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PROFESSOR: All right let's get start. Before we get into the lecture just a couple
thing. Turning in your homework, a few of you asked me to look at your midterms. I've
done that. In some cases there were adjustments. In other cases there aren't. You can
pick them up. Before we get into the lecture this is David Frazier. He's a first year
grad student and a member of American Nuclear Society here in Berkeley.
STUDENT: As, I'm the president of the ANS student section here on campus. I
have two announcements. One is the Northern California section has these dinner meetings
in San Francisco. They're a lot of fun. They have great speakers. They have a director
of bwr from Westinghouse coming on Tuesday the 22nd. It's $10. But it's a steak
dinner. A nice, it's great. We try and organize carpools. I'll send out an email again
about this. If you're interested email us back. We'll try and set up carpools to drive
over to San Francisco to attend this event. If we don't have enough drivers we'll BART
over. It's a short walk from BART. My second announcement . The ANS student
section is having a meeting on Wednesday. In two days, Wednesday the 16th. We're having
a representative from Aaron engineering and research come to talk to you about job
opportunities. And internships. They have offices in Walnut Creek and Campbell. But
if
you're from Northern California you might know where they were. One is about an hour
south of here and the other one is about an hour slightly southeast. Or, so no, yeah,
so
six p.m. It will be at six p.m. on Wednesday. You should get an email about that.
STUDENT: There's food there too [LAUGHTER]
PROFESSOR: That's the important part.
STUDENT: Yes there's food Leo. There will be pizza at the meeting. But, 6:00 p.m.
In 3105. The same place we had the first meeting if you attended that. You should get an
email about both of these events, today, this afternoon. Be on the look out for that.
Please respond, RSVP so I know how much pizza to buy. All right. Thank you.
PROFESSOR: Sure. I encourage you to participate in both of these things. These
dinner meets lings are interesting. Good speakers. And a nice dinner for a reasonable
price. So take advantage of it.
Before we get into chapter nine which is the one on beta decay, I think I mentioned
nearly everyday there's some news item in the paper on on line having to do with nuclear
something or other. As look at the news today I found this article having to do with a
suspicion people had awhile ago about what killed Yasser Arafat. There were questions
whether I died 10 years ago. There was allegations that he had been poisoned using a
radioactive isotope. Polonium 210. polonium 210. Online, folks, have examined in more
detail some of his clothing that was recovered after his death. They found small amounts
of polonium 210 present. This was nearly a decade after he passed away. If you go back
to the slides on the natural uranium sequence, the half-life is 138 days. This is a lot
of half-lives since then. There isn't much activity left. They talk about the sample
showing some million Becquerel's, 10 to the minus three decays per second. It's not very
much. But if you extrapolate backwards it would be Giga Becquerels at the time of his
death. If you wanted to determine this, you would have to exhume his body and do more
more detailed tests.
Polonium is an alpha emitter. The thing that makes it dangerous is if you ingest it.
The story went onto talk about perhaps it had been ingested into his body, injection
or
eaten some food that was contaminated. And the damage done to the internal organs as
a
result of that. If you're interested you can read some more up there.
All right. So we're moving onto chapter nine, which is Krane's chapter on beta
decay. You can see we're doing alpha, beta, you can expect next will be gamma. These are
the homework problems due a week from today. And we'll spend three lectures this week
going through the chapter.
The equation would be written like that. Although in the form I've written there
it's not balanced in several ways that we'll talk about.
One of things that people were thinking about as radioactivity was being discovered
they knew classically that certain things were conserved. In particular energies seem
to
be a conserved quantity. That before a given macroscopic interaction there was a certain
amount of energy in the system. If you took into account all the energies, the total
energy whereas conserved. Momentum was another isoquant. Angular momentum. Linear
momentum. They seem to be conserved quantity. When one studied radioactive decay you can
see these things still be conserved in the first kind of radioactive decay we talked
about, alpha decay, you have a parent, isotope, decaying into something two units less
charge and four units less mass and spitting out an alpha particle. Remember if you look
at the energies of the alphas that are emitted, I showed you spectra, that were in the
Krane's book that looks likes this. Discrete line, energies. If you looked at the height
energy alpha it was equal to the total Q-value for the decay. The difference between the
full Q-value and energy of alpha we, it seemed nice that this alpha decay energy was being
conserved. And so when people went onto study beta decay it was expected that if you had
some parent atom like this decaying into a daughter plus an electron or a positron, if
you
measured the energy of electron or positron you should see a spectrum that looked like
that. If that's what's being emitted in the decay the energy has to be spared between
the
two particles. If you look at energy and momentum conservation because of large mass of
recoil nucleus compared to the mass of electron almost all the energy of decay should go
into the electron. Ought to see something that looks like that.
