All right. What we are going to do today
is I am going to start talking about the development of atomic
theory. So in the next few minutes,
I am going to wiz through the observations that led to the
belief that atoms were the most basic constituent of matter.
And then, what we are going to see is that the atom can
actually be split up, that the atom is not the most
basic constituent of matter, that there is at least an
electron and a nucleus. And we are going to start
talking about what are the fundamental principles that have
to obtain in order for that electron and nucleus to hang
together to remain an entity. And what we are going to see is
that we are going to have to understand a new kind of
mechanics to understand how that electron and nucleus hang
together. And then, further on in the
course, we are going to see we are going to need that new kind
of mechanics to also understand how two atoms hang together,
how two atoms bind to form a molecule.
All right. But today, I will lecture for
the first two-thirds or three-quarters of the course,
and then I will stop, --
-- and then I will introduce the rest of our teaching team.
And we will talk about the mechanics of the course.
We will talk about the expectations of the course and
some details like that. Okay, so let's get going,
here. And now we could turn the
lights down because I am going to use the slide here in the
front. All right.
The ancient Greek philosophers. They certainly were known to
have pondered whether matter can be divided endlessly into
smaller and smaller pieces or whether there was a point at
which you couldn't divide matter any further.
And Aristotle, here, well, he was one of the
philosophers who argued that matter could be divided into
smaller and smaller particles, chopped up into smaller and
smaller pieces, ad infinitum,
matter was divisible. This is called the Continuum
Theory of Matter. Continuum because you don't
have any discrete points. It is a continuum.
No boundaries. But there was a contrary
philosophy, heralded by Democritus, who actually was
about a hundred years older than Aristotle.
And he held that matter indeed was composed of individual,
discrete particles. These discrete particles he
called "atomos." "A" for not, "tomos" for divisible.
That is the origin of our word, of course, atoms.
Now, in the fourth, fifth century B.C.,
there wasn't much evidence one way or the other for either one
of these philosophies. And I call it a philosophy
because it was a search for understanding reality by a
speculative, as opposed to an investigational or
observational, means.
But for whatever reason, it was Aristotle,
here; his continuum theory of matter prevailed all the way to
the 17th century. And here, in fact,
he is depicted by Raphael on a fresco on the walls of the
Vatican, holding court, the continuum theory of matter.
But just about at the same time at which Raphael painted this
picture, there were observations.
A set of observations that were being made that began to point
out that matter wasn't really behaving and reacting like a
continuum, that matter was behaving more like it had some
discrete nature to it. What were those observations?
Well, one of them was by this gentleman here,
Robert Boyle. And guess what his formal
occupation was. Chemistry?
That's a good guess, but his formal occupation was a
theologian, as most scientists were at that time.
And you, of course, know him for the empirical
observation that the pressure times the volume is constant as
long as the temperature is constant.
But he actually advanced one of the first ideas of an element.
And that is, he called an element a certain
primitive unmingled body. And that somehow you can take
these primitive unmingled bodies and put them together to form a
perfectly mixed body, a compound, a molecule.
So this was one of the first ideas of elements that come
together to form molecules. And then there was this
gentleman, Joseph Priestly. Guess what his occupation was?
He was a priest, of course.
And what did he do? Well, he looked at reactions
with dephlogisticated air, dephlogisticated air reacting
with materials. And what he observed was that
these materials reacted more vigorously in dephlogisticated
air. Well, what is dephlogisticated
air? Well, of course,
now we know dephlogisticated air is oxygen.
It is air with the nitrogen predominantly removed.
But it really took this gentleman, Lavoisier,
to really understand what Priestly was doing in his
experiments. And what Lavoisier realized is
that this dephlogistic air was kind of adding to the material
when it did this reaction. And he made those observations,
or he came to those conclusions, by doing some very
careful measurements of the mass before the reaction,
so the mass of the dephlogistic air plus the mass of the
material. And he found that indeed,
the mass after the reaction was equivalent to that before the
reaction. And so he was one of the first
individuals to realize that a chemical reaction can be written
down analogous to writing an algebraic equation.
