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Professor: First of all let me introduce myself. My name is Rick Norman. I have three names
which is first or last names. My birth certificate it says Eric Norman. I prefer Rick but if
you say Norman I?ll answer to that too. I just don?t like hey, you. Other than that,
that?s fine. This is Nuclear Engineering 101. Nuclear reactions and radiation. It meets
Monday, Wednesday, Friday from 12:00 to 1:00 and then as you know on Friday there's an
additional hour from 11:00 to 12:00. Typically what do I is use one of the two hours on Friday
as a problem, slash, discussion section. Since this is the first meeting of the class I'm
going to lecture for two hours today. Although I can't talk for two hours straight and you
probably can't listen for two hours straight so we'll take a break in the middle for about
ten minutes. The textbook is one that I've used before. It's not a perfect textbook but
it is the best one I've been able to find so far that covers the material. It's by Ken
Krane. You see a copy of it sitting here. Hopefully all of you have had a chance to
get a copy. There are issues with it. It's an old book. Its never been updated. Some
of the stuff is out of day. There are actually errors in it, which have never been corrected.
I'll go along and try to point those out and you'll probably discover new ones that I haven't
seen before. There are prerequisites for this course. Hopefully you all have taken Physics
7C. Who hasn't taken Physics 7C? Great. What I will normally do is give a homework assignment
that will be due a week after it's given out. And the TA?s will run the discussion, slash,
problem session where they go over the homework with you before it's due. They will not do
the homework for you. They give you hints and questions but it's up to you to do the
homework. And with regard to that, I certainly encourage collaborative work. If you get into
study groups and work together that's fine. What you put down on your papers and what
you put down on your homework and exams, I expect to represent your own work. If we see
duplicate homework coming in, you're not going to get credit for that. And one thing that
I know is because it's an old book and if it?s been used a lot here at UC Berkeley and
elsewhere, there are copies of the homework solutions out there. I know that. If all you
do is copy of homework solutions you get from somebody else, I guarantee you will not do
well in this class. First of all the homework doesn't count for all that much. But the exams
are based on the kind of problems that are given in the homework. So it's very important
that you understand the material on which the homework is based. And then you?ll do
fine on the exams. Copying from your buddies or from a previous solution set isn't going
to do it. The way the course will be graded is shown here. The homework will be added
up at the end of semester. And in total, it will count for 20 percent of your grade. I
will give two in-class midterms exams, and I'll show you when they?re tentatively scheduled.
Each of them will count 20 percent toward the final grade. There's a final exam, which
will be given at the end of semester. It will count for 40 percent of the grade. The final
exam is scheduled. It has nothing to do with me. The University scheduled it. So that in
principle none of you enrolled in this class could have a conflict in another exam at the
same time. It's the last day of exam week, December 20th, from 11:30 a.m. until 2:30
in the afternoon. The room has not yet been announced but when it is I will certainly
let you know. This is a slightly unusual class in the sense that we have a fair number of
graduate students and undergraduates here. Let?s get a show of hands of how many grad
students there are? Yeah, this is an unusually large number this year. And to be clear the
undergraduates and graduates are not competing against each other. What I say here really
applies to the undergraduates. The class will be graded on a curve. I never can tell how
difficult and easy it is. So I don?t know, is there a question? Sorry. Whatever the numerical
average after totaling up homework, exams, and final, whatever that numerical score happens
to be, it's going to be curved to a B, 3.0 grade. Hopefully it will be a nice symmetric
balance. We'll figure out the other grades. For graduate students, they will be graded
on a separate curve. What else? I will have office hours at tentatively scheduled for
Mondays and Wednesdays. 2:00 to three on Mondays and 11 to 12:00 on Wednesdays. We have three
outstanding graduate student is you. He have inevitably it never quite works this way.
I'll happy to schedule additional office hours that meet with you if your schedule doesn't
allow you to meet during minimal office hours. The lecture will all be placed on bSpace.
I managed to get them up before today's lecture. Hopefully you got an email telling you they
are there. I don't always promise to have them up before class but after class they
will be posted. I'm wearing this mike because the lectures are also being record. My voice
and whatever appears on the screen will be captured via webcast and you will access to
that as well. The homework solutions and exam solutions will be posted on bSpace right after
the material is distributed. Okay. So in terms of schedule, I've tried to lay it out week-by-week
in terms of what I hope to cover. And the reading assignments that go along with that.
I am going is to follow crane although not quite in numerical order in terms of chapters.
I jump around a little bit at the beginning. For various reasons. But then, after about
the third or fourth week it will pretty much be sequential throughout the book. I strongly
encourage you to read the book. A lot of students come in and think by listening to me they
can simply open up the homework assignment and do T it's not true. Read the book. It's
worth doing that before you try doing the homeworks. So this is what we're going to
try to do. And let's see ... I think right. So the first exam is tentatively scheduled
for the sixth week of course. We're on a slightly strange schedule in that we meet today. Then
we have the Labor Day holiday so this is not a full week. This is tentatively when the
first exam will be scheduled. Week of November 4th being the second exam. I tried to space
them equidistant throughout the semester. And inevitably I will get behind schedule.
So the last official week of instruction is the week of December 2nd. And the week of
December 9th is nominally a study week, review. I will use this to catch up a little bit when
I've gotten behind. The last two topics, the applications and accelerates are thing we
will talk about throughout of semester so they are part of the review. What else? Any
questions about logistics or mechanics of the class? Okay. G. What I'm going to do then
is let's see, I think what I will do is start the first lecture then. And at the same time
I'm going to pass out this nuclear wall chart which some of you have probably seen before.
And what I'm going to do is spend today basically talking my way around this chart. And on the
last Dave class I'm going to show it to you again. And hopefully convince you that we've
covered everything on there. You need some more? Who doesn't have one? Day of class.
Everybody have one? Okay. So for so long as there have been people on earth they've tried
it figure out what the earth and the world around them is made of. At various stages
in human his or her people felt they had answers for that. 2000 years ago this was thought
to be the averages. Essentially everything they could observe was thought to be made
up of combinations of four basic elements. They were identified as earth air fire and
water. The idea was if I picked up a rock it was some is combination of these. And if
he looked at a tree it was some other combination. This model stood for a very long time
2 particular things like gold and silver and platinum were recognized early only to be
quite value. People wondering it was possible to transform less available thing into valuable
things using chemical means. The folks who attempted to do this were known as alchemist.
People over, convert lead into gold in this picture. What we know today is that's not
possible by chemical means. What this guy is doing is totally hopeless, he can't possibly
do it. Bit time you're done with this class I hope you'll understand that by nuclear means
we can do it. Lead into gold. You'll convince yourself soon it's a good way to go broke.
You can do it by it's an expensive prong. You can do it one atom at a time and it takes
a lot of atoms to make 1 ounce of goal. In the middle of eight taken hundreds folks began
to do various experiments that identified more complicated structures. The idea you
needed more basic building blocks to explain what was being observed. This is Mr. Mends
leaf who is the father of periodic table we all know and lover. He began to realize not
only were there more elements that were need they have had certain similarities in their
chemical properties. He arranged them in the famous periodic table. There were family of
elements that behaved similarly to one another because of some structure. His table was incomplete
and he unless there was holes in the middle. On the basis of these similarities he was
able --
this is a more or less up-to-date version of periodic table. You've seen versions like
this in classes before. Approximately 92 naturally occurring elements. I say approximately for
reasons we'll go into later. The latest, the simplicity is hydrogen up in the upper left
hand corner. The heaviest of naturally occurring elements is uranium over here. The ones that
have the white lettering, especially here, and here, are all synthetic elements. That
means they don't occur in nature. they're made in the laboratory. Through nuclear means
that we'll talk about. And the reason I'm wearing this funny T-shirt today has to do
with that bottom row on the periodic table because the synthesis of new elements started
right here in Berkeley. By Glenn cyborg and his collaborates. He was a economist in the
chemistry department on campus. He received the Nobel Prize in chemistry on these heavy
elements. What he did was to bombard targets of the element uranium with various particles.
