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visit MIT OpenCourseWare at ocw.mit.edu. MICHAEL SHORT: Today we
launch into radioactive decay. And so this is kind of what
makes us, us in this field, right? Now that you've learned
the general cu equation we're going to look at some
very simple, specific cases, and specifically all the
different things that can come flying out of
nuclei and the orbiting electrons around them. First I'd like to try and
develop a generalized decay diagram. What are all the different
ways that nuclei can decay? And I had written one of these
up to show on the slides, and my one-year-old son fixed
it with a bunch of markers and crayons, so I think
we're going to have to redo this from scratch. So let's say you had a
generalized unstable nucleus over here. And we're going to start drawing
a generalized decay diagram. You'll see decay diagrams,
well, much like these. I've already shown
you a couple of these, like these decay
diagrams for uranium 235, soon as I clone my
screen so you can see it. There are a couple
of axes that aren't drawn on these
decay diagrams that will help you interpret them. And the first one,
the imaginary y-axis, is in order of
increasing energy. And the second imaginary
y-axis is z, atomic number. So this will help you
determine how we read these and how to actually write them. Now what are some of
the different ways you've heard of things that
can radioactively decay, or that you might have
read from the reading? Just yell them out. AUDIENCE: Alpha decay. MICHAEL SHORT: Alpha decay. So in alpha decay,
what actually happens? Let's say that we had a parent
nucleus with atomic number z and mass number a. What does it change into? Anyone know what an alpha
particle consists of? Yeah. AUDIENCE: A helium nucleus. MICHAEL SHORT: A helium nucleus. So let's just say helium. This will be a 4 and a 2. and there's going to be
some daughter nucleus-- we don't know what-- with z minus 2 protons and
a minus 4 total nucleons. So if we were to describe
alpha decay on a decay diagram, where would we write the final
state of this alpha decayed daughter nucleus? To the left or to the right? I know it's like 9:00 AM, but
someone just shout it out. You don't have to
raise your hand. AUDIENCE: To the left. MICHAEL SHORT: To the left. Yep. Something that's decreasing in
z and also decreasing in energy, we would draw an alpha
decay like this to the left. So let's say this
would be something more stable with a z minus 2-- make that clear--
and an a minus 4. What are some other
ways things can decay? I heard a whisper. AUDIENCE: Beta. MICHAEL SHORT: Beta decay. So what happens in-- usually by beta
decay, we're referring to beta minus decay,
which would be the emission of an
electron from the nucleus. Again, what's the
physical difference between a beta particle
and an electron? Nothing. What's the nomenclature
difference? The beta comes from the nucleus. Otherwise, when they
come out, they're kind of indistinguishable. So what happens in beta decay? Let's say we have the same
parent nucleus starting with z,a. We know it emits an
electron with no mass. And what else? This is just a matter of
conservation of things here. AUDIENCE: Anti-neutrino. MICHAEL SHORT: There
is an anti-neutrino which has pretty close
to no mass and no charge. And what about this
daughter nucleus? How many protons and total
nucleons would it have? Yeah. AUDIENCE: Should
have one more proton. MICHAEL SHORT: Should
have one more proton and how many more
total nucleons? The same. Yep, like that. And so how would
we draw beta decay on this generalized diagram,
to the left or to the right? AUDIENCE: Right. MICHAEL SHORT: To the right. It's increasing in z. I haven't defined any
scale, so let's just say that's a change of 0. That's 1. That's 2. And that's plus 1. That's plus 2. Hopefully we won't get to today. So a beta decay
would proceed thusly. So you'd have some other
stable nucleus with c plus 1 and mass number 8. What are some other decays you
might have heard of before? AUDIENCE: Electron capture. MICHAEL SHORT: Electron capture. So in electron capture,
what actually happens? Start with the same
parent nucleus. In this case, the nucleus
actually captures an electron from one of the inner orbitals. And so that, in effect, like,
neutralizes a proton, right, in terms of charge. So what do we end up with? Yep. So we'd have some
daughter nucleus. If it neutralizes a proton,
we'd have one fewer protons. And then how many
total nucleons? The same. Yep. There we go. And so if we were to draw
electron capture on this map, we would have one fewer proton. So we could have some sort
of decay by electron capture. And anything else? What other particles can
be emitted from a nucleus? Yeah. AUDIENCE: Positrons? MICHAEL SHORT: Positrons. So let's get this list going up. So if we start off
with a parent, z and a, we know we emit
a positron, which is the anti-matter
equivalent of an electron. So same general characteristics
