So that's a lot of my time,
rather than just 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 steady cam? MICHAEL SHORT: I got a question. MICHAEL AMES: OK. You've got a question. MICHAEL SHORT: What's the
weirdest thing you've ever been asked to count? MICHAEL AMES: The weirdest
thing I've been asked to count? That's already activated, or? MICHAEL SHORT: At all. MICHAEL AMES: OK. I don't know-- brain tissue. Fish samples that we actually
did the fresh fish samples. And you want to kind
of homogenize those. And we had this kind
of titanium blender-- you remember the Bass-O-Matic? We had this titanium blender
that we dropped the fish in, and you completely
homogenized the fish, and then you took a
little sample of it, and freeze dried it, and
then analyzed it for mercury. MICHAEL SHORT: [INAUDIBLE] MICHAEL AMES: Yeah, right. Because, I mean 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 we were going to
do this giant study using fingernails and toenails
for nutritional analysis. 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
week, or month, or whatever-- depend
where you cut the nails. And so I was going to
get a couple of hundred African children's toenails. That didn't happen. But I did analyze
my own toenails. Well, 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 would give up
toenails-- it's not a big deal. 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 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 we analyzed the hair samples
for arsenic and chromium, and then we plotted
out where they were, when the 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 and we gave the samples back. 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 in retrospect, that the contamination
from that area didn't get into the well water. That was in the mid-90s or so. Anyway, that was
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. So let's go down
the hall, this way. You all got to follow. And so this is
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 a whole
hundreds of kilograms of fly ash, just homogenize it,
sieve it, send it out to a lot of labs to analyze-- NIST is really good at this-- take all the data. And so this ash is characterized
for about 20 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, 5, 6, 7 milligrams. And I know what the
concentrations are in this. And so that's how I do
the comparative method. And so I got this. And they all look the same. And this is some soil from
Montana next to a mine, so it's nicely contaminated
with some metals. This is my IAEA mercury
and 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 cover what you
want without having to run five or six of them. This is 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 you who
weren't there, these are called rabbits because
it's the little thing that runs through the pneumatic tube. You guys are doing
[INAUDIBLE] 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 irradiation location. For short
irradiations, like what you guys are going to
be doing in a month, I send them in from here. That's OK-- I just don't
want to bump into that thing. 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 the control room and say, OK, turn
a bunch of knobs, and switches, and whatnot. And it goes schwoonk,
and in about 15 seconds it's next to the
reactor to the core of the reactor in the graphite. I usually run shorts. I'll usually irradiate
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 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 one or two good solid pieces. Because then I can take it out
of whatever it was irradiated, put it in a clean bag
or vial, and that way we don't have to do a blank
subtraction for the sample. Does that make sense? Because, otherwise, if
I take a little vial, irradiate 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 if we're not running standards you don't
have to worry about this-- that powdered standard stuff,
I never get that out of a bag. Because you'd never
get all of it out, and I'd have contamination
everywhere if I started cutting open those bags. So I do have to do a bag
correction for those. So when I do when
an irradiation, I always irradiate
a few empty bags, and then you do a
correction for those. Because the bags have got
aluminum, and antimony, and a bunch of things in them. And so then I take
a couple of samples, I throw them in a lead pig-- so I've 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 we're doing shorts,
I'll irradiate two samples at a time, because I
have two detectors. When I used to have
four detectors, I ran for samples at a time. So you irradiate it,
repackage it, count it. While those pair of