Was able to produce a number of these elements here. And when scientists and engineers find
thing they don't understand they tends to give them funny names. You'll, they weren't
all that imaginative when they first started this process. Uranium being the heaviest naturally
occurring element. When cyborg and company found the next element he thought of solar
system and thought of the planet you're rain I was. He decided to name first element I
don't understand uranium, what's beyond Neptune. He named this plutonium. They ran out of planets
at that point and began to get more imaginative. The element after that is americium after
America. This is sculpture yum after Madam Curie. And this is Berkelium, hence, of T-shirt.
I get upset with people who say Berkelium. This is California I didn't know, (on screen).
Et cetera. Cyborg went onto discover about 10 new elements along with his collaborators.
And the honor that he claimed was the biggest hands-on inner his life was to have a chemical
element named after him before he passed away. So element 106 is seaborgium. He's still the
only person that has that honor. When I taught this class a year ago these were empty boxes
because they had not officially been given name. This is (name) after the city in Germany
where it was discovered. This is Mr. ren kin who we'll talk about later. After exern couples
the next two are interesting. This is Flor oaf yum, name after the director of a laboratory,
and this is livermorium, name after the city of Livermore, it was a collaboration between
the folks of, where these elements were discovered. There's still some that don't have names yet.
And one of questions that we'll talk about in the course of this course is to what extent
we can expand the periodic table? How far can we actually go in making new elements.
There's a limit in how heavy the elements can be? The answer is we dents know. Folks
like you are going to help us figure out how far this can be extends. In addition not just
knowing how many elements there but their chemical properties is of great interest.
In addition to, folks are studying the chemical properties to see where they fit in this periodic
table. A little over 100 years ago people began doing experiments that were revealing
very surprising results. So Mr. Beck rel and Currie were doing experiments with minerals
and discovering that spontaneously these minerals would emit energy and particles. This was
never seen before. Experiments like these formed the basis of nuclear science. The implications
and applications of this really have changed the course of science, medicine and history
as you know and we'll talk about more throughout the class. What they were observing is manifestation
of relativity. We'll make use of this until the course of this class. Not in a terribly
deep level and not general relativity but special relativity. This is our friend Albert
Einstein who wrote down his famous equation that says E=mc2, what that really says is
energy and mass are very intimately related to one another. You can rewrite it and say
that mass is energy divided by c2. I do that to indicate mass can be converted into energy
but energy can also be converted in mass. We'll see had you had a manifest in a little
bit. Although it isn't taught this way when you talk about chemical reactions and look
at exothermic chemical reactions, ones that release energy the mass of the products of
that chemical reaction are actually a little bit less than the mass of things that make
it. That difference in mass has been converted into energy. The reason it isn't talked about
that way is the energy released are so small compared to the mass of particles involved.
An atomic reaction, what I mean by that is in chemistry what you're doing is rearranging
electrons. And typical energies are *** in electron volts. One electron volt is the
kinetic energy a electron achieves by going across a potential difference of 1 volt. And
in unit you might be more familiar with, 1.602 times 10 to the minus 19th jewels that's typical
energy for atomic transitions or reactions. For nuclear physics, nuclear transitions whether
they been reactions or radioactive decays the typical energies are about a million time
bigger. We talked about one MeV, 1 million electron volt. It's 10 to the six times bigger
than the ev, of course. That factor of a million is what makes nuclear physics and nuclear
reactions so important. It's why we can do nuclear power, for example, because instead
of burning tons and tons of coal we burn a gram much uranium and get the same energy.
Not in the same sense. We're not burning coal in a nuclear sense, we're burning in a chemical
sense where when burning uranium we're burping in a nuclear sense. We'll talk about that
later. Before I go further the class is a lot more interesting for you and me if you
interrupt me along the way. If you say something you don't understand or something's confusing
stick your hands up and I'll be happy to answer questions. This is the chart you got in your
hands. This was developed here in Berkeley. With folks from the university, from the laboratories
and from teachers around the country HO helped us volume this. Meant to capture the major
ideas of nuclear science of nuclear engineering on one piece of paper. I'll talk my way around
this. The thing in the middle which looks like the planet Saturn is not meant to be
that. It's supposed to be a description of an atom. In your chemistry classes you might
have seen, solar system. I'm sorry, it's simply not true. There aren't neat orbits that the
electrons are moving around the nuclei. That's because of something called quantum mechanics.
In this chart the way around that was try to depict the center of the atom, the nucleus
here and this fuzzy sphere around it is meant to represent the probability of finding electrons
at various distances from the nucleus. So is the contour highest here and falls of here
3 to an atom of my thumb orbiting around there. Probit is low but not zero. In the at the center the
atom is this thing called the nucleus. So what is an atom? An atom is the smallest element,
smallest that retains the chemical properties of an element. If you take a chunk of iron
and start slicing it smaller and smaller you can get to a point where you have a single
atom of iron sitting there. It will retain the properties of that chemical iron but you
can't slice it anymore. Can't have half an atom. Atoms are small. On the order of 10
to the minus 8 centimeters in size. Given the name angstrom. Although it's very small,
we can't see it P with our eyes we built instruments that can see it for us. Therefore, electron
microscopes on campus and around the world that image individual atoms now. It's not
a theory. There are actually individual atoms. We can manipulate them. You might have seen
an image from 20 years ago where folks from certain companies spelled IBM. The atom itself
is in a simple object. It's made up of smaller objects. Have electrons that occupy the most
volume of the atom. In a neutral atom, an electric click neutral system where same name
of positive and negative types exist, in a knew tram atom there are z electrons. Each
electron has negative one unit of charge. We measure units of charged electron. The
electron has a rest mass energy which means if I holds it in my hands or put on a balance
I can weigh T and I'm going to start off write away making use of Einstein's equation e equals
mucks c2 and write down masses, the mass of a electron is the .511 million electron developments.
To be correct I'll divide by c2 so in order to get the energy I have to multiply by the
mass. But very often I'll be sloppy in the way I speak and say the mass of a electron
is .511 MeV and hopefully you'll understood what is meant by that. In addition to having
a trick charge in mass the electron and all the particle we're going to talk about have
another intrinsic property seven we call it spin. It has the units of angular momentum.
This little s is the intrinsic angular momentum of an electron when sitting at relevant this
is a quantum effect we're going to struggle with throughout the semester. I guarantee
you. These are objects that are so small we can't see them. And they have a lot of properties,
which are very difficult for us to understand because we live in a macroscopic world, which
is governed largely by classical physics. When you get down to the realm of electrons
and nuclei breaks down and quantum mechanics applies. One of properties of these particles
is they have this intrinsic angular momentum even when at rest. I don't really know how
to understand this terribly well and none of us really do. The way I think of it and
most nuclear scientists and engineers think of it is they're little balls. And somehow
they're spinning. And that's where this angular momentum comes, for example, turns out the
model has, that I designed has to be wrong because if put in the number for how big a
electron might be, what mass in angular momentum is, it would have to be spinning fast are
than the speed of light. But that's not right. But something like that. So they have angular
momentum. If I look more carefully inside the atom I notice way down in the center there's
a much smaller object. That we call the nucleus. It?s about 10 to the minus 13 semesters in
size. That's given a name a femtometer or Fermi named after him. One of great nuclear
scientists from the 20th century. This is future orders of magnitude smaller than the
atom. And when you write it down like that it's hard it get your head around what that
really means. So the analogy I like to use is if you imagine taking an atom and blowing
up to the size of AT&T Park, the atom is that pick how big do you think the nutrition will
be in comparison?