except opposite charge. In this case, we'll give it
a 0 protons and 0 neutrons. And we end up with-- well,
the same daughter nucleus. So we could say that this
precedes by positron creation or electron capture. It's the same process,
or the same ending state. But can you have positrons
in any possible decay? We actually went over this once. Anyone remember? Yeah, so you're
shaking your head no. AUDIENCE: You have to
have a certain energy, but I can't remember
what the energy is. MICHAEL SHORT: We'll
get back into that. You're right. So I'll put a little
box around this because you have to have
a certain amount of energy in order to create the positron. And what else? What about the easiest one? What else can be
emitted from a nucleus? AUDIENCE: [INAUDIBLE] MICHAEL SHORT: I heard
a couple of things. Neutrons. So certainly if
you emit a neutron, there are some very
unstable nuclei, like helium 5, which
exists for what, 10 to the minus 26
seconds or something, that could omit a neutron. If we start off with
z and a, then we'll start off with a
neutron and a daughter with the same z and
a minus 1 total. So what would that look
like on a decay chain? You don't usually see this,
but we'll draw it anyway. It would go straight
down, right? So there'll be
some other nucleus. So it'd be the same
z, but an a minus 1. And it could decay
by neutron emission. Yeah, that totally happens. If you look at the
very, very right edge of the table of nuclides-- let's go back to the
home page for that-- and look at the
super neutron rich. Like helium 10. Who's ever heard of this? Doesn't even say, let's
say, two neutrons. So this is so unstable that
it just immediately spits out two neutrons. So yeah, these things happen. You won't tend to see this decay
in textbooks because it only happens for exceptionally
unstable nuclei. But yeah, that's true. It does happen. What else could happen? Remember we've been
talking about-- yeah. AUDIENCE: Gammas? MICHAEL SHORT: Right. Could be gammas. And so I'll make one
little extra piece here for gamma decay, which
is nothing more than a photon emitted from the nucleus. We start off with
a parent z and a. And this becomes-- well, what? Should I even write
daughter nucleus? I see some people
shaking their heads no. Why not? Yeah? AUDIENCE: You have
essentially the same atom. It's just one of
its electrons should be at a lower energy state. MICHAEL SHORT: Yep. Very close. You have the same atom, so
let's say the same parent, with the same number of
protons, the same number of total nucleons. And I'll just correct that
to say one of its nuclei is at a lower energy state. But otherwise everything
is completely correct. So why don't we put
a little star here to say that that was
at an excited state? Just like electrons can be
promoted to outer shells, pick up a little bit of
energy, so can nucleons. So can protons and neutrons. And this is going to
be a subject of, well, great discussion in 22.02. For now all you have to know is
that nucleons, like electrons, can occupy higher energy states. And when they fall down
to lower energy states, they can release that energy
in the form of a gamma ray. So you could also
have, let's say, squiggly line gamma decay
to something stable. And so this right here would be
the generalized decay diagram. Anyone ever heard
of one isotope that undergoes all these
possible decay mechanisms? Glad no one's saying anything,
because neither have I. There's one that comes close. Actually, if you look at-- no, that's not this
part I want to show you. I want to show you the big one. If you look at potassium
40, the nuclide we probably talked about the most
so far, it covers most of the space of this
generalized decay diagram. And there was a question
that came through-- at least, I think for
non-anonymous email, what is it that makes these
even, even versus odd, odd nuclei less or more stable? Anytime you have an odd,
odd nucleus, both the number of protons and the
number of neutrons, these nuclear shells
are not fully occupied and they're not that stable
compared to an even, even nucleus that has an even number
of z and an even number of n. Just kind of like
electrons, these things tend to travel in pairs. And not fully occupied energy
levels will be left stable. Potassium 40 happens to be one
of those odd, odd nuclei that is relatively unstable. And it can go either way. Either you can lose a proton
or you can gain a proton by competing mechanisms
like positron or electron capture or beta emission. So this one I like a
lot because it gives you almost every possible
decay with the exception of alpha decay and
spontaneous neutron emission. It's not that unstable. Then the only one really missing
from here, I found what I think is the simplest decay
diagram ever, dysprosium-151. There's only one thing it can do
is it can decay by alpha decay to its ground state. I want to point out a few of
the features of these decay diagrams so you know
what to look for. Up here is the parent nucleus. Down there is the