When started measuring energy strata of the electrons emitted in beta decay they were
saw something that looked like that. This was bismuth 210 decaying in the isotope we
just
talked about plutonium 210. What you see is not discrete energy, you see continuous
distribution energy from zero up to the full energy allowed by the value of that decay.
So this was a puzzle. It appeared on face value that energy was not being conserved
here.
This was the energy available in the decay. And yet most of the time, the electron
carried away far less energy than that.
It got worse as people did more sophisticated experiments. This is what's called a
cloud chamber. This is a device which produces tracks of charged particles when they go
through the vapor which is inside. Usually the vapor is alcohol vapor. What was going
on
in this particular image was there was a radioactive nucleus. Helium six. That was
sitting right up there where the two lines come together. And it was initially at rest.
And it underwent a beta decay. And what you see here is this curved track here which is
the electron that was emitted in the beta decay. Then you see a short stubby line that
goes off down and to the left. That's the recoiling lithium six nucleus. If you think
about it, there's a real problem here, because the helium six was initially at rest.
Momentum should be conserved. And if you just imagine the momentum vector the electron
and the momentum vector of the lithium six, they obviously can't add up to zero. They're
not pointing in opposite directions. It looks like linear momentum isn't conserved
either. Furthermore if you look at the spins of nuclei involved, helium six is a nice
even-even nucleus. Two protons, four neutrons. So it's spin is certainly zero in the
ground state. The lithium six, you've worked through this problem. It turns out the
lithium six has a spin of one. And the spin of the electron is a half. So a half plus
one can't possibly equal zero. So it looks like not only is energy not being
conserved
be a radical idea. The idea was there was yet another particle emitted in that decay
that was not observed. He called that particle the neuron but that name later got onto
the particle we, later this particle that Pauli invented was called the neutrino. And
it
was a radical idea because back then, this was even before the neutron, the thing we
call
the neutron has been discovered. The only particles people knew about were protons and
electrons. The idea of inventing an uncertain particle was radical. Today we have
hundreds of different particles and inventing one more was no big deal. In those days it
was a big deal and people didn't take it seriously. This is Pauli when he came up with
the idea back in 1930.
From the data I've shown already, that continuous energy distribution, the fact the
particle didn't leave a track in the cloud chamber and the angular momentums didn't add
up, you can infer a bit about what this neutrino had to be if it was real. So the
properties that he stated had to be there were, it had to have no electric charge because
otherwise it would have left a track from the cloud chamber. We don't easily understand
its energy. It escapes from the detector. It must interact weakly. The fact that the
beta spectrum that you do see goes all the way up to the endpoint energy allowed by the
Q-value suggests this particle if it has any mass must be very little mass.
It does carry away energy and linear momentum and in order to conserve angular
momentum its spin has to be a half h bar. So what he was saying was in every beta
decay, and the example that I showed was the bismuth 210 beta decay, the bismuth beta
decays in the daughter nucleus, polonium ten. spits out an plan, would that everything is
conserved.
In general, you don't observe the neutrino, the fact that you see an electron
spectrum which is continuous implies that the electron and the neutrino are actually
sharing the decay energy. I'll show you later on there are ways to measure the energies
of these neutrinos, and actually see energy is being conserved.
Okay. As I said, the idea of neutrino wasn't taken seriously for quite a while
because apart from any indirect inferences that it should be there there was no direct
experimental proof. And the reason is these neutrinos does interact incredibly weakly.