samples are counting, you come down here, you
irradiate the next two, so that you're
just kind of always irradiating and counting. I usually do a 10-minute
irradiation for shorts. I'll do a fairly quick
count-- five minutes-- right after I get the
sample down there, and that's looking for
stuff with half-lifes under 10 minutes. The shortest half-life I
look for is for aluminum. It's 2 and 1/4 minutes. But things usually have a
lot of aluminum in them, so I see aluminum pretty well. For shorts, I'll
count all the way up to about sodium, which is
almost 15 hour half-life. Longer stuff, I'll do a
longer irradiation to count. There's a little overlap
on my shorts and longs. That helps me do QA on things. And if I run two standards,
I'll check the concentrations from one standard to the other. That's another little QA thing. What else we got? MICHAEL SHORT: What
question do you guys have? MICHAEL AMES: Questions. MICHAEL SHORT: Now that
you know how this done. MICHAEL AMES: It's
pretty straightforward. MICHAEL SHORT:
What sort of things are you going to be bringing in? MICHAEL AMES: Yeah,
what do we got? AUDIENCE: Probably middle
Bronze age pottery shirts. MICHAEL AMES: Oh. Yeah, yeah. OK. There is a lot of
archeology that NAA got used for that a lot. I don't think we
ever did it here. Fred Frey, who's a professor,
retired now, from EAPs-- Earth, Atmospheric,
and Planetary-- he did a lot of
geological samples. And I forget where it was that
they did all the archeology. One of the things
NAA is really good for is rare earth
elements, which are hard to measure
by other methods. I can get very low
limits on that. And by picking out various
rare earths and the ratios, it can help identify where
things are from in the world. MICHAEL SHORT: Yeah. AUDIENCE: Can I use
a bird as a sample? MICHAEL AMES: If you give me
a little, tiny piece of it. AUDIENCE: OK. MICHAEL AMES: I mean, you know-- I AUDIENCE: Like, how
small [INAUDIBLE]?? MICHAEL AMES: Well,
see, that's the rabbit. So it's definitely
got to fit in there. AUDIENCE: OK. MICHAEL AMES: The
thing I really like-- excuse me, where's my vials? I used to have some
smaller ones up here. But that should definitely
fit in one of those. Like, see that guy. AUDIENCE: OK MICHAEL AMES: 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-- to be able to find. So no powders. And you could maybe get
it with your fingers. But 20 milligrams, 50
milligrams, 100 milligrams is just in the right ballpark. AUDIENCE: OK. MICHAEL SHORT: What else are
you guys thinking of bringing? MICHAEL AMES: Doesn't matter. We'll look at what
comes in, and-- yeah, I might veto
some things or not. But we'll see. We'll see what we got. MICHAEL SHORT: OK. AUDIENCE: What are
those little bricks for? MICHAEL AMES: Well, we
got bricks everywhere. So 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
dosimeter on now, but I usually have got the
symmetry and a ring badge. And then it kind
of comes over here, and this is where
the heat sealer is. So I can heat seal it here, and
then I'll have a pig over here. MICHAEL SHORT: They're
just painted lead bricks? MICHAEL AMES: Yeah, these
are just painted lead bricks. And you know, these have
been here longer than I have. And sometimes things
just are somewhere, and you never move them. These, I think, are
older than me too. This lab has been doing NAA
since the '70s, I think. Anybody else? AUDIENCE: Is there
a single brick that I could just hold
to see how heavy it is? MICHAEL AMES: The
full size bricks-- like, that size, 2 inches,
by 4 inches, by 8 inches, weighs about 25 pounds. There's usually a bunch
of them floating around. Here, you want this game? That one's not quite full size. AUDIENCE: Wow. That's pretty heavy. MICHAEL AMES: They're heavy. They're lead. Anybody else want to toss it? No, OK. [LAUGHTER] 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
lead bricks on your feet. So I've got steel toast. If I miss the toe, I'd
probably break my-- I don't want to think about it. And they move much bigger
things in the reactor. Have you toured the reactor yet? AUDIENCE: [INAUDIBLE] MICHAEL AMES: So there's
that giant crane there, and they move five-ton
pieces a shielding. And that's the other
dangerous thing in there, 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. [LAUGHTER] You know, like, four-foot,
half-inch steel-- boom. MICHAEL SHORT: That's
what happened to my foot. MICHAEL AMES: Yeah. OK, good. And people trip and
fall off ladders. And it's the usual
industrial accidents. AUDIENCE: [INAUDIBLE]
cut off your toe. [INTERPOSING VOICES] AUDIENCE: Well, my
toes are still here. MICHAEL AMES: Good. Yeah. I mean, I've broken