daughter nucleus. And these energies
are not absolute. They're relative to the ground
state of whatever the daughter nucleus is. So simple example helps show
you that gadolinium-147 doesn't have a binding energy of 0. This is relative to the ground
state of gadolinium-147. And that will tell you that
the Q value for this reaction is 4.1796 MeV. These things are usually listed
in MeV unless said otherwise. You also might notice a pattern
that most alpha particles tend to come out
around 4 MeV or larger. The answer to why is going
to be given in 22.02. Yep. AUDIENCE: Where do these
percentages come from? MICHAEL SHORT: These percentages
tell you the probability that each decay will happen. AUDIENCE: Oh, yeah. Like how do we derive-- how do we find those out? MICHAEL SHORT: Ah,
these are usually measured because
it can be-- let's say things get quantum
and difficult in terms of calculating these. And our knowledge
of wave functions of, well, higher and
higher a or z nuclei gets a little more tenuous. So a lot of these
would be measured. You can look at the number of
alpha particles of each energy that you observe, and then you
get the average probabilities. For this one, it's simple. There's 100%
probability that this is the only thing that exists. The other things to
note, the half life will be given up here, in
this case, at 17.9 minutes. So relatively long half
life compared to helium 5. And we'll be going
over what half life is and what they are on Friday. And then the last thing
are the spin states of the initial and
final nuclei, which we will not cover in this class,
but you will cover in 22.02. So don't worry about
those now, but do know that when you need
to go find the spin states of the initial
and final nuclei to see if certain
transitions are allowed, this is where
you're going to go. Any questions on what you see
here on how to read these decay diagrams? Cool. OK. Then let's move on to the
simplest of them, which, in the table, can look
the most complicated. So here you can see that
there's a whole bunch of different probabilities for
different alpha decay nuclei. This is one of those more
complex examples where the easiest thing to
do is just measure, see how many alphas
you get at each energy, and this will give you the
approximate probabilities that each decay happens. And you'll notice here
that the final energy states for each of these
alphas is not necessarily 0. This will tell you what they
are relative to the ground state of, in this case, thorium 231. So you can emit an alpha
from any combination of nuclear shell levels
inside this nucleus. And you might end up
with a new daughter nucleus whose protons or
neutrons are in excited states. And the way you remove
those excited states is gamma decay, like
we talked about here. So a lot of alpha
decays are immediately followed by a chain
of gamma decays, or what we call ITs, or
isometric transitions. So you'll see a couple
bits of notation. For example, gamma
decay, you may hear it called isomeric transition. We'll try to give them all so
that in the various readings you have, you know what's what. So notice here, you can
have, with a probability so small that they
didn't bother to draw it, an alpha decay 2.634 MeV. And then any series
of gammas from, let's say, from this
state to that state, and then from this
state to one of those or one of those, and then
another one down there. So an alpha decay
may be followed by a whole bunch of gamma
transitions, or as few as none. If you want to see what
the alpha energies are, well, let's head to
the table of nuclides and look at uranium 235. So if we look up U 235,
you can see that it alpha decays to thorium 231. And I'll show you
the part of the table that I didn't show you in
the slides, which is then you've got a table of
alpha decay energies as well as relative intensities
and what's called a hindrance. This stuff right here
comes from the fact that different
alpha decay energies can happen with
different probabilities at different times. So the half life of a
particular alpha decay can be slightly different. And this is another one of
those really kooky things, where certain energy alpha transitions
will happen a little more often initially then finally. But we don't have to
worry about that yet. I just want you to know that's
why the hindrance is there. And so you can look,
from this table, what's the probability that each
of these alphas will come out. And there's going to be
some uncertainty associated with these. This is going to usually
be some sort of measurement uncertainty. Then you might
also ask, why is it that the highest
energy alpha ray is not the same
energy as the Q value? So for this, it's a greatly
simplified application of the Q equation that
we learned last time. So for here, what are
the two equations that we need to conserve if we have
a system consisting of-- we have our initial nuclei
going into our final nuclei. And they go off in equal
and opposite directions. If it's alpha decay, then we