Well, Lavoisier also did a lot of work with isolating elements.
He identified 17 metals and nine nonmetals as elements.
Well, for all of his efforts, we all know what happened to
Lavoisier. Because of his connection to
the French monarchy, the judge at his trial claimed
that the republic has no use for savants.
Lagrange at that time, a French mathematician,
said, "It took but a moment to cut through that head,
but it will require a hundred years to produce another like
it." Well, there was another Frenchman at that time,
J. L.
Proust. He was a little more
politically savvy. He high-tailed it over to Spain
and led a long and healthful life as a professor in Madrid.
But what he did was he did some experiments.
And he observed that when two or more elements combine,
well, they combine to form a compound, they always combine in
definite proportions by weight, and it didn't matter what the
method of preparation was. And because he made this
observation over and over again with many different elements,
this became known as the Law of Definite Proportion.
Again, some indication that matter had a discrete nature to
it, and it wasn't just the continuum.
Some numbers were involved here.
But it really took this guy, John Dalton,
English schoolteacher with a lot of interests.
He was aware of the observations of Boyle and
Priestly and Lavoisier and Proust.
And what he realized was that he could begin to understand all
of those observations if he went back all the way to Democritus
and Democritus' idea of atomos or atoms, these individual
discrete particles of matter. And so he set forth some
postulates, some postulates which of course now are known as
Dalton's Atomic Theory. But what he said was that each
element is composed of atoms. He said that atoms of any given
element are identical. He said that compounds form
when atoms are more than one element combined.
And he realized, of course from Lavoisier's
observations, that atoms are neither created
nor are they destroyed. Now, just an aside,
John Dalton, with his breadth of interest,
he also was the first individual to document color
blindness in human beings. And, in fact,
we do call color blindness Daltonism.
See, we are getting you ready for medical school already.
But what I want you to recognize here is that Mr.
Dalton didn't actually do any of the experiments himself.
Although, from what I know of him, I think he could have done
the experiments himself, but rather he was aware of the
seemingly disparate observations made by Lavoisier and Boyle and
Proust. And he just said,
well, you know, if I take those observations
and I use this framework, well, then I can understand
them. They make sense within this
framework. And this is a powerful approach
in science. A lot of science progresses
this way. That is that there is this
collection of seemingly disparate observations,
and then all of a sudden somebody comes along and sees an
organizing principle in all of those observations and puts
forth then these postulates. That is what Dalton did here.
Now, of course, these postulates weren't
accepted immediately. And rightfully so,
because they were just postulates, they needed further
substantiation. And that further substantiation
came in terms of the work by this gentleman,
Joseph Gay-Lussac, the Law of Combining Volumes.
It came by the work of this gentleman.
This gentleman is Lorenzo Romano Amadeo Carlo Avogadro's
hypothesis. And, of course,
you can all read Italian, so you can read what is on the
stamp here, right? It just says equal volumes of
gas under the same conditions of temperature lead to the same
number of molecules. See, you didn't know you could
read Italian, but there it is.
And further substantiation for this idea of an atom and the
discreteness of matter came from this gentleman Ludwig Boltzmann.
Gas Kinetic Theory. He proposed that well,
you know, pressure, that must be due to these atoms
that are moving around and hitting the walls of a vessel,
those impacts give rise to the pressure that is exerted on the
walls of that vessel. And then, finally,
it took this gentleman Cannizaro, and it took his
statesmanship. Because what Cannizaro did,
and now this is the later 1800s or so, what Cannizaro did was
that he got the scientific establishment at that time.
And the scientific establishment at that time,
of course, was this small group of pale males.
But he got them to listen to Dalton's Atomic Theory and then
the ensuing experiments of Avogadro and Gay-Lussac,
etc. And, finally,
he got them to say, yes, there is something right
about this atomic theory of matter, the idea that mass was
made up of discrete particles called atomos or atoms.