a few, but not here. MICHAEL SHORT: So, cool. Thanks a ton, Mike. MICHAEL AMES: Sure. And I'll see you guys
in a month or something and have fun
running the reactor. FRANK WARMSLEY: Well,
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 worth 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 will moved much faster. And we don't want
to run into a chance if you accidentally
going too high, so that's why we use a low
worth absorber on the way up and a high worth
absorber on the way down. And I just want to
show you the controls. With me today is Tim. To actually do
this experiment, we need two licensed
people in here, one at least has a
senior reactor operator. Both Tim and I are
both senior licenses, so we have that covered. The only way you can actually
do these manipulations are if you're in my
training program-- I'm 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. So I just want to show you some
of the controls of the reactor. First, we have our
shim 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's
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 our fixed
speed, meaning they can only move at the exact
same rate at all times. Moving the shim blade
in an upward direction or the regulating rod
in upwards direction, take an underhand
grip and pull up or twist upwards until it stops. Moving it 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 or the regulating rod. The experiment we're doing is
basically change reactor power by half a megawatt. And we're currently
at 500 kilowatts we're going bring the
reactor up to 1 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. Sp the first one is going to
be using a regular rod to move the reactor power up. What's the reactor power? We have about nine
different instruments that tell us what the reactor
power is at all times. But the ones we're going to
be paying attention to are channel seven 7 and channel 9. These two channels are what
we used to basically tell us what the wrecked power is. Channel 7 is what we control
our automatic control at. 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's going too low, it'll cause the regulating
rod to drive outwards to increase the
amount of neutrons making the reactor power go up. Channel 9 is a
linear power channel, and it basically tells us
what the power level is based on a 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 microamps, on this channel. And that's 8.5 microamps
equals 550 kilowatts. You're going to be
bringing a record up to 1. Megawatt and since it's linear,
it'll be double that-- so 17.1. Now, you want to be careful
when you raise reactor power. So when you start to
add power to the reactor by raising a regulating rod, 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
we're at, we have period-- the reactor period. The reactor period
is amount of time it takes reactor
power to increase. At the power level
we're at, we're not allowed to go shorter
than a 100-second period. So here is one of
three periods 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 a 100-second period. If it does, you have
to stop pulling blades. The other thing we
have to watch for is to make sure that the
power level, channel 9, 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% of the power level
you're going to-- since we're going
up to 1 megawatt, that's about 800 kilowatts-- you want to be able to drive
the absorber in and hold the absorber in. You'll drive 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 the period by driving the absorber
back in the regulating rod. And you'll keep holding it
in until you see the number not only stop increasing, but
actually go down a little bit. As soon as you see it
going down a little bit and go of the
regulating rod, You haven't stopped the
power at this time, you've just decreased
how fast it's going up. And then the power
level will sill go up, but a much slower rate
than it was before. And once it reaches the power
level you want to stop at, the 1 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 a 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 a log book that says I'm going to lower
ranked 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 10 times the
regulating rod, so things will happen much faster. So you'll be able
to drive this in and reactor power will change
much faster than before. Same thing-- as you get closer
to the power level you start at, the 500 kilowatts,
you don't want to undershoot and go too low. So right around 600 kilowatts
or so, start driving or shim blade out to slow down
how quickly the power level is going down. And once you get back to the
place where you started it, we'll use a regulating
rod to fine tune it to keep the reactor power