have no little initial nucleus. We just had a large
initial nucleus at rest. And afterwards, you've got
a small final nucleus, which we know is the alpha particle,
and a large final nucleus, which we'll call the
daughter product. And let's say this
is the parent. It's a much, much simpler
system than the general one we analyzed last week. So what are the
equations that we'll use to serve to find
out what's the energy of this alpha particle? Anyone? Same three answers as always. Yep. AUDIENCE: Mass,
energy, and momentum. MICHAEL SHORT: Yep. Mass, energy, and momentum. I'm going to lump these two
together because they're kind of the same thing. So let's just go with
energy and momentum. So what is the initial
kinetic energy, or let's say, the initial kinetic
energy of this parent nucleus we can assume to be 0. What about the final kinetic
energy of the system? Well, there's only
two particles. There's going to be some kinetic
energy of the alpha particle plus the recoil kinetic energy
because if the alpha goes in one direction, the
daughter nucleus has to go off in the other direction. And the total energy
comes out to Q. This Q value you can get
by conserving mass, where we can say that the
mass of the parent has to equal the
mass of the alpha plus the mass of
the daughter plus Q. So that's where we can get Q
if we don't know it already. Luckily, we know it already. So there we've used mass. There we've used energy. And now what are the momenta
of the initial and final states here? Anyone? Just shout it out. What's the initial momentum
of the parent nucleus? AUDIENCE: 0. MICHAEL SHORT: 0 equals-- what's the momentum
of the alpha? Anyone remember that
trick if we want to say p equals mv equals what
more convenient form that contains the energy? Square root of 2 mt. So let's go with that. So there'll be the
square root of 2 mass of the alpha, kinetic
energy of the alpha, minus the square root
of 2 times the mass of the daughter times the
kinetic energy of the daughter because these have to have
equal and opposite momenta. So all we have to do is
move that one over here. This makes that equation easy. Everything's got a
square root of 2. We can square both sides. And we end up with a
pretty simple relation, mass of the alpha times the
kinetic energy of the alpha is the mass of the daughter
times the kinetic energy of the daughter. We don't usually care
about the kinetic energy of the recoil nucleus
or the daughter because the range is so
small that we usually don't get to measure it. But we are trying
to measure what are the actual alpha
particle energies so that we can reconstruct
this table down here. So we can take our energy
conservation equation and rearrange it to isolate
td, the kinetic energy of the daughter, and say
td equals Q minus t alpha. Substitute that in here. And let's rewrite
what we've got. Mass of the alpha, t alpha,
equals mass of the daughter times Q minus t alpha. If we multiply each term in here
by md, we get mdQ minus md t alpha. Then we can take all of
the t alphas on one side. So we'll just add md
t alpha to each side. So we have m alpha
t alpha plus md t alpha equals md Q. We can
factor out the t alpha here. And then we can divide each
side by m alpha plus m daughter. Cancel out the ma plus md. And there we have the answer. The kinetic energy
of the alpha is just the q value times the
ratio of the daughter mass to the total mass. This should look
awfully familiar. When we did this in the frame
of neutron elastic scattering or any other reaction,
we had the same equation with just different notation. So do you guys
recognize this firm, where we had t3 equals Q
times m4 over m3 plus m4. It's the exact same result,
just different notation. Last time we did it in the
most complex way possible. This time we started off with
the simplest possible equations for alpha decay. In the end it's the
same Q equation. We just didn't bother with
all the other terms and angles and things that we don't need. So is everyone clear
where this came from? Cool. And that's why
you're never going to see an alpha
particle that's got the same energy as the
initial minus the final energy because the recoil nucleus,
or the daughter nucleus, takes away some of
that kinetic energy in order to conserve the
momentum of the system that was initially at rest. Another way to say
this, for those who like center of
mass coordinates, is the center of
mass of this system was just the parent nucleus. It was at rest. The center of mass of the final
system has to remain at rest to conserve momentum. But again, I won't go
much into center of mass because I find it a
little unintuitive. I'll stick with a laboratory
frame of reference. So any questions
before I move on? Alpha, I think, is the simplest
case of radioactive decay. And I think now you know all
you need to know about it. Yes. AUDIENCE: So why do you
get so many different types if we just calculated it? Like mb, in mass
[INAUDIBLE] change? MICHAEL SHORT: Not ma and md. But ta and td would change. Yep. So in this case, for