Well, nowadays we of course can actually image individual atoms
or molecules. And what you see here is an
array of 28 CO molecules. And these 28 CO molecules are
arranged in the form of a little man or a little woman,
I will let you figure it out, but these are CO molecules
sitting on a platinum surface. And so each one of these orange
balls here is a CO molecule, but when CO binds to a platinum
surface, it does so with the carbon end down and the oxygen
end up. And there is a really good
reason for why that is the case, and we will talk about that
when we talk about molecular orbitals.
What you are seeing here is really just the tops of the CO
molecules. You are seeing the oxygen end
of the CO molecule. All right.
Well, this image here was taken by something called a scanning
tunneling microscope. And, I am sorry to say,
but this was actually invented just before you were born.
And it was invented, it was actually worked on by
Ruska, and then perfected by Binnig and Rohrer,
and they won a Nobel Prize for their work.
And the way the technique works is the following.
Let me have the board lights here.
I am going to do some board work.
What you do to do this is that you take a tungsten wire,
and you do a little chemistry. You etch the tungsten wire down
to as fine a tip as you can. You put it in some potassium
hydroxide, you send some current through it, do a little
electrochemistry, and what you will get then is a
pretty fine tip at the end of this tungsten wire.
But then, what you do is you take that tungsten wire and you
attach it to a piezoelectric crystal.
A piezoelectric crystal, and let me put it this way
here, a piezoelectric material is some material that if you put
a voltage across it, it expands a little bit,
a little bit meaning ten, 20 angstroms.
And so now, if you attach the tungsten wire to that material,
you have some control on the angstrom scale.
So, that is what happens in order to move that tip around.
But then what you do is you take this tip and you bring it,
say, within five angstroms of the top of this CO molecule.
If I have my platinum surface here and my carbon here and here
is my oxygen, what I am going to do is I am
going to bring this tip, say, within five angstroms here
of this oxygen and of the CO molecule.
And then I am going to put a negative voltage on this
tungsten tip here. And I am going to take the CO
molecule, I am going to take the platinum surface and I am going
to grind it. Now, in this tungsten tip there
are, of course, electrons.
And, since this is a metal, metal has a characteristic
where some of those electrons are not strongly bound to the
nucleus. They actually roam around the
solid. And this is a high energy
state. Given that electrons are
negatively charged, and they are in an environment
of this negative potential, that is a rather high energy
state for those electrons. So if I were to draw an energy
level diagram here, this is energy,
and I am going to represent those electrons on the tungsten
tip, it is going to be at a sum high energy level.
This is electrons on the tungsten.
However, there are also some electrons down here,
and they are at ground potential.
These electrons are at a lower energy, so I am going to draw an
energy level representing them. This is the electrons on the
platinum. And so this coordinate,
here, is kind of like a distance.
So this is the electrons on the tungsten, over here are the
electrons on the platinum. And what these electrons on the
tungsten tip would like to do is to be here on the platinum
because that is a lower energy state, but the problem is that
there is a gap right here. There is no material between
the tip and the oxygen end of the CO molecule.
If you do it in a vacuum, there is a vacuum here,
there is a vacuum gap. And so for the electrons to go
from here to here, well, there is a very large
barrier. This is a very high energy
state if an electron were in between this gap here.
I am going to represent that energy change as the electrons
go from the tungsten tip to the platinum surface as a barrier
like this, a very large barrier. Now, you have seen these kinds
of, we call them reaction coordinates, in chemistry in
high school. That is, you have seen
situations where we might have, if we are doing an energy level
diagram, this is the energy of the reactants out here.
This is the energy of the products.
And in between there is this activation energy barrier that
we call E(act). In other words,
you have to put energy into the system.
In order to get the reaction to go, you have to put energy into
the system before you get any energy back out.