STUDENT: Mosquito.
PROFESSOR: That's about right. That's just about right. I mean the size of a mosquito
buzzing around home play. That's the five orders of magnitude difference between the
atom and nucleus. you might think the nucleus is so small, who cares, what can it possibly
matter? It matters a lot until the sense it contains more than 99.9% mass of the atom.
It's also not a fundamental object. If we look closely and go back to this little image,
the reason there are different colored balls slowing here is the nucleus is maids up of
two type of particles. Known as neutrons and proton. In a neutral atom as I said before
there will be the same number of positive elec charges as negative. If there's z electrons
in the neutral atom there will be z protons in the nucleus so the opposite charges cancel
out and the atom is linear equivalent circuit trick will I neutral. Also some number of
neutrons. Call that number n. And neutrons and protons can be isolated from atomic nuclei
and their masses and property can be determined. We find a proton has plus one unit of electric
charge. Mass in these energy equivalent units is 9:30 8.28 MeV over d half bar is Planck's
constant divided by two pi. The neutron is electrically neutral. Has no electric charge.
Mass is a little bigger than the proton. Also has half unit of angular momentum. You know
that the opposite electric charge of electron and proton are what hold the atom together.
The electric stack charge that holds the electron to the atom and make it stable. Something
else has to be going on in the nucleus because the proton has positive electric charge. Those
protons are going to be repelling one another because all positively charged the. On the
other hand the neutron has no electric charge so it's not a magnetic interaction which is
holding the nucleus together. It's a different force entirely. We call it the strong nuclear
force which holds neutrons and protons together inside the nucleus. The nuclear force is complicated
and unusual in the sense we call it the strong force because it's much stronger than the
electric market force or gravitational force that you're familiar with. You can sort of
understand already it has to be stronger than the electromagnetic force because the protons
all have positive charges. , They?re preliminary hearing each other and yet held inside the
nucleus. On the other hand the nuclear force is different from either gravity or electromagnetism
in the sense both of those forces with infinity range. You know the force from two-point charges
goes as 1/R2. Gravitational force between two masses goes like 1/R2 which, means out
to infinity separation there's electromarket or gravitational force. Nuclear force is really
strong but also very short range. Turns out the range of nuclear force is smaller than
the size of typical atomic nucleus. While it's strong because it's short range, can't
influence thing at large distances. We'll see how that manifest itself in a little bit.
We denote atomic nuclei by this norm clay, which you are. X is the chemical symbol of
if it's hydrogen, h. Uranium it's u and so on. Z is the number of protons in the nucleus.
N is the number of neutrons and a is the sum of z and n. Typically since A equals Z plus
n we won't necessarily write down all three of them. You might see us say something like
uranium 238. The ideas being you have access to a periodic table. If it's the isotope 238
you can say it has 238 minus neutrons, 146. Neutrons and protons themselves are not fundamental.
And that's also indicated back in this drawing because here's, plus one are the neutrons,
inside the neutron you see three other walls. Inside the protons there will be three similar
walls much they're not really walls but this is the best we can do to depict this. Inside
each neutron and each proton there are smaller units. And these things that are indicated
in red are known as quarks. This is another example people giving funny name to things
they don't understand. In the 1950s people were trying it figure out what are the fundamental
building blocks of universe. And first it was the four elements. That seemed okay. Then
got up to 92 elements. That seems like a lot. Then there were back to three particles. Neutron
proton and electron. That seems doable. Then people started building accelerators. Smashing
thing together and they discovered hundred and hundreds of
4 proton and their cousins that we'll talk about are maids Intellectual property of economics
off quarks. Some. Each has thrive these objects in it turns out there are six different types
of quarks. They have different properties. The name, which is given to this property,
is another funny name. Called flavor. Doesn't mean it tastes different but they're distinguishable
from one another. By the way each quark in addition to coming in six flavors comes in
three different colors. Doesn't mean red, green, and blue, but there's some other quantum
number that distinguishes them from one another. In addition each quark has an anti-quark associated
with it now you have 50 or 60 particles. Again people are thinking that's way too many for
that to be the ultimate building block of universe. You probably heard of things called
string theory. People think make the quarks are made up of little pieces of vibrating
string. Who knows? We don't know what the ultimate building block is yet. Are there
things inside the quarks in maybe? Are there mosh times of quarks than the six we know
about? Maybe. Lots of interesting questions. I mentioned we have gravity. Electromagnetism.
Microscopic stores we're used to. I mentioned the strong nuclear force. A turn out there?s
a fourth force known as the weak force, which is obviously weaker than the strong force.
Weaker than electromagnetism but stronger than gravity. Responsibility for type of radioactive
decay. Called beta decay. It's just about noon. And this is a perfect place to ache
a little break and we'll start talking about radio decay and I'll do a demo for you. I'll
give you a homework assignment during the break. One of the things we look to do is
get a little better feel for the preparation of class before we delve into the heart of
the matter. This is a questionnaire I'll ask each of you to fill out. You can put your
name on it if you want. You don't have to. The point is to get a feel for what background
you have already. This is not going to affect your grade in any way. Help my lecture go
better. If you'd like to use the restroom facility, get a drink of water. We'll break
for about 10 minutes and start again at 12:10. Did everybody have a chance to sign the sheet?
I'll leave it up solar energy.
Is that too dark? Okay. So that's a good example of pilot romantic I looked at my watch wrong.
I thought it have noon but it was early. Hopefully everybody's back and we'll start again. What
I want to talk about now is radioactive decay. This was discovered about 100 years ago. This
gentleman shown here Ernest Rutherford did a lot to clarify what was going on in radioactive
decay. By doing a number of clever and simple experiments and again, another illustration
of giving funny name to things you don't understand he found three basic kinds of radioactive
decay. The first one he discovered he decided to name after the alphabet. Called it alpha.
The second beta, and the third gamma. He doesn't understand what these were at first. By doing
experiments very much like the ones I'm going to show here he figured it out. And in the
chart and on the screen here, are illustrations of three radioactive decays. The first being
an alpha decay. The example there is the did he ray of radioactive decay. Seaborgium. After,
has 16 protons in its nucleus. That's what makes it seaborgium. This particular isotope
has a totals atomic mass of 263. Which means it has 263 minus 106, which if I can do the
math in his heads is 167 neutrons in its nucleotides. Turns out 106 protons are too many for any
nucleus. All those protons are repelling each other because of positive electrocharge they
have. And the nucleus would like to get rid of that electrocharge it reduce the energy.
The way it does it to emitted two protons and turns out two neutrons bounds together
in what we call the alpha particle. Helium four is the nucleus of helium four atom. Two
protons and two neutrons bound together. That gets spat off by the seaborgium. Turns out
different chemical L. By reduce the proton number by two units we change from element
10 computer integrated manufacturing to element 104. That's rutherfordium. Nature by itself
does what the alchemists were trying to do. Turns one chemical into another not through
chemical means by but nuclear means. That is alpha decay. Another reactive decay shown
is beta did he came there are two versions of beta decay shown here. This is a decay
that has, when nucleus has either too many neutrons for the number of protons or vice-versa.
The example of the first beta decay which is beta minus decay is that of a very famous
isotope called carbon-14 that we'll talk about later. Carbon has six protons in its nucleus.