different alpha decays, they'll have different Q values. So the Q value of, let's
say, this top alpha decay is this energy here,
4.676 MeV minus 0.634. So use a different Q and you'll
get different ta's and td's. So don't worry. You'll get chances to try
out these calculations on the homework,
where I'll actually ask you to calculate some
of these from this equation, make sure you get the
same values as the table. Any other questions on alpha
decay before moving on to beta? Just going in order
of the Greek alphabet. So beta decay is a
kind of funny one. You don't tend to get
a beta particle out at the energy of this Q value. You actually end up
getting a spectrum. And this measured spectrum of
different beta kinetic energies is what led to the
thoughts that there must be something else carrying
away some of that extra mass or some of that extra energy. I say that like it's the same
thing because it totally is. And this is what
led to the thinking that there's got to be some
other very difficult to detect particle. So the theorists
here we're saying, if we know the initial and
final energies from beta decay, and we know that we get a
spectrum of different beta energies and the
probability of finding a beta particle at energy
Q drops to, like, 0, you'll almost never see it. There's got to be something
else carrying away the energy. So this idea of the
neutrino, or in this case, the anti-neutrino, was
proposed a long time before it was confirmed. And finally we know why. And one of the questions
I want you to think about, because it might be on an
exam in exactly two weeks, is if this is the relative
number of electrons from beta decay as a
function of energy, what does the number of
anti-neutrinos versus energy look like in order to maintain
conservation of energy? So it's something I want
you guys to think about, but I'm not going
to tell you what it is until the
solutions for an exam. In the meantime,
another thing to note is that these beta
decays can also be followed by any number
of gamma transitions. I've given you a simple one. If you want to look up simple
ones to test your knowledge, go with the light elements. They don't have
that many nucleons and they won't have
that many transitions. For example, if we pick
a beta decay nucleus, something simple. Let's go with lithium,
which typically has-- the stable isotopes are
lithium 6 or lithium 7. So do you think
that higher or lower mass number lithium will
tend to go by beta decay based on this generalized
decay diagram? It's what? AUDIENCE: [INAUDIBLE] MICHAEL SHORT: Lower. Lower proton number? Well, we've got to stick
with the number of protons because we need
to remain lithium. So in other words, do
you expect lithium 4 and lithium 5 or lithium 8 and
lithium 9 to go by beta decay? AUDIENCE: The higher ones. MICHAEL SHORT: The higher ones. OK. If you guys remember
the mass parabolas from a couple of weeks
ago, we delineated where you'd expect
beta decay in order to increase the proton number. So if you've got too many
neutrons and not enough protons, chances are beta decay
will help equalize you out. So as a guess-- I haven't even
tried this at home. Let's see. Let's see what happens
with lithium 8. Oh, look at that. Beta decay. It can also decay by
beta plus 2 alpha, which is another word for
the nucleus just blows apart. It's interesting, too, if you
read Chadwick's paper again, the way he described a
beryllium nucleus is consisting of a neutron plus
two alpha particles. Interesting, huh? Lithium 9 could decay
by--or let's say lithium 8. What do we have? Beta plus 2 alpha. Yeah. So Chadwick
described any nucleus as consisting of these
elementary-ish particles that you could measure. And in this case, you kind
of see a physical example. When this nucleus
blows apart, it just becomes two alphas in a beta. Interesting. But let's look at the
beta decay to beryllium 8. Pretty simple. You may ask why can't you
have beta decay directly from the highest energy to
the ground state energy? That is a 22.02 question
that I'll mention. There are allowed and unaligned
transitions between spins and energy states. So if you're wondering why
isn't every line drawn, in the case of really
complex nuclei, there aren't enough pixels
on the screen sometimes. But for the simple
nuclei, there are actually rules of selection
to decide when you can make this transition. But a lot of beta
decays will usually be something like a beta
decay followed by a gamma. So let's see a couple
of well-known examples. For example, carbon-14. This is the basis behind
carbon dating, one of those rare instances when
you have a beta decay directly to the ground state. It's about as simple as it gets. And because the half
life is 5,730 years, it's really useful
for dating when did an organism or
piece of material die on the timescale of, let's
say, tens to tens of thousands of years. Once you've gone
past a few half lives and there's very
little carbon-14 left, there aren't a