And that is what happens in a chemical reaction,
we put energy into the system before we make it go or can make
it go. But in this particular case,
the electrons, they don't behave like most
reactants. The electrons right here,
you know what they do? These electrons,
they go right through that barrier.
They don't care that there is a brick wall there.
They just go right through the barrier.
We call that tunneling. And how in the world can that
happen? Well, that can happen because
electrons, unlike most atoms and molecules over here,
are quantum mechanical particles.
And they do not obey classical mechanical rules.
And that is a subject that we are going to start talking about
today and tomorrow and for the next few days.
These electrons, they just tunnel right through
that barrier and get over here to the other side.
That means, in this experimental setup,
if I were to connect a wire from this tungsten tip here to
the platinum, and I put in an ammeter right
there, so I measure the current, I would be seeing some current
flow, some measure of this flow of electrons from the tip to the
tungsten. And so that is what is done in
the technique. But, now, how do you get this
image that I showed you earlier from this kind of arrangement?
Well, what you do is you now take this tungsten tip and you
mount it on a piezoelectric crystal.
I forgot to tell you sometimes piezoelectric crystal,
quartz is a piezoelectric, barium titanate is a
piezoelectric. But you mount it on a
piezoelectric crystal that will allow you to move from side to
side. I move now my tungsten tip over
a little bit. And I know exactly how much
over I moved it because I have calibrated my piezoelectric
crystal. But now what do you see?
Well, if you just moved it over, you didn't change the
vertical distance, if you just moved it over,
what do you think would happen to the current here?
Decrease. It would absolutely decrease.
Why? Because you now have changed
the distance between the oxygen end and that tungsten tip.
Over here, on this diagram, you made this barrier thicker.
And the thicker you make it, the more difficult it is for
those electrons to get through, so the current is going to go
down. In order to bring the current
back up, what you are going to do is you are going to take that
tungsten tip and you are going to move it down slightly so that
the distance now, between the tip and the oxygen,
is going to be the same as it was in this particular position
from here to here. So, then you bring the current
back up. But, again, you know exactly
how far down you moved that tip and how far over you moved that
tip. You have got now two points.
Now we have got to keep going. What are we going to do to
scan? Well, we're going to move this
tungsten tip over again. And, again, the current in this
particular case is going to go down.
In order to bring it back up, you are going to move this tip
further down so that the distance between here and here
is the same as it was originally.
So, reestablish the current. But, again, you know exactly
how far down and how far over you moved the tip.
And then what you do, you assign a different color to
the different distances above the CO molecule.
And, if you assign different colors, you can get this image.
For example, if we can dim the lights on the
blackboard again, we will look at the slide.
If the tip is very far from the surface, we would give it kind
of a whitish color. And as it gets closer and
closer to the surface, we give it a darker and darker
orangey color. And then finally,
when it is so far down that it is actually in contact or
tunneling to the platinum, we give it a blue color.
So, that is how you get this image.
That is the basis of this technique.
Now you also notice that these CO molecules have a peculiar
arrangement. And this is not due to,
in the most au courant language, intelligent design.
Rather this is due to a very patient experimentalist,
i.e. graduate student,
who spent 24 hours putting these CO molecules into this
particular position. How did he do that?
Well, he did it in the following way.
He first took a few CO molecules and put them anywhere
on the surface, just to expose the surface to
some gas, and then he imaged the surface to figure out where they
were. And so if these CO molecules --
My soccer balls are the CO molecules.
And if my foot here is the tungsten tip.
You just imaged the surface to figure out where they were,
because we knew where they were.
Then he has got to move these CO molecules.
He brings the tip close to one of the CO molecules.
And then, if you put a voltage pulse on that piezoelectric and
actually jerk the tip, you can jerk it such that you
hit the CO molecule and it goes flying away.
That is nice, but now where did it go?
Well, in order to find out you have to image the whole surface
again. And you would find that it is
somewhere all the way over here. Now you really want it over
there, so you repeat the operation.