where would want it to be. There'll be another
logbook entry, and your time on the
console will be completed. So with us today we actually
have two MIT students who are actually in
my training program, and they've actually done a lot
of these manipulations already. AUDIENCE: Ladies first. FRANK WARMSLEY: Sarah. Let's go. AUDIENCE: [INAUDIBLE]. It's been so long
since I've done one. FRANK WARMSLEY: I'll take that. 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. So it would be very
difficult for you to get to someplace
where it would cause a problem without
us being able to stop it. I don't know if you want
to move or anything, but the supervisor normally
sits kind of right in your way so that they can keep
eye on what's happening. AUDIENCE: Are we doing doing
any announcing for these? FRANK WARMSLEY: You can go
ahead and make the announcement that we're starting
power manipulations, and then the last person will
make an announcement that we're done with power manipulations. AUDIENCE: Commencing
power manipulations. Commencing power manipulations. FRANK WARMSLEY: Right now,
the reactor is on autocontrol. And when we do
these manipulations, the reactor operator is
going to take manual control. That'll cause an
alarm to come in. And this will only happen
for the first time. So one of the things she's
going to do after she makes her logbook entry-- AUDIENCE: Are we
filling this out? FRANK WARMSLEY: No, we'll
do that at the end-- is she'll take manual
control of the reactor, an 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. AUDIENCE: All right. I hope to get to 1 megawatt
at 17.11 [INAUDIBLE].. FRANK WARMSLEY: OK. AUDIENCE: [INAUDIBLE] [ELECTRONIC SOUND] FRANK WARMSLEY: Now,
she's pulling out the red rod all the way. You see the red rod
number going up. The period is getting shorter. It's no longer at infinity. It's getting closer
to 100 second. And channel 7 and channel
9 are increasing in value. Another way you can see
it is we have a display on the front 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 hasn'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 started at 500 kilowatts. It's already up to 630
kilowatts and increasing. And the period that
was at infinity is now around 160 seconds. So she's watching, and she sees
the 800 kilowatt value here on channel 7 or channel
9, and she's started to driving the regulating ride. So she's slowing down how quick
the power increases going. 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. AUDIENCE: [INAUDIBLE]
back on auto? FRANK WARMSLEY: No. She's closing in
on the 1 megawatt. One of the things the note
is that when she started, the [INAUDIBLE] was
around 0300, 0310, and she's almost
right back to there. When you raise reactor 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 addition by bringing the
absorbers back to about where they started from. AUDIENCE: We're at 17.1 FRANK WARMSLEY:
We're at 1 megawatt? AUDIENCE: Yeah. FRANK WARMSLEY: Go ahead and
make your log book 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, we'll guide you through those-- the log book entries that
she's making and so forth. AUDIENCE: The [INAUDIBLE]. FRANK WARMSLEY: 30.6. OK. AUDIENCE: Should [INAUDIBLE]? FRANK WARMSLEY: Yep. So one of the things that could
change the reactor is xenon. It's a poison that builds into
the reactor while we operate. Poison in that it
absorbs neutrons not leading to fission. And it has two
ways of being made and two ways of
having it 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. AUDIENCE: [INAUDIBLE] half a
megawatt at 8.56 microamps. FRANK WARMSLEY: OK. AUDIENCE: Use the
same shim blade? FRANK WARMSLEY:
Yep, use blade 6. And what happens is when
we lower reactor power, the way we remove most of
the xenon from burn up, basically the neutrons being
absorbed by the fission process. 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 it's own. So you would have to
do a lot of re-shims. 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 lowering reactor power. AUDIENCE: Do you want to
have her do a re-shim now? Or do you want me to? FRANK WARMSLEY: No. I think we'll be able to get
at least one more person. So once again, she's
lowering 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 driving the absorber
out again to slow down how quickly the power
level is going down. And when she's
done, the shim blade will end up about at the
same point where it started, the 13.42 inches out of
the bottom of the core. AUDIENCE: It might not make
it all the way back up to [INAUDIBLE]. FRANK WARMSLEY: It'll be close. Compensate with the
reg rod if you need to. 30.8. OK. And that's the end
of the exercise.