lot of decays left and your counting
statistics get crappy, and it gets harder and
harder to carbon date things. The basis behind this is that
all living organisms that are intaking and exhaling
carbon by some means remain in isotopic equilibrium
with the carbon surrounding them. And while most carbon is
CO2, and food and whatever is carbon-12,
you're going to have a little bit of
carbon-14 production from the upper atmosphere. This is usually a
cosmic ray phenomenon, which we'll get into when
we get into cosmic rays. The moment you die you
stop intaking carbon, and the little bit of carbon-14
in the cloth and the food and your body, whatever,
starts to decay naturally with a very regular decay curve. And so this is the whole
basis behind carbon dating. And in the next
p-set, you'll actually see how this was used to
debunk the Shroud of Turin, or the supposed burial
cloth of Jesus of Nazareth, because the carbon dating
data just didn't check out. As much as people really wanted
to feel like we found it, no. Science. That's the answer. No. Another well-known one
we've talked about before is molybdenum 99 decaying to
technetium 99 meta stable. Notice how here,
any number of beta decays and any cascade of
very fast gamma transitions, they almost all end right
here at this state of about-- let's see, there's two numbers
written over each other. But it's about 140
keV or 0.14 MeV. This transition from this
state to the ground state is a slow transition. So you can actually
build up technitum 99 in what's called
series decay, which we're going to cover on Friday. And then you can use
these 140 KeV gamma rays to do medical imaging. So when you get a medical
imaging procedure done, chances are this
is how it's done. You get moly 99 out of a
reactor or an accelerator, chemically isolate
the technetium 99 meta stable, which lasts on
the order of six days or so, very quickly get
it to someone, inject it, and image where do
the gamma rays go, or where do the
gamma rays come from? One last notable one is
responsible for a lot of, well, problems when folks
go urban exploring in old dentist's offices. Nowadays they have
electrostatic x-ray machines at dentist's offices. But back in the day, you
could get a little button of cobalt 60, which would emit
two very characteristic gamma rays in addition
to its beta decays. So normally what happens
is cobalt 60 decays quickly to an excited
state and gives off two gamma rays in
succession, which would be used for imaging. Problem is that's
the a cobalt source. And if you don't know what
it is, and you're like, oh, cool, what's this blue thing, I
think I'll put it in my pocket and keep it-- that has been responsible
for some injuries from some folks that
didn't know any better. And then how do you
detect the neutrinos? We talked about the theoretical
reason why they exist. Let's actually see
how they're measured. There is a hollowed
out salt mine of some sort called
Kamiokande in Japan. It's a humongous hole in the
ground filled with water, for a reason, and lined
with tens of thousands of highly sensitive photo
tubes that can pick up tiny, tiny amounts of light. The reason for this
is because neutrinos, as you saw in problem
set 1, are always traveling near the speed
of light in a vacuum. So if the speed of
light in a vacuum, let's call that 1, and the
velocity of the neutrino-- wasn't it something like 9. 999c or something like that? It was pretty high. The speed of light and
water is significantly less than the speed of
light in a vacuum. When you have a material or
a particle that goes faster than the speed of light in the
medium that it's traveling in, then you can produce
what's called Cherenkov radiation,
which I think I've mentioned once before. It's kind of like a
sonic boom in that you get a conical shockwave
of energy radiated from that particle that tells
you which direction it's coming from. But instead of a sound
wave, you get light. And this whole
detector is designed to look at the ellipses of
Cherenkov radiation released by neutrinos and anti-neutrinos. So what happens is
if a neutrino happens to interact with the water here,
it produces Cherenkov radiation lighting up a ring
of these detectors so you can tell
it's energy and you can tell where it came from. So if you, let's
say, can correlate a supernova or some sort
of crazy galactic whatever with a slight
burst of neutrinos, then you've got a pretty
significant astronomical event. It also led to my
favorite BBC headline ever, "Particle physics
telescope explodes." You'd see this on, like,
Fox News or something. No, this was the BBC. What happened here is
one of these 30,000 or so tubes was
slightly defective, couldn't hold the
pressure, and it burst. And the resulting
sound shock wave from one photo tube bursting
blew up about 11,000 of them. So yeah, the particle physics
telescope kind of did explode. They did rebuild it
and it's still going. It was an expensive repair
because all 11,300 something tubes had to be rebuilt.