That's what makes it carbon. This particular nucleus has eight neutrons so its atomic mass
is 14. That's too many neutrons for six protons. And so the way it tries to reach a lower energy
state is to convert one of those neutrons in a proton. Remember the neutron is electrical
new radical. The protons is positively charged the as far as we can tell is absolutely conserved
in any nuclear process we know about means whatever value at the beginning of process
will be the same at the end is a electrocharges. Sincism six positive units of I better ebdz.
I just said I converted neutron in a proton. So I end up with nucleus that has seven protons
in it. That's neither nitrogen. One chemical has turned into another. But I have one extra
positive charge, to balance itch it emit negatively charged particle which is the electron. In
order to conserve other quantum numbers that we care about, namely angular momentum, energy,
linear momentum... The other beta decay shown here is an example of where you have too many
protons for the number of neutrons and the nucleus would like to reduce number of positive
charges. The way it does that is convert a proton in a new electron. And here the isotope
that is shown is fluorine 18, nine protons and nine neutrons in nucleus. One convert
no a new electron. Fluorine become oxygen. In order to balance electrocharges again a
positively charged object has to be emitted this time, that's a beta plus particle. This
is the anti-particle of the electron. We call it positron. It has essentially the same properties
as the electron except instead of having one unit of negative electrocharge it has one
positive units of electrocharge. There was to be another neutrino emitted in that process
as with. Their decay is known as gamma decay. The being example here is a nucleus called
dysprosium 152. It's represented by something had a look like a football. This arrow indicates
it's rotating rapidly. Again in most of textbooks you'll see picture of nuclei being shown as
spheres. Most nuclei in lowest energy states or grounds states are spherical or nearly
spherical. If you make them rotate rapidly and we'll talk about how to do that later
on, you can distort the nucleus. In fact, you can make it look like a football. The
way these nuclei slow down rotation and return from this football shape to more spherical
shape is emit the third radiation that we call gamma decay. Gamma raise are font, the
same particle had a allow us to see one another. In typical nuclear transitions the energy
of the gamma rays are such that the wavelengths of the photon are so short that we can't see
them. They carry average energy and momentum and angular momentum, but they have no charge
and no mass. So it emits photons, gamma rays but remains being dysprosium 152. How did
he tell there are three different kind of radioactive decay? You can't see these things.
That's one of problems with nuclear radiation. You can see fell smell or taste it. If you
can, you're in deep trouble. In a normal situations that we deal with in the laboratory or in
any other kind of environment. Even a nuclear power plant you can't sense this radiation.
We have to build devices that can sense it for us. Although
5 that's filled with gas. There?s a thin window here that Laos the radiation to enter. There's
a screen over it to prevent idiots from sticking finger through the window. Inside there's
a wire that has high voltage on T the kind of radiation we're talking about here is known
as ionizing radiation. What that means is it has sufficient north it rip electron off
neutrality, let's say the way is at high positive potential, negatively charges electrons will
be attracted there, positively charged ions will drift to the walls. I end up with current
pulse that comes out of this every time ionizing radiation is registered there. If I turn this
on, and I'll turn this so you can see this, okay. So you'll hear a little chirp every
once in a while. You'll see the needle move. I don't have any radio sources around it but
I will bring some in a minute. The chirping is indicative of what weigh call natural background.
We live in a world made up of the 92 elements I talked about. Some of them are intrinsically
radioactive. There are alpha beta and gamma rooms in this room now that are coming out
of the walls and floor because of material the building is made of. Some of them are
inside our body as well from the food we eat. When this device is picking up now is the
natural background radiation. Later on I will bring a more sensitive detector and see what
isotopes are present in this room now and it will surprise you a little bit. So that
device, actually why don't I come over here. Move over here. And do a little demo. Okay.
So there's the Geiger counter. Itch sources that put out one type of radiation. Either
alpha beta or gamma. What Rutherford showed was that you can distinguish them from one
another essentially by seeing how much material it takes it stop them. And so let's start
first with the alpha particle. This is the source of one of those synthetic elements
I talked B this turns out to beamericium 241. Which I'm sure you have in your home believe
it or not. It's in the smoke detectors in your home. We'll talk about how they work
later on. So the americium 241 is there. I'll bring the Geiger counter over to. Hopefully
you can see the needle moving and chirping. Something is coming out of there. I claim
it's the system of two protons and two neutrons bounds together. Turns out the energy of alpha
particles are a few million electron volt. That's the typical scale of decays. The alpha
particle is heavy because it's got two proton and two neutrons bound together and two units
of positive electrocharge associated with it. Turns out it doesn't take much material
to stop T this is just an ordinary piece of paper. It's counting quickly. I'll put the
piece of paper there. Now bring it over. It essentially stops. Doesn't totally because
of that room background much but if I move the paper, so an alpha particle is really
stopped by very little material which is a very good thing because your skin is thick
enough to stop almost all alpha particles financial you're in a environment where there's
an alpha emitted it's not going to be a problem. Your skin will stop it. Potential danger of
something like that is if you manage to get it inside you. If you ate something contaminated
with it. Then it can get in direct contact with your organs the next one are betas. The example here is
an isotope called strontium 90. Turns out to be a major fission product at that we'll
talk about later in the semester. It's inside that little disk. Bring it over here. It's
more active than the alpha source. This thing is counting a lot faster. I'll put the paper
offer testimony maybe it's counting a little slower but certainly hasn't stopped. I'll
take the plastic that's good a quarter of an ink thick. Put it over the source. That
stops it. This is a typical beta. The energies are a couple MeV. But because they're much
lighter in mass than the alpha particle and have only one unit of electrocharge, it takes
more material to stop them. But quarter inch plastic is snuff to stop most beta particles.
If worker will use a shield that is what is tick or glass, something transparent they
can see there but that thickness is enough to shield them from the beta particles. The
third is gamma rays. This is cobalt 60. This is a synthetic isotope use if had in a lot
of medical treatment. No photons. No mass, no electrocharge. The Geiger counts see them.
They go through the paper like it's not there. They can through the plastic like it's not
there. And this is a piece of lead that's a quarter of an inch thick. I'll put that
on there. Again it counts a little slower but certainly doesn't stop. In fact, you need
three or 4 inches of lead to a ton wait these gamma rays and then it probably wouldn't go
to zero. In tether of properties of these Asian simply by looking at how much material
it takes to stop them you can figure out what they are the gamma rays are harist to stop.
It takes a lot of material to prevent them from getting into our bodies. Once in there
they can penetrate our bodies deeply and do harm. Distance from a source helps because
the radiation falls off like a lot of r and maximize amount of time mere the radioactive
materialism these are extremely weak radioactive sources. You're not in danger. Never do anything
that would cause exposure to you. These are safe. If you, you'll get to play around with
these things a lot. Any questions about that? Okay. So much for show and tell for today.
I'll try to bring in more demos as we go through the semester. The trouble is it is pretty
far removed from everyday experiences. So we have to use devices like that to see this
stuff. That's what Mr. Rutherford did. This is a class in nuclear radiation and reactions.
And so the two major classes of reactions that we're going talk about are shown here.
They're on your chart. I'm sure you know they're known as function and fission. The example
shown here first is fusion. The idea is fusion is you take light nuclei bring them together.
Get the nuclei together so the strong nuclear force with overcome the reaction. And fuse
the nuclei together and make something heavier. The example shown here is reaction that take
place in the hydrogen bomb. And we were attempting to do with national emission facility at Lawrence
Livermore National Lab. Fusion of two elements, this is deuterium. One proton and one neutron
in its nucleus. That are bound together by the nuclear force. About one atom in 10,000
of all hydrogen that you find on earth is deuterium. The other 9,999 are a single proton
with no neutrons in the nucleus. We just call that hydrogen. The other isotope is tritium.