Well, 24 hours later you get this little man.
[LAUGHTER] And I know it was 24 hours later.
It is going to be a while before this kind of
nanotechnology, assembling a molecule by a
molecule, beats the synthesis in a beaker to put the molecules
where you want them. But, even though this kind of
visual observation of atoms and molecules really was impossible
a hundred years ago, the evidence that I alluded to
or quickly went through earlier was really quite compelling for
the existence of atoms. And the observation or the
belief that the atom was the most basic constituent of
matter, the elementary particle. You couldn't have anything
smaller than an atom. And, in fact,
at the end of the last century, it was generally believed that
the theoretical structure of the universe was complete.
Nature was understood. There were no more discoveries
to be made. And, after all,
there were, by this time in the late 1800s, a lot of advances.
Well, Newtonian mechanics, that had already been known for
250 years, mechanics that guides the motion of all bodies around
us, even astronomical bodies. Thermodynamics was completely
developed. Statistical mechanics was
developed, statistical mechanics, which relates the
microscopic description of the behavior of matter to the
macroscopic description of the behavior of matter.
And also there were these optics experiments of Young,
Freznel and Hertz that seemed to put to rest the question of
whether or not light was a particle or a wave.
Boy, those experiments seem to be absolutely conclusive that
light was a wave. Those experiments demonstrated
Maxwell's equations, Maxwell's equations that
unified the field of optics and electromagnetism.
So by this time there were all of these accomplishments.
The idea was that everything was done, and the idea was
remaining, that the work that remained was largely to
investigate the next decimal place.
Everything else was done. However, at the same time,
by the late 1800s, there began to be two sets of
observations, two tracks of observations that
if you look closely, began to illustrate that maybe
things weren't quite so clear. Maybe things were quite as well
understood. And what were those
observations? Well, one of those observations
is the discovery, that we are going to start
looking at today, that the atom is not the most
basic constituent of matter, that you can take an atom apart
into an electron and a nucleus, at least an electron and a
nucleus. So, that is one track.
The other track is that light appeared to behave in some cases
like a particle and not a wave. And one of those cases is this
observation here of the photoelectric effect.
So, what we're going to do is look at both tracks of
observations here. And we are going to see how
these observations made it such that it was impossible to
explain how an atom held together, how an electron and a
nucleus held together within the classical way of thinking,
within the Newtonian mechanics, the mechanics that you are
going to be looking at this semester in 8.01.
You cannot use that mechanics to understand how this electron
and the nucleus stay together. You cannot use that mechanics
to understand how two atoms are bound together.
We need a new way of thinking. And it is these two tracks of
observations that led to the discovery, in a sense,
of this new kind of mechanics that we are going to be talking
about. Okay, so let's start on one of
these tracks. And that track of seeing that
the atom is not the most basic constituent to matter.
And the first observation was done by this gentleman,
J. J.
Thomas. It was the discovery of the
electron. Okay, so I am going to need the
lights on again.
All right. What J.J.
Thomas was interested in doing was understanding what deep
discharges were made of, so he had a glass tube that was
evacuated. And in it he had what we're
going to call here a cathode. And he had an anode.
And, as I said, a glass tube pumps out the air
and then he fills it up with hydrogen, H two.
And what he does is he puts a large negative potential on this
cathode. And on the anode,
he puts a large positive potential, and he cranks up the
potential difference here. And he keeps cranking it up,
until at some point the gas begins to glow.
And it is at that point that this discharge here is ignited.
And this is a kind of plasma. And he wanted to understand
what is in this plasma. He was just curious.
He wanted to know. And so what he does is that he
pokes a hole here in this anode. There's a hole.
And he lets out a little of this discharge.
And he lets it out. And my chalk is breaking.
He lets it out. And way back here he has some
kind of a screen, a phosphor screen so that not
only does this discharge here kind of glow as it's moving
along, but when it hits the phosphor screen,
it lights up. And so that's nice.