And if you notice, there's a guy on a boat there. How do you install them? Well, you float
on a boat quietly, and put the photo tubes in,
and raise the water level, and float to another
part of the detector quietly, and continue
installing the photo tubes until you're done. AUDIENCE: [INAUDIBLE] MICHAEL SHORT: Yeah. You don't. Yeah. Don't sneeze. So yeah. Favorite BBC headline ever. Thanks again, science. For positron decay-- OK, we've got about
10 minutes left-- for positron decay,
this is the energy that you need in order
to make a positron. It is approximately exactly
double the [INAUDIBLE] rest mass of an electron. And the question usually
comes up, well, a positron has a rest mass
energy of 0.511 MeV. Why do you need double
that to make the positron? Because in order to conserve
the charge of the system, you have to shed an
orbital electron. So the system has got to be
able to lose two electrons in the process, one
positively charged and one negatively charged. And so that's why the
Q for positron decay is just going to be-- remember, this symbol's
the excess mass here, excess mass of the parent minus
excess mass of the daughter minus 2 times the rest mass
of the electron squared. To refresh your memories a
bit, find some empty space. The excess mass is
nothing more than the mass minus the horrible
approximation of the mass. So the excess mass and the
real mass are directly related. And these are things
that you can look up. Just to remind you
guys that excess mass and mass and binding
energy and kinetic energy are all related, again,
by the Q equation. It's probably the last time
I'll say it because I think that's about 100, by my count. Positrons can be used for
some pretty awesome things. And in the last
five minutes or so, I want to show you some
work done by Professor Brian Wirth at the University
of Tennessee, Knoxville on positron
annihilation spectroscopy, using anti-matter
to probe matter and find out what
sort of defects exist. And as a nuclear
material scientist, I'd be, well, terrible
if I didn't inject a little bit of
materials and how we use nuclear stuff in 22.01
in order to probe that thing. So the way that positron
annihilation spectroscopy works is that, well, matter's
mostly empty space. And then in a regular
crystal lattice, where the atoms are arranged
in a very regular array, let's say these atoms have
their orbital electrons. The empty space between
is also arranged in a very regular array. And positrons annihilate
with electrons to produce-- well, we'll find
out in a second. But where in matter
would they want to live, or where would they last longer? Not near an atom, but
near the space in between. So you can map out the
empty spaces in matter in a regular crystal and
calculate an average positron lifetime. If you were to fire a
positron into this matter, how long would it
sit and bounce around before colliding
with an electron and releasing that
extra rest mass energy? It turns out if you have
crystalline defects, the positrons tend to
last a little longer. There's a little
more empty space, which is to say there are
more places with a slightly less probability of
finding an electron. And so they last longer. And you can measure the
lifetime of positrons before they enter the material,
and then how long before they produce their characteristic
destruction gamma rays. So if you think about it,
you have a positron coming in with a rest mass 0.511 MeV. And it collides with an electron
from some orbital nucleus that has the same rest mass. The positron and the electron
annihilate sending off gamma rays in opposite
directions, where the energy of this gamma
is same thing, 0.511 MV. So you can tell
when a positron was destroyed because you instantly
get 1/2 a MeV gamma ray. Or actually, you get
two 1/2 MeV gamma rays. Then the question is, how
do you tell its lifetime? Let's go back to something
that I didn't quite point out, but I want to show you
now, is this positron decay is immediately followed
by a 1.27 MeV gamma ray, which in PAS, or Positron
Annihilation Spectroscopy, we call this the
birth gamma ray. This gamma ray is emitted the
instant this nucleus is born. And the positron takes a little
bit of time to get destroyed. So you actually look
at the difference in time between sensing the 1.27
MeV gamma ray and the 0.511 MeV annihilation photons. And that is measured
in, let's say, hundreds of pico
seconds with resolution of around 5 picoseconds. And you can then tell, from the
lifetime and how many survive, what sort of atomic defects
might exist in the material. So if you want to count
the number of missing atoms or vacancies in
a material, which is extremely important to those
of us in radiation damage, you can do so with positron
annihilation spectroscopy. So I think I wanted to show
you a little bit about how this works. You start off by making a
radioactive salt sandwich. You take some sodium
chloride, specifically of the isotope sodium 22,
which is giving off positrons all the time. And you sandwich that
radioactive jelly between the two slices of bread,
better known as your sample. That way you catch
every positron that gets out so you don't
lose half of them to one side. You've got two detectors
on either side waiting. So there's some probability
that the photons emitted are going to go in the
direction of the detector. So you miss most of the
signal, but so what? Whenever you actually sense
a 1.27 MeV gamma ray followed by two 511 KeVs
here, then you know you've had a positron
annihilation event, and you can actually count
the time between when those things happened. And you can see the
number of counts and get the average
positron lifetime from finding out how many
counts you get every five pico seconds, for example. There's something to note
about these counting spectra. Anybody know why they're
so smooth up here and then they're so
delineated down here? Anyone have an idea? You're going to see this a lot
in 22.09, when you actually count theta particles or alpha
particles and your counting statistics get a
little crappier. This is a log scale of