One proton and two neutrons bound together. It's radioactive. Half life of about 12 years.
This has to be made somehow. If you bring the two together they will fuse into a composite
system of helium four known as two protons and two neutrons bound together. That's the
alpha particle. And all nuclear reactions all we're doing are rearranging the neutrons
and protons. Not creating new ones or destroying them. If you notice here, the number of protons
on the left-hand side of the equation, one plus one equals two, and the number of neutrons
on the left-hand side of the equation, one plus two equals three is balanced. So all
we're doing is rearranging they will. Turns out energy is released in that process, we'll
see that in a bit. Okay. This always happens. Despite the fact that the catalog says at
that there's an additional hour on Friday somehow everyone doesn't find this out. For
those of you just coming in, there are two hours on for example everything I've said
so far is online already and we'll see it on the webcast. I would like to make sure
you all get a handout, questionnaire and syllabus before you leave. So that's fusion. Taking
light nuclei, bring and together and make heavier nuclei out of them. Energy can be
released in that process in certain circumstances although not all. Fusion. Nuclear fission
is the opposite process. Start with heavy nuclei. The example here is the one we use
today in micro power plants. They produce northing, it's the fission, splitting apart
of heavy nuclear. In this case U235. The way we make it
6 neutral can sneak up on the nucleus. There's no are pulling between the nucleus and electron.
If they get close -- they make a composite system which would be uranium 236. Turns out
it would be in a very highly excited state which decays most the time by splitting apart
in the process we call fission. What can be produced are known as fission fragments or
fission products. There are hundreds of different ways this split can happen. This is one example
of that. So in this drawing, the U236 composite system has split apart in zone on 134 and
strontium 100. Notice I had 92 protons here. I have 54 plus 38, which adds up to 902. I
conserved the number of protons in the process. But I had 144 neutrons to start with and only
have eight plus 62, 142 neutrons so far. That means two extra neutrons have to be emitted.
This is a very important process that I get two free neutrons in addition to the fission
fragments. What that allows is a chain reaction to happen. What I mean is you start out with
fission here. I get fission fragments and energy. I get extra neutrons, which can capture
on different uranium nucleus and initiate another fission. That's the basis of nuclear
power plants. It's also the basis of chain reaction in nuclear weapons. Fusion can produce
energy and fission can produce the energy. You can I'm saying you can take heavy ones,
split them apart and get energy out. Seems like you can make a loop and make perpetual
motion machine out of this. Believe me you can't do that.
STUDENT: What kinds of factors determine what exactly happens in the split.
PROFESSOR: You mean like in the fission reaction.
STUDENT: Yeah.
PROFESSOR: That's a really good question. There are lots of factors, which go into it.
Some have to do with the energies. Descending upon the particular fragments that come out
there will be a different amount of energy releases. It also has to do with details of
nuclear engineer instrument states with the particular nuclei and particular momentum.
It's a complicated process and we can't predict it well. We don't have a theory that allow
us to, we can measure it experimentally and see there's a broad distribution of fission
fragments which was a maximum at certain mass and z numbers. But predicted from first principles,
we can't do that yellow light. Fission is a very complicated process. Even the fusion
process is complicated in the stents this particular reaction, tritium and deuterium
coming together. There are two reactions that can happen. Either this one or similar reaction
where a proton comes out. Usually in fusion reactions there are fewer possible outcomes.
It's easier to predict. But again, these reactions are governed by quantum mechanics. We can't
predict with certainty the outcome of any one reaction. All we can predict are probability
distributions for certain outcomes. That's also true in reactive decay as we'll see in
a lot of reactive decays there are lots of ways the system will end up. We can only tell
ahead of time which are more likely to occur based on similar considerations, energy, momentum,
things like that. There are lots of different ways neutrons and protons would be arranged.
We've talked about the periodic table. Which is the chart of the elements. There's a similar
chart of what we call the nuclides. All the different atomic nuclei in terms of number
of neutrons and protons. It's arranged here. There's one of these on the wall outside my
office if you came upstairs. On the vertical axis is number of protons in the nucleus.
The horizontal is the number of neutrons. Each of these boxes represents one particular
nucleus. One particular isotope. The ones in Black are the stable ones. The ones that
occur in nature. The different colored ones are all radioactive and decay in different
ways depending on where they were relative to the stable nuclei. We'll find out the neutrons
and protons inside the nucleus are not sitting at rest. They're moving in complicated ways
needed nucleus. Just like in atomic physics you learned about atomic shells, shells of
electrons and how had you have closed shells those elements are especially chemically inert.
Noble gases in particular. Week going to see in nuclear physics the shells that the neutrons
and protons are in. When we have a closed or fills shelve neutrons or protons they're
particularly stable in the nuclear sense. Turns out the numbers, which close the shells,
are a little bit different than those you find in atomic physics. Two, eight, 20, 28,
50, 82, and 126. We'll spend a fair bit of time talk about that later on. Nuclear physics
obviously is important here on earth. We use in generating energy. We use it in medicine.
We have all kind of applications of T it's been important in the entire history of our
universe, that's what this part of chart is meant to indicate. Our universe we believe
began about 15 billion years ago in an event we call the Big ***. Incredibly high teams
and density were produced there for a short period of time. The universe expands and cooled.
During this hot dense period we believe every particle that ever was or will be was created.
And those particles, if they were radioactive decayed ultimately producing the particles
we see today. Some point the universe got cool enough that the quark created in the
Big *** got together. They formed neutrons and protons. As the universities cooled the
neutrons and protons got together and began making chemical elements. Eventually the neutrons
and protons and chemical elements got together under force the gravity. They form stars.
Turns out the reason the stars shine are nucleus fusion. They're producing energy threw nuclear
reactions. Along the way they produce all the chemical elements we know and love. Nuclear
physics has played role in the entire history of our universe in this day. These aren't
just theories anymore. We have done enough experiments that we know they're facts. These
on the bottom are meant to represent the facilities that we're using today to study various aspects
of nuclear and particle physics of you may have heard of something called the relativistic
collider. High energy machine, which are used to probe what's going on night neutrons and
protons and trying to look at the quarks themselves. There's a facility another as the Jefferson
laboratory, studying the distributions of quarks inside the neutrons and protons. Is
to study the nuclear reactions happening today in stars we use low energy accelerators like
the ones up at the launch Berkeley lab and Lawrence Livermore lab. In the future use
is one being billed at Michigan State University to be able to do similar experiments on radioactive
nuclei. This is not just a theory. Nuclei in many ways behave like charged liquid drops.
You know that water is a neutral is liquid. At least at room temperature. If I heat it
up I can make water boil and turn it into a gas. If I cool it down I can freeze and
make into ice. Similar happened at the nuclear level. Nuclei we talk about in the laboratory
we can think of being at the absolute zero of temperature. We can heat them up either
lie radioactive decays or nuclear reactions. If we get them hot enough them boil particles
off. That's what this drawing is trying to indicate here. And this drawing is trying
it indicate normal nuclei are over here. If I heat them up we can get them to boil often
neutrons and protons. If I heat up enough we can dissolve the neutrons and protons and
produce free quarks. We think that happened in the early universe during the Big ***.