In the 1950, Fred Reines and Cowan, did the first experiments to detect neutrino, they
were looking at particles created in nuclear reactors. You'll see why it was
anti-neutrinos being produced in reactor. What they did was to bring a detector that
had
a lot of hydrogen in it, a lot of protons. And expose it to neutrinos emanating from
a
work nuclear reactor. These particles, the electron anti-neutrino can interact with a
proton, and produce a neutron and a positron. Notice that electric charges is conserved
here. I've got an electrically neutral object. Something has positive charge here turns
into a neutral and positively charged object there. energy is conserved angular momentum,
everything else good is conserved.
What they do in order to establish that this was really going on, is to detect both
neutron and positron following that reaction. It turns out, these reactions happen very
rarely. Even when sitting right next to a nuclear reactor. You need to beat down all
the
other possible sources of background that mimic the signal you're looking for. And this
coincidence between the neutron and positron is a good way to eliminate sources of
background. The same reaction and the basic technique is being used to monitor nuclear
reactors now. You can learn what's happening inside a nuclear reactor without having to
go in and take samples by measuring the spectrum of neutrino that are emitted. So they
detected this in the 1950s. In the mid-1990s Reines won the Nobel Prize in physics for
that discovery. Neutrinos are weird and they have interesting properties that we're still
studying. Ray Davis another gentlemen when won the Nobel Prize in physics for neutrinos
took up this idea and brought a different material newer a nuclear reactor. Chlorine,
so,
the same particle Reines was looking at. And looking for it to turn into argon plus an
electron. And from what I've said so far that reaction should go. In fact, Davis
discovered it doesn't happen. He doesn't see this at all. And so what Davis inferred was
there was a different particle than what Cowan and Reines were looking at which would have
allowed this reaction but it's the antiparticle. So there's a neutrino and a
anti-neutrino and according to Davis's experiment these things are not the same.
Now, these days we can produce beams of neutrinos and shoot them at targets and watch
them interact. This is a bubbling chamber picture. I believe it was taken at CERN, just
to calibrate you the accelerator would be about a mile down in that direction. It doesn't
really matter what the beam was. It's probably a proton beam that slammed into some
target. At very, very high energies. All kind of particles would be created. And
between the place where the target was and where this bubble chamber is located there
would you be roughly a mile of dirt and rock. And the idea is that the dirt and rock
would stop every other particle except the neutrino from reaching the bubble chamber.
And
so the neutrinos are coming up this way. They come in, and right here one interacts with
the nucleus. You can see that right there. And out comes a spray of particles. You
might say, these particles leave tracks, you can see them. But I don't see the neutrino
coming up. That's exactly right because the neutrino has no electric charge. And the
only thing the bubble chamber or the cloud chamber can see are charged particles. So
you
don't really see the neutrino come in but you see something spontaneously happen here.
For what otherwise would be no good reason. And a lot of particles are created. How do
you know that's a neutrino and not something else? The honest answer is you don't. But
the people who did this for a living will tell you they see more events like this when
the
accelerator is on than when it's off. If you don't like that you're not going to like
anything else about neutrinos because that's as good as it ever gets. Because they
interact weakly and don't have charges they're very difficult to detect. What I didn't
say for neutrino that have energies of a few MeV like the ones we're going to talk about
in beta decay, the mean free path, distance things travel before they interact is
something like a light year of lead. 6 trillion miles of lead. Doesn't mean they're
weaving through, they're going right through without interacting.
STUDENT: Are the bubble chambers in a magnetic field.
PROFESSOR: This one must be, you're saying because of curvature of the tracks, yes,
it has a magnetic field. Specifically so you can determine the charge of the particles.
Very good observation. Yes.
So in order to see neutrinos interact at all you need enormous numbers of them first
of all and very, very large detectors, in an experiment like this, they probably see
a few
events a day.
Okay. Why do we care about neutrinos? The reason we care in nuclear engineering has
to do with monitoring of reactors. I'll spend time talking about that later. And I used
to give this explanation and I was a little embarrassed in the context of a nuclear
engineering class, but given we're using them to monitor reactions and what happens in the
to the nuclear fuel in a reactor I'm not embraced anymore. So. It has to do with
understanding the properties of neutrinos and what they mean for the evolution of our
universe.
