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PROFESSOR: So, our first
question here is about
limiting reactants.
So, that's something you will
encounter in your review
reading for the sections, that
kind of review -- what we hope
you have picked up from high
school or will pick up quickly
by doing some review.
So, how about we have everyone
take ten more seconds on the
clicker question, get your
final answer in here.
All right.
So, let's see what we have.
All right, so it looks like
we weren't showing the
percentages here, but it looks
like hopefully most of you
were able to get the correct
answer of H2 being the
limiting reactant.
It looks like we're still
figuring out -- this room was
just renovated, we're still
working out exactly how the
electronics work.
So, normally we'll see a
percentage of how many of you
got it, but I'm going to say it
was probably about 95% got
the answer right.
So, good job there.
If you didn't get the answer
right -- we'll send these
questions to your TA, so any
time you get a clicker
question wrong and you're
confused, bring it up in the
next recitation section
and you'll be able
to discuss it there.
So, starting in, we can switch
over to the to the notes now.
When we left off on Wednesday,
what we had really been doing
is trying to give you an
overview of all of the
different topics that
we're going to be
going over this semester.
And also, to make a couple of
those connections between the
principles we're learning, and
some of the exciting research
that's going on at MIT in the
Chemistry Department, and
also, to give you the idea that
we are going to be trying
to make these connections
between the chemistry and
things like human health
or medicine.
So, now we get to actually take
a step back and start at
the beginning, because before we
can talk about some of the
more complex issues, which
involve interactions between
molecules reacting or even
when we're talking about
individual molecules -- the
bonds that form between
individual atoms -- before any
of that we actually need to
establish a way that we're going
to describe and think
about how an individual
atom behaves.
And the way that we'll do this
is starting with talking about
the discovery of the electron
and the nucleus here.
Once we go through that, we
will be able to talk about
describing an atom using
classical physics.
So, once we have an atom and a
nucleus, what we'll try to do
is apply the classical
mechanics to
explain how that behaves.
What we'll find is that this
fails, and once this fails
we're going to need
another option.
Luckily for us, we have quantum
mechanics, which we'll
be talking about for the
next few lectures, and
we'll dive into that.
We might get a chance to
introduce it today, but
certainly in next class we'll
be introducing this new kind
of mechanics that's going
to allow to describe
the behavior of atoms.
So, I want to point out that it
makes a lot of sense for us
to start with the discovery of
the electron and the nucleus,
because it really highlights
one of the big issues that
comes up in all chemistry
research that you do, and that
is how do we actually study,
or in this case, how do we
discover atoms or sub-particles
that we actually
can't see at all.
And there are lots of solutions
that chemists come
up with -- there's always new
techniques that allow us to do
this, and these are just some
of the first, and we'll go
through them in a little
bit of detail here.
So, this all starts, in terms
of putting it in its
historical context at the turn
of the Century, we said we'd
start right in on the
20th Century of
where chemistry was.
And where we where at the start
of the 20th Century in
the late 1890's is that we were
at a place where there
was great confidence in our
understanding of the universe,
and our understanding of
how all matter worked.
So, people in the chemistry
community and in the physics
community had this general
feeling that the theoretical
structure of the entire universe
was pretty well
understood.
And they had this feeling
because there had just been
this huge boon of discovery,
of scientific advances that
included Newtonian mechanics,
it included Dalton's atomic
theory of matter, also
thermodynamics and classical
electromagnetism.
So, you can understand they
really felt quite confident at
this time that we could explain
everything that was
going on, and in fact, a really
telling quote from the
time was said by a professor at
the University of Chicago,
and what he said is, "Our future
discoveries must be
looked for in the sixth
decimal place."
So, basically what he's saying
here is we pretty much
understand what's going on,
there's nothing new to really
discover, all we need to do is
measure things more precisely.
So, that's not exactly the case,
and we're going to start
in at the point where right
around this time of great
confidence of feeling all has
been conquered, there are some
observations and discoveries
that are made that completely
break down these theories.
For example, in terms of the
atomic theory of matter, at
the time at the turn of the
Century, the understanding was
that atoms were the most basic
constituent of matter, meaning
you couldn't break atoms up into
anything smaller -- that
was it, you're done.
And with using Newtonian
mechanics, it was assumed
since this type of mechanics
worked so well to describe
everything we could see, it
could even describe the
universe and planets, that, of
course, we could use Newtonian
mechanics to describe how an
electron -- actually, we
didn't even know about an
electron here, but how atoms
behaved, and it turns out this
is not the case, and the first
step in discovering this is not
the case, was accomplished
by J.J. Thomson, and J.J.
Thomson is credited for
discovering the electron.