Goes from phase tricks from liquid to gases to plasmas. This isn't a theory. We use accelerators
to study these phenomenon for us. And so at the relativistic hev yon collider at the Brookhaven
collider on Long Island. They accelerate nuclei of gold to something like 2 billion electron
development per atomic mass units. Two hundred GE v times 197 that's the mass of gold knew
close. They have colliding beams. They have one going in one direction and another in
other direction. They bring together and let them hit head on. That makes gold, gold, if
I have two protons, I have 158 positively charged object there. They build detectors
to 7 actually happened. You have 158 charged
particles it start W my friends who do this for a living will tell me in that image there
are 10,000 charged particles. They weren't there before the collision. They are created
as a result of the collision. And that's an example of E equals mc squared. The energy
the collision went into creating these 10,000 particles. In addition there are another 10,000
neutral ones that you don't see in that image. By studying that you can phylogenetic out
what was going on. What they believed happened they dissolved the nuclei and dissolved the
neutrons and protons. For a very tiny period of time made this thing called the quark gluon
plasma. Hold the quarks knew the ?
STUDENT: How much, Big *** is less dense neutron.
PROFESSOR: Less dense?
STUDENT: Because the x-axis on the bottom left figure ?
PROFESSOR: Right. So, yeah. I won take that too literally. You're right. At some point
the density had to be much higher. The density of neutron star is, you're right. It, that's
a good point. I'll have to talk to my friends who did that. The Big *** is tricky because
it's not a static thing. It's evolving in time. What you really think of as starting
out up here and coming down in this direction as the universe is expanding and cooling.
Could be they picked a particular instant in time to though that meaning. I mentioned
that we have extended periodic take through nuclear reactions making heavier elements.
The facility is up at the Lawrence Berkeley lab. Others around the world. This meaning
on your chart was made a number of years ago, when the heaviest element was 112. We're now
up to 118. We use nuclear reactions to fuse together lighter systems to make something
heavier. All of these heavy elements are radioactive. The way they're identified is by looking at
the chain of decays. Mostly alpha decay. Almost 112 emits alpha and turns into 110 which turns
into 106 and 106. By piecing to go chains we can figure out what the parent was. We
don't know where the ends of periodic take is yet. I mentioned that nuclear reaction
it's what's fueling the stars, the way they produce energy is nuclear fusion. This was
a theory vend in the 1930. Wasn't until fairly recently that we did development experiments
that allow us to prove this was happening. The trouble is we can't look into the center
the sun with our eyes. If you go outside like today you can measure how much energy is coming
from the sun. About a kilowatt per square meter. But the photon coming from the surface
have lost any memory of how they were actually created. What we believe and know is actually
going on in the sun is this process of fusing hydrogen together to make helium. Later we'll
go through the details of how this work. By four protons fuse together to make one helium
four nucleus. Notice I have four positive charges but only two here. I have to spit
out two positively charged particles of those are positive electrons. Turns out again, I
need it spit out other particles, Newton owes. They can come right out of the center the
sun as if the sun were not there. If you can build a detector that can actually detect
neutrinos I can look in the center of sun and see what's happening there. An experiment
was done up in Canada a number of years ago. Called the Sudbury neutrino observatory. This
is 40 feet in diameter stilled with a special water known as heavy water which was properties
for, was able to measure the energy and the number of neutrinos coming from the sun and
tell they came from the direction of sun. Confirm this is the correct idea for what's
happening in the stars. We also learned some interesting things about knew taken owes that
we deny foe before, they're more, they have maxes as indicated particles have different
flavors. I acid six different quarks. What this experiment showed is neutrinos change
flavors in the eight minutes it takes to get from the center the sun to the earth. We'll
talk more about that later. And finally, so this is a nuclear engineering class. We'll
spend time talking about the application. You know that radioactive decays and nuclear
reactions are used in medicine and biology. We use them a lot to generate power on earth.
Both from fission today and hopefully fusion in the future. They're used to study properties
of materialism they have space applications that you may know about. Certainly environmental
issues associated with them. Art and archaeology is thing you don't normally think of in physics.
We'll talk about throughout the class. Okay. So I managed to get through lecture one. Any
questions about that? Okay. And since we do have two hours today I'll go on and see how
far I can get on this. Let me jump to the ends in case I don't get there because I want
to make sure I indicate there's a homework assignment. Normally I'll try to give the
homework assignments on Monday and they'll be due the following Monday. But because woe
meet here today and Monday's a holiday we're off kilter already. I'll give you this assignment
today. It will be due a week from this coming Monday. Next Friday there will be a problem/discussion
section where the GSIs ask could go over this with you. This is the length of homework assignment.
Typically six problems. Again that's all posted. So one of the things we want to know is what
are the elements, the isotopes that we have access to here on earth. So if you go and
dig up dirt out of the ground or took a look at rocks and analyze them, via chemical means
you can figure out how much of all the different chemical elements we have on earth. They're
arranged in this chart. This is the abundance by the number of atom of a particularly chemical
element relative to silicon. Things are normalized here. On this chart silicon ask a million
and everything is relative to that. You can see silicon is a quite a bit chemical element
and being plot as atomic number. So the number of protons in the nucleus. Oxygen is more
abundant than silicon. You can see there's structure in this. It's not random. There
are peaks and valleys in these abundances. There's a trends that generally the lighter
elements are more abundant than the heavy elements but there's a lot of structure in
there. That structure is reflective the nuclear properties. Notice on earth its silicon being
magnesium, oxygen, aluminum, iron, calcium; those are thing that the rocks and dirt are
made of. Relatively rarer are things like hydrogen; notice helium isn't even on the
map here. I bring that up because we'll see a contrast to that in a minute. This is what
the crust of the earth is made of. We can look more broadly that's just what's available
on earth by look at the stars. And believe it or not you can figure out the elemental
composition of stars easily. It's based on something I think you know already. If you
look at light and accepted it through a prism, imagine I have a light bulb and take the white
light and accepted through a prism we break it up into the all the colors of spectrum.
On the other hand if I have a gas, a hot gas of some particular chemical element, so let's
say it's hydrogen, for example, I take the light from that and sends through a prism
I don't get a continuous spectrum anymore. I get discrete colors, discrete lines dollar
emitted at particular wavelengths or frequencies for that particular chemical element. If I
have a source the white light and sends through a gas that happens to be cold, those chemical
elements in the cold gas will absorb light but only at the frequencies or wave length
appropriate for those particular elements. I can get either emission or absorption line
spectra to identify what the elements are in the hot or cold gas. These are examples
spectra. This is hydrogen at 30,000 degrees helium at 20,000 degrees and so on. You can
see the lines, which are distinct for each chemical element. And so if I go outside on
a nice dark night and look up, this is the kind of thing I see. These are stars. And
I can take the light from one particular star, and sends it through a prism or the equivalent
of a prism and 8 stuff in between. But I can look at the
stuff sitting on the surface. I discover something different from the distribution of elements
in our IVS as opposed to what's on earth. What I find is that set five% of all the mass
in the universe that we can see is in the form of the lightest chemical element, hydrogen.
23% is helium. An element we don't even find on earth. In fact, helium was discovered in
the sun before it was discovered on earth. That's why it's called helium. Helios, the
sun. 2% is everyone else. Which doesn't sound like much. Ninety-eight percent is hydrogen
and helium, two% is everything else, except that's us. We're in that 2%. So the. So it's
almost everything we care about. Talk about where at that 2% came from. And much answer
is it's by nuclear reactions from stars. It's a fact. It's remarkable thing when you think
about it. The atom in your body was at one point inside a star. It's true. If you look
in more detail about this elemental distribution of things in or flax I and in the solar system
as a whole you make a similar chart. This is now logarithm of abundance *** function
of z. This looks different from the chart for the earth because now hydrogen is the
most abundant thing. Most of the hydrogen in or solar system is sitting in the sun.