Now we've talked a little bit about quarks so far. And I said that the neutron and
protons inside atomic nuclei are made up of quarks. I said they're made up of up and down
quarks, funny names for things don't understand. Turns out that associated with those
quarks are two particles we've also talked about, the electron and the electron neutrino.
from the experiments there are other quarks. They seem to came in from pairs. There
seems to be a different kind of leptons. Leptons are particles that don't participate in
strong interactions. There is the electron, and heavier version of mu. And associated
with each of leptons is a distinct neutrino. So there's an electron neutrino that somehow
knows it's from the electron family. There's another neutrino that knows it's associated
with muon and a different one associated with tau. they called these properties of
neutrons that distinguish them from one another flavor. Just like the quarks have
different flavors.
The neutrinos are very, very light. They have very small masses. And all these
particles would have been created in the Big ***, the thing that started our universe
15 billion years ago. Most are short-lived and decay away. Except for the up and down
quarks and the electron, all the other guys that have gone away. But the neutrinos are
stable also as far as we know, and so all the neutrinos created in the Big *** are
still
present in our universe. You can calculate how many of them there should be. They're
roughly 100 of them per cubic centimeter of each type everywhere in the universe today.
So you put out your hands and there are a large number of neutrinos going through that
volume each second.
If each neutrino has mass of about five electron volts then the total mass of
universe of neutrinos would be enough to stop the expansion of universe. We know that
isn't true anymore. When we made this slide 10 years ago we didn't know that. But the
mass of neutrino turned out to be important in determining how the universe evolves.
Still don't know what the neutrino masses are. That is an area of a lot of current
research trying to pin down what the masses are. One way to get at it is to look at beta
decay carefully. The idea is if you look at the spectrum electrons emitted in beta decay,
and measure the number of them as a function of that energy, if the mass of neutrino and
to be careful I should say the mass of anti-neutrino was actually zero then the spectrum
of electrons that are emitted work up to the full Q-value for the beta decay. On the
other hand if the neutrino has a finite mass, that means it has a finite rest mass energy.
The spectrum of electrons couldn't go all the way up here because you have to create
a
nonzero mass particle in that case. So the spectrum would end some distance below the
full Q-value. And so people have spent enormous amount of time and effort looking for
whether the beta spectrum goes all the way to the Q-value or no. You can imagine a if
trying to measure a very small mass you would be better off doing this in a system where
the Q-value for the beta decay is as low as possible. So the most studied system for do
this work is that of tritium. So the heavy isotope of hydrogen that is unstable is
tritium. It beta decays into helium three plus an electron and electron anti-neutrino.
And the Q-value for beta decay is 18.6 convex it's not the lowest Q-value but it's one of
lowest. People have spent years looking at the spectrum. At this point there is no
definitive evidence for nonzero mass. What's been established as a limit if this particle
does have a mass, it's less than two electron volt. Remember the mass of the electron is
511,000 electron volt. This is a lot smaller than that. But we have reason to suspect
it's not exactly true. And I'll show you that later on.
There's an experiment that is just getting ready to take data over in Germany now.
it's going to study tritium beta decay. The goal of experiment stow decrease the
sensitive here to .2 electron volt. Hopefully over the next few years they'll record data
whether they see a signal or whether we can put a decimal point in front of that.
Neutrinos have other interesting properties. This isn't a class in neutrino physics
but, I'm going to give you this spiel anyway. Neutrinos as I've said carry energy and
momentum and angular momentum. They have intrinsic angular momentum of half h bar.