counts, or in this case, counts per five pico seconds. 10 to the 0's better known as 1. So you're looking at one
count or two or three. You're looking at
the discrete event. You can't have one
and 1/2 counts. So you're going to
see this kind of thing quite a lot when you're trying
to count very rare events. And if you're down in
the weeds like this, let's just say your
statistics aren't that good. But since this is a logarithmic
scale, 10 to the 4th is better known
as 10,000, that's enough to get good
statistics and fit a nice curve to this
positron lifetime thing. This is what one of them
actually looks like. And you can kind of tell. Inside there is where all
the positrons are coming out. So that's probably
lead shielding. Here's two detectors
on either side. And here's another detector
to detect that 1.27 MeV birth gamma ray. So if you get those three
events happening all at the right time, you've
got a positive event that you can count. And last thing I'll mention
is you can actually use this, like I said, to gut not just
the number of vacancies, but the number of
different size defects. You might have two or
three missing atoms next to each other, which will have
different positron lifetimes. And you can actually count
the number of each of these to get the diameter or the
size of these atomic defects. And this is one of
the ways of confirming our models of radiation damage,
which is, like, all I do. That's half of our group. If you want to
read anything more about positron
annihilation spectroscopy, all the stuff in
these slides were from these references,
which you can look up easily on the MIT libraries. We have access to everything
because that's MIT. We just buy everything there is. So I'd encourage
you to look here if you want to see more
details on how this works and why it works. So because it's exactly
five of five of, I want to open it up to any
questions on alpha decay, beta decay, positron decay,
or the decay diagrams that we've developed today. Yes. AUDIENCE: What is the most
dangerous kind of decay? MICHAEL SHORT: What is
the most dangerous kind of decay to be exposed to? So in this case, you'd want to
say the energy of the particle is held constant, and the
number of those particles is held constant. And actually, we're going
to answer this question when we get to medical
and biological effects. But let's do a little
flash word now. Let's assume, if you want to
see which one of these decays is most dangerous, we'll
have to say constant-- constant-- energy of decay,
constant activity, and what else can we hold constant? Well, constant you. Let's say the same number of
particles end up hitting you. That depends on whether they're
inside or outside your body. If you were to ingest
material, then alphas would be your worst
because alpha particles are massive and
charged nuclei, which means they interact very
strongly with matter around them. So if you ingest
them and they end up incorporating into your cells,
where they can just get next to DNA, they can
just blast it apart. However, an alpha source
of equal strength held in your hand would do nothing. The dead skin cells are enough
to stop alpha particles. And we're going to
find out exactly why when we look at
the range and stopping power of different
particles and matter. From the outside, alphas won't
really get through your skin. Betas might get through a little
bit of your skin, but not much. Gamma rays will mostly
go right through you. It's neutrons that
are the real killers. Those neutrons are
heavy but uncharged. So they interact
kind of strongly. When they do hit,
they pack a wallop and they do a lot of damage. And they're mean
free path, and you is on the order of 10 centimeters. So a neutron source from the
outside can do a lot of damage from the outside. The alphas and the
betas would be stopped by your skin and clothes. The gamma rays, almost all of
them will go right through you. And you guys will actually
have to do this calculation to find out how many
gamma rays would you absorb from a
gamma ray emission, and how many go
right through you. The hint is most
of them get out. So there's an exam
question we used to ask in 22.01 that I was
asked during the first exam, is you've got four cookies, an
alpha emitter, a beta emitter, a gamma emitter, and a neutron
emitter of constant energy and activity. You must do one
of the following. You have to hold one in
your hand at arm's length. You have to put
one in your pocket. You have to eat one, and you
have to give one to a friend. What do you do and why? Anyone have an idea? Pop quiz. Yeah? AUDIENCE: Probably give the
neutron one to a friend. MICHAEL SHORT: That's right. I can tell this is
the west, because when I asked a group of Singaporean
students the same question, they would eat the neutron
to save the friend because of Confucian ethics. Yeah, it doesn't fly here. Your answer is correct
because this is America. What would you do
with the other three? AUDIENCE: Eat the gamma. MICHAEL SHORT: Eat the gamma
because most of the gammas will just get to
the friend, right? What about the
alpha and the beta? AUDIENCE: [INAUDIBLE] MICHAEL SHORT: Yeah. Hold the beta at arm's
length because there's another aspect of shielding
betas that we'll get into. When betas stop
in material, they produce some low energy
x-rays called bremsstrahlung. So you'd want to get
those far from you. And the alpha in
your pocket will just be absorbed by the pocket. Yeah, so that's
the right question. So you're not going to
see that on the exam. But good news is you pretty
much got the right answer because this is America. Probably time for one more
question if anyone has one. Cool. If not, then I
want to remind you Amelia will see you on Thursday,
so do come to class Thursday. I'm going to change the
syllabus to reflect that. And we'll have two
hours of class on Friday to get through decay and
activity and half life, followed by an
hour of recitation. So I will see you
guys Friday, and we'll see what mood I'm in depending
on how the nano calorimetry goes. Could be a fun measurement.