The next most abundant element is helium. Again element all of that in the sun. There's
a very small amount of next elements in the periodic table. Boron, there's a set of peaks,
carbon, neither, oxygen, Nye on, turns out those are all multiple alpha particles bound
together. You can think of carbon as three alpha particle stuck together. Oxygen is for
and so on. We'll see why there might be extra amounts of these things. Again reflective
of their nuclear properties. There's a drop again as you go up toward mass 50. There's
a peak around maximization 60. That's not an accident. Reflective of nuclear engineer
properties. Then fall off as you go heavier in mass. There are these two peak around,
around mass 130 and 140. Another two peaks around mass 195 and 208. Those are reactions
of details of nuclear structure that we'll talk B. If you want to figure out if detail
how much each chemical element is there and how much of each isotope there is we need
it straight thing according to mass. We do at that using a mass spectrometer shown here.
In all of these devices what I start out with is neutral matter. Take some material, which
is electrically neutral. Let's say I remove an electron from the species and make a positively
charged ion that has one positive charge on it. I send through some accelerating voltage.
It's moving in this direction. It's a positively charged ion. Micro iron, uranium, whatever,
I send into object that I call a velocity accelerator. This is a region where both electro
and magnetic field. The electrofield is pointing up in this direction. And the market I can
field is meant to be coming out of the board at you. The head of arrow is coming at you.
This is a positive electrocharge. If I think about what's going to happen, hopefully you
know from your E and m classes if I have a charged object and it's in an electrofield
there will be an electroforce on it. That force is a vector, it was a direction and
magnitude. The direction will be in the direction of electrofield for a positive electrocharge
and opposite if it's negative. I claim this is a positive charge. The force will be in
the direction of electrofield. And there will be a magnetic force because this particle
is moving. And willing are the magnetic force is more complicated. Given by the charge which
is positive times the cross product, the vector product of the velocity and magnet featured
this positive charge is going to be pushed in this direction because the electrofield.
It will move that way. There's also a magnetic field. I used right-hand rule it figure out
which direction the magnetic force will be. Velocity is pointing this way and magnetic
field is coming out the bored. Right-hand rule says occurring, my thumb point down indicating
that's the direction the market force. They're in opposite -- for a particular velocity they
can cancel out. If the velocity equals e over b these two forces are equal if magnitude
and opposite in direction and they cancel out. That's what's known as velocity filter.
I end up with particle that emerge from this all with the same velocity. Those that have
either too high or too low will get bent and runs into the walls. Only those are the right
velocity come out. Those, just to confuse you the way the magnetic field is drawn here
it's going into the board. Now there's a magnetic force qv cross v that's going into the board.
It's going to tend to bend particles in this direction. In the region of constant magnetic
field the particles will move many circular orbit given by this equation. This is the
centrifical force of the particle, mv over r, this is the mark force producing that effect,
qvb. You can solve this equation and finds the radius of curvature is going to equal
the mass of the particle times e divided by qb. e and b are fixed by my m. q is one positive
units of charge. That means the radius of curvature is directly portional to the mass.
The lighter the particle, the tighter the orbit, the heavier the -- if I have a detector,
that can measure the number of particles as a function of position here, meaning as a
function of radius I can figure out the masses of the particles. This is how people figure
out the isotopic distribution of one particular chemical element. So, for example, this was
worked on here at the you can Berkeley campus by John Reynold in the physics department.
He was interested in measuring the isotopic abundance of xenon that was trained inside
a meteorite. The noble gases tend to come up. Sent through a device like the one I just
showed you, this is the discretion of xenon isotopes he found. Mass is increasing from
right left here. Each one of these peaks corresponds to a particular mass of a xenon isotopes.
These lines indicating here are the abundances you find on earth. If you find terrestrial
xenon which turns out to be rare but not zero abundance in the earth's atmosphere and measure
the relatively abundance of them you find of horizontal line shown here. For almost
all the isotopes in this meteorite, they were very similar to what you find in the atmosphere
of earth, except for this one, mass 129, it showed more abundance of that isotope than
neighboring ones which Reynolds termed the radioactive decay of iodine 129. Turns into
xenon 129 for radioactive decay. This is the lower left hand corner of that chart. So what's
being plotted here on the nuclear chart as opposed to the periodic table is the proton
number going vertically and the neutron number going horizontally. Over here, is hydrogen.
Hydrogen one has a single proton in its nucleus. That's right here. And it has 99.985% of all
hydrogen is that one isotope. It was a half up the of floor momentum as indicated before.
Right next to it is deuterium. One proton and one neutron bounds together. It's rare
but not zero abundance and earth. Point one five percent. These numbers are all in percent.
The fact it's color-coded in black means it's stable. The neutron is shown over here. No
electrocharge. One unit of mass. One-half unit of floor momentum. Notice it's not black.
The neutron is actually radioactive. If you have a fry neutron sitting here it will undergo
beta decay in its half life is about 10 minutes. One of questions I'll ask later on is, if
a new electron is itself radioactive, if I stick it in something like deuterium, that's
stable. It's not a trivial question. With the hydrogen I go here it tritium. The 12
year half life is radioactive. It's not shown in black. It's shown two greenish color. Will
beta did he say into stable mass helium three. there are other isotopes which are also radioactive
having more neutrons in them. I go to helium. Almost all the helium is the alpha particle,
two protons and two neutrons bound together. There's, I can keep going up the chart here.
The point is there are stable nuclei that will tends to have roughly equal numbers of
neutrons and protons although as we go higher up in the chart you'll see there's a tendency
to have a few more neutrons and than 9 have too many protons for the number of neutrons. This will undergo
beta plus decay or similar decay we'll talk about later called troth capture decay. Moving
up further, so up around mass 40 or so, continuing on the chart of nuclides you can see it fills
out. Each chemical element has a lot of different isotopes. Usually only a few that are stable
and many more that are radioactive. I pick out here, potassium, it's an interesting one
because it contains an example of naturally occurring radioactive nuclei I messengered
earlier. Potassium 40 is a rare but naturally occurring radio isotope. It's a little hard
to read, 016% of that potassium. Is. On this chart its inconsistent, shown in black but
has a half life. It's half life is comparable to the age of earth is it's still present
own earth. One point two seven billion years. The earth is about four and a half billion
years old. Although there haven't been any nuclear reactions to speak on happening on
earth since it was form. Some of it has survived the four and a half billion years and it's
still present today. When you eat bananas, as I go further here's calcium. Calcium is
interesting, it has a lot of stable isotopes for reasons we'll talk about later. Having
to do with those closed shells of neutrons and protons. Remember I mentioned 20 and 28
were magic numbers. This is '20s and 20, this is doubly magic. This is 20 and 28, this is
also doubly magic. There are lots of other stable isotopes as well. Again beta minus
decay is here. Beta plus and capture decay is here. These numbers here, these have to
do with the spins and par dies as we'll discuss of the particular nuclei when in ground states.