turns out they have a happened in this associated with it. what I mean by that is if I
look at the particle we call the neutrino, and imagine there's neutrino moving from left
to right, with a linear momentum p indicated by the purple arrow there. then it's
intrinsic spin s would be pointed in the opposite direction. So you can think of it as
a left-handed corkscrew moving like this. As opposed to the anti-neutrino which again
if
moving from left to right, its spin is pointed in the same direction of the momentum, it's
a right handed corkscrew. You'll see in the literature and I think Krane talks about this
something called helicity. It's the measure of the handedness of a particle. It's given
by this expected formula. The dot product of the spin vector and the linear momentum
vector divided by the magnitude of that product. And for neutrinos, this value is either
minus one if it's neutrino and plus one for an anti-neutrino. If it's anti-neutrino, it's
spinning like that, right handed. If it's a neutrino it's spinning left-handed. Turns
out the beta particles also come out with a handedness. They also have intrinsic angular
momentum of a half. If they are produced in beta decay, they will come out with an
intrinsic helicity that's equal to minus velocity divided by speed of light if it's a beta
minus particle or plus v over c if it's a positron. This helicity is feature of
mechanism that produces them. So this isn't intrinsic property of all protons or
positrons but only those produced as a result of beta decay. They come out with a
handedness because of we can interaction that produces them.
STUDENT: Are there examples of particles that have north integer helicities. For
example, s and the linear momentum vector were not necessarily parallel or
anti-parallel.
PROFESSOR: So this statement that they're plus or minus one is is only true for a
massless parliament if the particle is massless. So far we're assuming neutrinos are
massless. The reason these helicities is not plus or minus one is because the electron
and positron have a finite rest mass and therefore velocities can never be exactly c.
STUDENT: Is there a case where the spin vector and linear momentum vector are not
parallel or antiparallel.
PROFESSOR: Well that's what I'm saying, for the electron and positron they're not.
The fact, if they're exactly parallel then these ratios would be plus or minus one.
Here's, they canal be, plus or minus one. That he err they're.
STUDENT: They're always the same value.
PROFESSOR: Well no. Remember the spectrum of electrons you get is a continuous
spectrum from zero up to the endpoint. Therefore, the velocities. Electrons are
different. They're very slow-moving electrons which will have low velocity helicity as
opposed to ones moving faster which will have high value across the beta spectrum. This
thing will change in magnitude. You can define this helicity for any particle. You can
define for a particle that has integer spin like a photon, for example. That's an
interesting question. Pion, and other particles as well.
Okay.
STUDENT: Is there any particle application, helicity.
PROFESSOR: Yes. So when we talk about the details of beta decay, this will play a
role in the relative directions of electron of neutrinossee emitted in the decay. So that
are we haven't discussed whether a beta decay occurs in the sense everywhere the particles
are going. This helicity will force the particles to go offer in the same or opposite
directions preferentially.
They three kind of beta decay, the third is related to the second one the the example
we showed before was that of bismuth 210 beta decay. What's really going on if you look
in detail in beta minus decay is a neutron is neurng a proton. And spinning out an
neutrons for the 83 protons this nucleus has. And so in order to reduce the excess of
neutrons over protons, it can lower the total rest mass energy by converting one of those
neutrons into a proton which stays inside the nucleus. Neglects proton number 83
increases to 84. Now I have polonium 210. In order to conserve energy momentum all the
other good stuff you have to spit out this electron and neutrino. If you have a nucleus
that has too many protons for the number of neutrons, the other kind of beta decay
happens. Namely beta plus decay. The example is of that the sodium 22. It has 11
protons and 11 neutrons. On those those are equal numbers and turns out you can lower
the
energy of system by converting one of these protons into a neutron. And the way that's
accomplished is the proton turns into a neutron plus a positron plus a electron neutrino.
If you go back and look at the masses of particles which is given in the back of
Krane, you'll find this reaction can spontaneously go even for a free neutron. A neutron
is heavier than a proton plus an electron plus a neutrino. On the other hand this
reaction cannot go spontaneously. So if I have a free proton sitting here it can't turn
into a neutron plus positron plus neutrinos because the sum of these masses is greater
than the mass of that. If I embed that in the sodium 22 and look at the rest mass here,
it's greater than the sum, and therefore it will happen.