He was a physicist in England,
and what his laboratory was
studying is something called
cathode rays, and cathode rays
are simply rays that are emitted
when you have a high
voltage difference between
two electrodes.
So, if you look at this set up,
what he did when he was
studying these rays is he had
an evacuated tube, which is
schematically shown here, where
it's evacuated of all
it's air and filled instead just
with hydrogen gas, and he
had this high voltage difference
between an anode
and a cathode, and he actually
put a little hole in the anode
here, so these cathode rays that
were produced could shoot
out of the cathode and actually
could be detected as
this luminescent spot on
a detector screen.
So, lots of people were studying
cathode rays at the
time -- one reason is they
actually gave off this bright
glow -- if you put them in an
evacuated glass tube, you got
these crazy patterns
and glowing colors.
So, for that reason
it was a very hot
issue in terms of research.
But also, no one really knew
what these were and Thomson
was seeking to figure out some
more properties of them, and
he had the theory that maybe
they were actually charged
particles of some sort, and
others had proposed this in
the past, but they didn't really
have an experimental
set up to test it.
And that's what Thomson did.
And what we did was he put two
detection plates on either
side of these cathode rays,
and when he put a voltage
difference between these two
plates, he wanted to see if he
could actually bend the rays and
test if they're actually
charged or not.
So, when the voltage difference
between the plates
is zero, or when we just don't
have the plates there at all,
the cathode rays are not bent,
they just go right in a
straight line, and they can be
detected on this screen.
When he actually cranked up the
voltage between these two
plates, what he saw was really
amazing to him, which is that
he actually was able to bend
these rays -- this had never
been observed before in any
capacity, and he was able to
detect on his screen that there
was this deflection, and
he could even measure
the degree of the
deflection that he had.
So, we know now that we have
charged particles.
Are these negatively or
positively charged, based on
this evidence?
STUDENT: Negatively.
PROFESSOR: Yeah, that's right.
So, what we have here, cathode
rays we now know are
negatively charged particles.
And, in fact, he named these
negatively charged particles.
Does anyone know what
he named them?
No, not electrons --
very good guess.
He named them corpuscles.
Has anyone heard
of corpuscles?
A little bit.
Yeah, so it was later named that
these particles were, in
fact, electrons, and that's
what they are.
J.J. Thomson continued to call
them corpuscles for many,
many, many years after everyone
else called them
electrons, but I'm sure no one
minded because he did, in
fact, discover them.
And he was actually able to find
out more than just that
these were charged.
From classical electromagnetism,
he could
actually relate the degree of
deflection that he saw to the
charge and the mass
of the particles.
So, using that he could say that
delta x, and we'll put
sub-negative, because we know
now that these are negative
particles, is proportional to
the charge on that particle
over m, which is the mass.
So, we have e being equal to
the charge of the negative
particles, and m, of course,
is equal to the
mass of those particles.
So, Thomson didn't stop here,
he actually continued
experimenting with different
voltages.
And what he found was if he
really, really ramped the
voltage up between those two
plates, he could actually
detect something else.
And what he could detect here is
that there was this little
spot of luminescence that he
could see on the screen that
was barely deflected at all --
certainly in comparison to how
strongly this first particle
was deflected.
The second particle was
deflected almost not at all.
But what he could tell from
the fact that there was a
second particle at all, and the
fact that it was in this
direction, is that in addition
to his negative particle, he
also, of course, had a positive
particle that was
within this stream of rays
that were coming out.
So, of course, he can use the
same relationship for the
positive particle, so delta
x now of the positive is
proportional to the charge on
the positive particle all over
the mass of the positive
particle.
So, this is interesting
for several reasons.
What did he manage to pull out
information-wise from using
these two relationships?
And actually to do this, he made
a few more observations.
The first, which I just stated,
is that the deflection
of that negative particle was
just far and away more
extreme, much, much larger
than that of
the positive particle.
The other assumption that he
made here is that the charge
on the two particles
was equal.
So, how could he know that
the charge on the two
particles was equal?
And actually he couldn't exactly
know it -- it was a
very good assumption that he
made, and he could make the
assumption because he, in fact,
did know that what he
started with was this
hydrogen gas.
So, he was starting
with hydrogen.
If some negative particle was
popping out from the hydrogen,
then what he must be left with
is h-plus, and since hydrogen
itself is neutral, the h-plus
and the electron had to add up
to be a neutral charge.
So, that means the charges of
the two pieces, the positive
and negative particle,
must be equal in
terms of absolute charge.
So, using this relationship, he
could then actually figure
out by knowing, which he knows
how much each of them were
deflected, he could now try to
think about whether or not he
could make some relationship
between the masses -- between
the mass of the positive and
the negative particle.
So, this relationship he was
looking at was starting with
the deflection, and the absolute
distance that the
particles were deflected.