That has to do with neutrons and protons and how they're aligned. Thus far we discovered
roughly 3000 different isotopes. They're shown in this chart. Indicating the stable ones
in black or at least the long lived naturally occurring ones in black. These are coded by
half lives. Beta minus decay is here. Beta plus decay is here. The half lives range from
10 to the minus 20 seconds up to billions and billions of years. We'll see why we have
that range as we go on. Okay. Where do we get these energies? Either from radioactive
decays or nuclear reactions. It all goes back to e equals m V. The idea is if you look at
any particular nucleus or better yet, any particular neutral atom, and look at the mass
of the particles that went into creating that, and compare it to the mass of final system
you'll fine they're not equal to one another. And this is expressed in what we called the
binding energy. If I go over here, capital m of z and a is meant it represent the mass
of a new traditional study. That has z proton in its nucleus and hence, z electrons in neutral
atom and atomic mass a. I have a neutral atom, say U2 35, for example, I've got 92 protons
in the knew calculus, that's what makes it you young yum. Because it's -- the way I calculate
this mass is I say, I take z which, in this example is 92, times the mass of a neutral
hydrogen atom. Not the mass of a problem the reason I do that may seem odd but it's a way
that I don't have to keep track of electrons. Because it turns out in all the nuclear reactions
we talk about and all the radioactive decays, thing will have the same electrocharge at
the beginning and ends. If I'm thinking of neutral atom, I start with a knew tram atom,
and I will ends up with a new traditional atom. I absorb them into this. I take z time
the mass of a neutral hydrogen atom. In this case 92 time the mass of a -- I what I finds is, the sum these is greater
than the mass of system I ends up with. The amount by which it's greater is what we call
the binding energy. The binding energy in this calculation is defined as positive number.
The higher the binding energy, the smaller the mass of the final atom is compared to
the mass of what went into making T the typical binding energy we talk about it in atomic
systems are ev. Whereas in nuclear system they're millions of electrons volt. In nuclear
physics we'll use atomic mass units to measure the masses of atomic nuclei or atoms. The
convention is one atomic mass unit is usually written one u. It's defined to be 112 and
the mass of a new traditional carbon 12 atom. If I measure what that is experimentally and
convert into energy units one atomic mass unit is 9031.502 MeV (on screen). If I measure
this binding energy for different nuclei and blot it I get this chart. This is a plot of
what we call the average binding energy I calculate what the mass of z times that mass
of a hydrogen atom plus n time the mass of neutron and deduce what the binding energy
is, in this plot I divide that by a. The total number of neutrons and protons in that system.
I calculate what's called the average binding energy better nucleon. Neutrons and protons
are known as nucleons. I plot this as the number of nucleons in the nucleus and I get
this funny curve which start out here. Here's hydrogen, hydrogen one. It's got one proton
and no neutrons. By definition the binding synergy has to be zero this point at zero,
zero. Whether I add a new electron to it and make deuterium, had a system is is bound.
We'll see it's bounds by 2.2 million electron volt. If I divide by two because a is two
I DGAT1 .1 million electron development as the average binding energy 40 deuterium. As
I add prongs and neutrons binding energy goes up for awhile. Notice there's a new peak at
helium four and then it drops. Continuous to go up. Reaches a maximum around mass 60.
And then gradually falls. This is the famous you nuclear binding energy \can you be\cub.
This is why I can get energy both from fission and fusion. I was talking deutero, moving
my way up the binding energy curve. On the other hand when talk about fission, I was
starting here with U2 35 and splitting it apart and moving that way. That also produces
energy. Because there's a peak monotonic middle you can see the issue. I can't do this in
a circular way. I can fuse for awhile but I reach a maximum here and as I try it fuse
heavier nuclei together I fall down that way. That costs me energy. Similarly if I fission
uranium and come back leer it costs me energy it try it fuse it together. You either make
money down here do you go fusion or make money up here doing fission but you can have it
both ways. We quantify this, one is in terms of mass, another thing is called mass defect:
It's another waiver writing down masses. If you don't want to do it you don't have to.
The important thing is to be able to calculate how much energy is released to make a nuclear
reaction happen. This is measured in when we call a Q value. This is similar 20 chemistry
where you calculated energy releases in exothermic reaction or. Species a+b combine and make
system c plus d. The q value is defined to be the sum of the masses of reactants, a and
b minus masses of the products. Again just to keep life simple always do these calculations
in terms of masses of neutral atoms. If this number turns out to be positive it's an exothermic
reaction, releases energy, meaning mass of racketer ant is greater than mass products.
If you look necessity back of crane a book he shows masses for many atomic nuclei. You'll
need to make use of them in some of the homework problems. Get used finding nuke data on websites.
There's a place called the isotopes project at Lawrence Berkeley lab up the hill. Accumulates
and evaluates this data free of cost on the Internet. That's their URL. Other data tables
are masses of all the known nuclei. This is the mass in atomic mass units for deuterium. An atom of deutero
roughly this is the mass and atomic mass you want for an atom of tritium. I abstract the
mass of atom of helium four and mass of a neutron. I find this reaction has a positive
q value. Meaning it produces energy. Seventeen point five eight million electrons development
every time one of those reactions occurs. If I look at the fission reaction that was
on the chart, you can 235 plus neutron making xenon 134 plus strontium 100 and two neutrons,
looking up these masses, this is 10 I
end up with positive q value again, energy is released, 181.2 MeV every time I get a
fission to happen. On the other hand to try 20 show that not all reactions have positive
q values here trying to fuse together iron and iron. Take two iron nuclei and fuse together.
Look up the masses of irons and mass of flower yum, do the mathematic. I find this is negative.
Meek it will not happen unless I supply at least that much energy. That's a reflection
of this binding energy curve. I'm starting with nuclei in this case at the top of binding
energy curve and trying it move in that direction. I can make that happen but I have to provide
that extra energy which in this case turns out to be 43.911 MeV. So some reactions will
produce energy, will some will require energy. Same will radioactive decay. If it's spontaneous
energy is going to be released. Q value will be positive. You have to calculate the q value.
If it's positive it will happen at some level. Maybe not very fast but it will happen. If
it's negative it won't occur unless someone provides the energy.
STUDENT: In the final reaction you omit any energy carried away by gamma. Presumably it's
Less than (ï) 43.911. Any reason you leave two out.
PROFESSOR: In fact that's a good question. Nervous system I haven't considered the kinetic
energy of any of particle here. The only thing I entered are the rest masses. Here the rest
mass of photon is zero so that's why it didn't appear. You can ask where does this energy
get. I get 17 and a half out of this reaction. It appears in the kinetic energy of the final
products. So even if I can do it these reactions at rest imagine I can somehow bring the deuterium
and tritium at rest. The helium four, they have to move. They carry away that much energy.
Similarly with the fission, they're going to fly apart and share this much energy. In
this particular case there's no energy releases. I would have to provide it.
STUDENT: In the bottom reaction is there [inaudible]
PROFESSOR: In this reaction occurred yes. In all of these cases we're going to spend
time talk about the mechanism by this which these reactions happens. These are examples
of compounds nuclear reaction, where the nuclei fuse together. There's an intermediate state
where they, in this case the tellurium, unless I provide at least this much energy I don't
have enough to make a tellurium nucleus. That's this negative sign. If I provided that much
energy I would produce the tellurium in its grounds state. As I provide more energetic
make higher and hyperbola state of tellurium nuclear. We do it. We got through the lecture.
Let me point out there are other textbooks on nuclear, you don't like crane. It's the
best one I found. I put three different textbooks on reserve in the nuclear engineering library.
They all cover the same material but using different language and examples. If you don't
like crane look at these. They're all excellent books. Finally just reminds you of the homework
assignment. This is the first one on chapter three having to do with nuclear binding energy
calculating q values. Due a week from Monday. Remember Monday is Labor Day. We wouldn't
have class. We will have class next Wednesday and Friday. Use the second hour next Friday
as probable/discussion section where questions about the homework will be entertained. Okay.
So for the surveys, please just put them on the table here as you leave. If you haven't
picked one up, please pick up one and fill it out. If you haven't had a chance to sign-in
... I will see you Wednesday. Have a nice holiday.