The third beta decay is related to this one. It's same process except instead of
emitting positron you can take this equation, taking the positron and dragging it over to
the other side of equation and remember you have to change this guy in a electron. You
can rewrite the equation as proton plus electron goes to neutron plus neutrino. And this
is known as electron capture. The idea is, that you don't normally have bare nuclei
sitting around. Usually we have electrically neutral atoms which means sodium 22 would
have a actual complement of bounds atomic electrons around it. From our limited
discussions of quantum mechanics but from your studies of hydrogen atom before you know
that these electrons have a distribution of probabilities to be is somewhere, in fact,
there's a know zero probability the electron will be inside the nucleus. What's it's
inside the nucleus it can be captured by one of protons there. this is a electron capture
decay. And whenever positron decay is possible, electron capture decay will also be
possible the the exercise in the true. There are cases where only electron capture decay
and positron decay cannot happen and we'll see why in a little bit.
Now we're going to talk about the details of energy release in beta decay and how you
calculate it. And the reason this gets a little complicated is the first time we see has
to do with saying before about us normally dealing with neutral atoms. To some extent
you
have it think about what happens to the electrons involved in these beta decay processes.
So let's imagine we have some parent atom, x, z protons and neutrons
spontaneously beta minusing decay into some other atom y. Reduce theing neutron number
by one unit. The proton number by one unit and spitting on a proton and -- for the moment
I'm going to calculate the Q-value for the decay not using atomic masses as I said you
should. Do it using nuclear masses so I don't have to be thinking about the electrons for
a moment. So the Q-value as we always do is look at the sum of masses that we start with,
minus the sum of the masses we end up with and multiply by c≤. Initially the only thing
I've got in this case is the nucleus of species x. (refer to Powerpoint 14). At the
end I've got three things. Species y, the electrons and I've got the neutrino. So
today this arithmetic I have to take the nuclear mass of x minus nuclear mass of y
minus mass of electron created in the beta decay minus the mass of that neutrino and
multiply by c≤. From experiments that have been done apart from that tritium
experiment, but other experiments as well we know the mass of neutrino is not zero,
but
it's less than .055 electron volt over c≤. In everything we're going to do from now on
we're going to neglect mass of the neutrinos. Now I'm going to go back and say I don't
have deal with bare nucleus. I really deal with neutral atoms. What is the mass of a
neutral atom of species x? It's the nuclear mass plus z time the mass of a electron
because in this nucleus I have z protons, so the neutral, I better have z electrons.
Those electrons are bound to the nucleus by the coulomb interaction. If I want to be
careful, and I want to calculate the total atomic mass of species I should be subtracting
away the binding energies of all those electrons. That's what this sum is. Meant to
represent the sum over all z electrons and I sum up all the individual binding energies
of each electron, one s, two s, 2P, are whatever. Similarly for the daughter atom,
the mass of that daughter atom is the mass of nucleus of that atom plus the z plus one
times the mass of electron, because the daughter has z plus one protons in its nucleus.
Again, to be accurate I subtract away the sum of binding energies of all the electrons
in
the daughter atom.
Okay. So now I'm going to go back to the Q-value equation. And write the Q-value
now, now suppressing it as the atomic mass, is expressing, minus z time the mass of
electron, remember this was the nuclear mass I had on previous slide. To get the nuclear
massive it talk the atomic mass minus z time the mass of electron, all times z≤ and
now it's plus the binding energies, minus the mass of the daughter, minus the mass of
z
plus one electrons plus the binding energies, minus the mass of the electron that was
created in the beta decay. So if I rewrite this now and combine everything, the Q-value
for the beta decay is the atomic mass of the parent minus the atomic mass of the daughter
times C≤ plus the difference into binding energies between the parent and daughter atom.
(refer to Powerpoint 15). Normally, the difference of binding energies is very small. A
few electron volt. So typically this difference between the binding energies of the
parent and daughter is neglected. We're going to say that's zero. It isn't quite true
for almost all the case we care about it's close enough. Therefore, after all this spiel,
the Q-value for the beta decay, beta minus decay is simply the difference in atomic masses
between the parent and daughter atoms. Notice there's no electron mass there anymore.
STUDENT: So during the initial, when the beta minus occurs the same emitted electron
goes to the electron shell.
PROFESSOR: Usually is no. So the question is what happens to the electron that
gets emitted in the beta decay, this one. If you think about it, I've get a new
traditional atom initially. All the atomic orbitals are full for that neutral atom. Spit
out a electron and the energy of electrons and beta decay are on the order of 1 million
electron volt. Where typically binding energies are maybe a few thousand electrons.