But then, what he does is he takes two parallel plates and
puts them above and below this luminous beam,
and there is a positive charge on one of these and a negative
charge on the other. And lo and behold,
when he increases this potential difference,
this delta V, what happens is that this
luminous beam, some of that luminous beam is
actually deflected a little bit. And so now there is another
very bright spot. And he can measure this
deflection. And we are going to call it
delta X. Now, since some of this
luminous beam was deflected toward a positively charged
plate, what kind of particles did he decide were in this
luminous beam? Negative particles,
because they're attracted to the positively charged plate.
So, he called this deflection delta X.
We will call it delta X sub minus.
Now, he knew enough about electromagnetism at that time to
realize that the amount of that deflection has to be directly
proportional to how much charge was on the negatively charged
particle. And I am going to call that e
sub minus. Because the more charge,
the easier it would be to deflect it.
And he recognized that the amount of deflection has to be
inversely proportional to the mass of that negatively charged
particle. Because after all,
the more massive that was, the more difficult it was going
to be to deflect it. And then what he did is he
cranked up delta V as much as he could.
And here I am taking a little liberty with the story.
I'm telling essentially the essence of the experiment,
but it is a little more complicated than what it is I am
going to tell you right here. But he cranked that up.
And when he did, he realized that there actually
were some other particles that were being deflected toward the
negatively charged plate just a little bit.
All right? Not a lot.
Just a little bit. And, again, he could measure
that deflection. And he called that,
or we are going to call that, delta X sub plus.
These have got to be positively
charged particles because they are attracted to the negatively
charged plate. And again, he realized that
delta X sub plus is proportional to the charge on
that positively charged particle and inversely proportional to
the mass of that positively charged particle.
All right. But now, here comes his
thinking. What he guessed is that these
positively charged particles were H plus,
a hydrogen ion. How did he know that?
Well, this was a guess. However, he did know that in
this plasma, this discharge, that there were hydrogen atoms.
And how he knew, that is something we're going
to talk about in a few days. But he knew that.
He also knew H here, these hydrogen atoms that are
produced in the plasma, somehow the plasma breaks the H
two bond, these hydrogen atoms were
neutral. And so he said,
well, if it's a positively charged particle,
well, gee, it must be that something was removed from the
hydrogen atom to make it positively charged.
And that something must be this negatively charged particle that
I'm observing, because I knew that originally
the hydrogen atom has to be neutral.
So therefore, I am going to guess that the
magnitude of the charge on the negatively charged particle is
equal to the magnitude of the charge on that positively
charged particle. And if that it is the case,
then I can take a ratio here of the deflection of the negatively
charged particle to the deflection on the positively
charged particle. And since these two are equal,
I am guessing that, since these two are equal,
then this ratio has to just be equal to the mass of that
positively charged hydrogen atom to the mass of that negatively
charged particle. All right?
And now here is the important point.
The important point is that no matter how he made these
measurements, no matter how he did that,
the deflection for that negatively charged particle was
much, much, much larger than the deflection for that positively
charged particle. That then meant that the mass
of this positively charged particle, which he guessed to be
a hydrogen atom, must be much,
much larger than the mass of the negatively charged particle.
He also knew at that time that a hydrogen atom was the least
massive atom, but here is an experiment that
showed that there was a particle that was less massive than a
hydrogen atom. Hey.
But up until then, it was the atom is the most
basic constituent of matter. You cannot chop it up anymore.
But here was the evidence that there was a particle less
massive than the hydrogen atom. Eventually it is called an
electron. But this is the first evidence
here that the atom wasn't the most basic constituent of
matter. Now, it actually took another
ten years with the Millikan oil drop experiment to actually
measure this ratio correctly and to determine the mass of the
electron. We won't go into that.
But this ratio here, you probably all know,
the mass of the electron is about 836 times that of the mass
of the hydrogen atom or hydrogen ion.