These electrons very too much energy to be captured. No, almost all the time the
electrons go off into the continuum. No longer associated with the atomic in which the
beta decay happened.
STUDENT: [inaudible] protons into the balanced.
PROFESSOR: Very good. Very good. So what you're saying is correct. That after
this beta decay, if I think of having a neutral atom to start with, and I spit out an
electron, and turned one of neutrons into a proton, what is the electric charge of this
thing left behind now? Plus one. It's got one more proton than it has bounds electrons
much I've created a positive charge ion there initially after the beta decay. Argued
that that electron won't stick to that atom. So at that electron goes off and gets lots
somewhere. What will happen is almost all the time this process is happening inside
some
object, we don't know formally have isolated atoms sitting in free space. This positively
charged ion will finds an electron and grab it and neutralize itself. At the end of day
after beta decay, you'll end one an electrically will I flu traditional object. It's
a
For positron decay, I'm into the going to go through the algebra, you do the
calculation the Q value the same way. Turns out in this case because creating a
positively charged object, the positron, the electron masses don't all cancel outs in the
process. The Q-value for positron emission is the rest, atomic mass of parent minus the
atomic mass of daughter atom, minus twice the mass of the electron all times c≤. That
means is in order for this process it happen, in order to emit a positron the q values
has online banking greater than twice the rest mass energy much electron. For electron
capture decay, a neutral atom is swallowing up a bounds atomic electrons turning into
the
daughter which have z minus one protons in it. If you think of the reaction we're
talking about before with the positron being emitted and rearranging it, the only other
type of particle I'med here is a electron neutrino. And so now, if you think about it
in
terms of the numbers of electron around this, I had z electrons initially in this
neutral atom. Swallowed up one. And end up with z minus one protons if this nucleus
and therefore there should be z minus one electrons orbiting it. Still have a neutral
atom. I don't have a positively our negatively charged ion there. However, again if you
think about it a little more detail, the electrons here are in orbits associated with the
particle z protons in it. all of a sudden one of those prongs disappears. And so the
electrons here in the wrong atomic states for that particular atom. And so they will
rearrange themselves. And so this atom if you like is formed in excited atomic state
even
though electrically neutral. The Q-value for the electron capture decay is then the mass
of parent atom minus mass the daughter atom minus the binding energies of whichever
electron is actually captured. You think think of it in the following way. If I have a
electron bound to some nucleus, effectively its mass is less than the mass of a free
electron. Some of its rest mass energy has been given up in the binding process. The
Q-value is into the as big as if you had a free electron coming N so each atomic orbital
will have a different binding energy. Depending upon which orbital the electron was in
before captured, it will change the binding energy it needs to be put in that formula.
The Q-value for beta decay range from about two keV at the small --.
STUDENT: As far as which electron gets captured there are preferences for different
shells or --
PROFESSOR: Absolutely. So what I was saying before is the reason electron capture
Deaning can happen relies on the electron being inside the nucleus. And the probability
for that depends own which wave function you're talking about. So the most likely shell
if which electron capture will happen is the one s orbital. Because if you calculate
what the distribution of probability is, it's highest for one S. It goes down as you
increase the principle quantum number, two, three, four, two also goes down with the
angular momentum. If you go to, for example, the table of isotopes, big book that has ALT
nuclear properties, in the book it will show you the squares of wave functions of
electrons if every orbital in every known atom you can see if in fact the biggest
probability will be for the one s. If you run into problems associated with electron
capture u the first guess will be it's being captured from the one s orbital. That's
the one will have the highest binding energy. This term will be the most important for
that particular decay. It gets strong when you get up to very heavy nuclei where you
said
before most atomic binding energies are electron volt. If you look at uranium and look at
the one s orbital in uranium, that electron is bounds by almost 100,000 electron
development. If you have low energy beta decay that eliminates the shell you can capture
from. If the binding energy is too great you can't capture and you have to be to the l
oar n. We know how to calculate probabilities because it's basically just atomic
physics. That's why they can tabulate the number very well.
Okay. The q values range from about two keV up to about between MeV. And
typical Q-value \for most\foremost beta decays is about a MeV. You see bra when talking
about alpha decay, there was also range of Q values although much narrower than this.
From alpha decay it went from about if you are to 10 roughly. Here we have of factor
of
10,000 variation in the Q-value. The half-lives also show large range of values. But
again we're talking about larger value of Q values now. the shortest beta decay we know
of
has half-life of 10 milliseconds. The longest is about 10 to the 16th years. An enormous
range. We'll see why you get that range if a little bit.
As I said a minute ago beta plus decay can only happen in the Q-value where the beta
plus decay is greater than the rest mass of electron. In the case of sodium 22 that I
was
talking about, it turns out the difference in rest mass energy between here and here
is
more than twice the electron mass, therefore, it can't happen. But, even if that weren't
the case, if the energy were less than twice the rest mass energy and rest mass couldn't
happen. This could still happen. There's no threshold for that.
An electron capture decay with a radiation is emitted. We already said it. The only
thing that gets emitted is an electron neutrino. And what would be the energy
distribution of those neutrinos? Would it look like a continuous spectrum?
STUDENT: Relatively sharp.
PROFESSOR: It should be a line. One exact energy.
STUDENT: Isn't there energy taken away from the larger mass.
PROFESSOR: Exactly. But -- I didn't say it would be equal to the Q-value I said it
would be a unique energy. If the decay went like in this would be just like alpha decay
of I have a fix energy here and therefore have two particles sharing that fix energy.
They will share the energy but because this particle is so much more massive, this one
will carry away almost all the energy. In fact a electron capture decay you should get
mono energy neutrinos emitted.
Okay. Now one of interesting thing is, the neutrons as I said before, is
energetically allowed to decay in a proton, electron and an anti-neutrino the rest mass
energy here is greater than the sum over there. in fact, a free electron, if you had a
neutron sitting on stable, would beta decay a -- free neutrons are unstable. And yet
we've been talking about nuclei made up of neutrons and talking about stable nuclei.
Why
in the heck do neutrons inside bound nuclei into the beta decay?
STUDENT: Possible they do but the electrons protons pairs up and makes a new neutron
and we can't observe it.
PROFESSOR: So that process has a cross-section which will be calculate. It's small.
It's very unlikely that that's what's going on.
STUDENT: Bounds lost energy.
PROFESSOR: You're right. So are the protons. And the first order they're all
bounds about by about the same amount of energy. This is for a free neutron.
STUDENT: Interact with something before we can observe decaying.
PROFESSOR: No. I just put a neutron on the table and sit back and watch. It will
undergo beta decay. You know I like to watch. That really does happen. People have
observed.
STUDENT: I think that for non, that the reaction associated with the cross-section
of absorption higher than that associated with half-life.
PROFESSOR: Say that again.
STUDENT: Likely to be absorbed by something by the time it decays.
PROFESSOR: It's in a bound nucleus. Say I have carbon 12. You're saying it would
be difficult to have a free neutron. People have built traps where they confine a neutron
neutron in spree separation. That's about the right half-life.
STUDENT: Because the free neutron doesn't experience coulomb potential.
PROFESSOR: It's electrically neutral. It doesn't.
STUDENT: The proton that comes out is being, experience a coulomb potential. So it
would have a negative effect.
PROFESSOR: Into the, nope. Okay. Good. This is good. So here I've got carbon 12.
This is the basis of mass table. It's absolutely stable as far as we know. Has six
proton and six neutrons in it. nothing happen. Sits there forever. Yet if I pulled one
of these neutrons out and put it in the trap so it wouldn't touch nickle it could decay
in
10 minutes. We've actually discussed the reason for it. I'm going to let you think about
it.
STUDENT: No.
PROFESSOR: Then you come up with the an.
STUDENT: Spin parities. Spin and parities, have to be paired up.
PROFESSOR: No they have the same spin and parity, neutron and proton, both a half
plus. It's a tease, I know. Yeah. I'm going to let you think about. It it's
1:00 o'clock. This is a good place to stop. We'll pick up here on Wednesday, either
you're going to tell me the answer or I'll tell you.