So, what he could set that equal
to is he knows what x is
proportional to in terms of
the negative particle, so
that's just the absolute value
of the charge over the mass of
the negative particle.
He could divide all of that by
the absolute value of the
charge of the positive particle,
all over the mass of
the positive particle.
And as we said, he made the
assumption that those two
charges were equal, so
we can go ahead and
cross those right out.
So, what that told him was if
he knew the relationship
between how far they were each
displaced, he could also know
something about the
relationship of the two masses.
So essentially, there was an
inversely proportional
relationship between how far the
particles were displaced,
and what the mass of the two
particles turned out to be.
So, because he, of course,
observed that the negative
particle travelled -- it was
deflected much, much further
by those plates, what he could
also assume and make the
conclusion of is that the mass
of that negative particle is
actually larger or smaller?
STUDENT: Smaller.
PROFESSOR: Much, much smaller,
exactly, then the mass of the
positive particle.
So essentially, what he found
here is the relationship
between the mass of an electron
and the mass of the
rest of the atom, the rest of
the hydrogen atom there, which
is an ion in this case.
And, in fact, it's so much
smaller, it's close to 2,000
times smaller, that we can
make the assumption that
essentially the electrons
take up no mass.
I mean they take up a teeny
bit, but essentially, when
we're thinking about the set up
of the atom, we don't have
to account for them as using
up a lot of the mass we're
discussing.
So, Thomson came up with a
model for the atom due to
this, and this is called the
Plum Pudding model of the
atom, and he was, as we said,
English, so plum pudding is
kind of a British food.
Has anyone here ever
had plum pudding?
A couple of people.
Okay.
I've never even seen it, so
that's good -- you must be
better travelled than I.
So, the idea that he had here
was he treated the whole of
the atom as sort of this
positive pudding, so the
majority of the atom was just
kind of this goopy, positive
stuff that you could think
about, and within the pudding,
he had all these negative
charges, which were the
electrons, and they were the
raisins or the plums that were
in the pudding.
So this was a revolutionary
model of an atom when we
thought of the fact that before
this experiment, the
understanding was an atom could
not be divisible into
smaller parts, and now here we
are with subatomic particles
with electrons, and this
wonderful Plum Pudding model.
So, for those of you that
haven't actually had plum
pudding, which myself
is included, I threw
a picture up here.
This was my first glance at plum
pudding, and I guess you
can see that this must be that
positive part -- most of the
plums are within that, and you
can see all these little
raisins or plums in here, that
would be that negative charge.
So, that already was a big
advancement from where the
understanding was at the time.
We already moved way forward and
completely revolutionizing
the understanding of an atom in
that there's something in
an atom -- it's not the smallest
thing there is.
However, as you know, we
didn't stop at the plum
pudding model, which is good,
because it's a little goofy,
so it's nice to move on from
that and move on we did.
About 10 to 15 years later,
another physicist, Ernest
Rutherford, actually put this
plum pudding model to test,
and he did it through studies
that he'd been doing on
radiation that was emitting
something
called alpha particles.
So, Rutherford, some of you may
recognize that name, is a
very famous physicist who made
a lot of contributions in
terms of radioactivity.
When he was studying these
alpha particles, he was
actually the first person to
identify the difference
between different types of
particles that radioactive
materials emit.
And he got this particular
material that he was studying,
radium bromide from his good
friend, Marie Curie, who,
obviously, also was a leader,
really the leader in figuring
out much of how radioactive
materials work.
She has two Nobel Prizes
for her work
in radioactive materials.
And something that maybe many
of you think, which I know I
always think when I hear about
radioactivity studies in the
early 1900's, is oh, my gosh,
this sounds really dangerous,
right, they're using radium
bromide, and this is pretty
dangerous radioactive
material.
So, for those of you that don't
know radium is extremely
radioactive, even in the range
of radioactivity, and one of
the major problems with it is
that if it does get in your
body, the radium is treated
as calcium in your body.
So, you can imagine what happens
as it gets deposited
into your bones, which is not
the ideal situation after a
long day in the lab.
So, this is really a pretty
dangerous situation that's
always interesting
to point out.
He got this from Marie Curie --
you can imagine they used
the postal service, I'm not sure
how else they would have
transferred it to each other.
So, it really brings
up some issues.
The first thing I did when I
heard that is actually look up
to see how, in fact, Ernest
Rutherford did die in 1937,
and you'll be happy to know,
it actually wasn't from
radiation poisoning or from bone
cancer, so that's really
good that that worked out okay
for him, and that he did get
to, sort of safely, at least
end his life before the
radiation ended it.
But it's really interesting
the studies that he did do
with radium bromide, and he was
studying the alpha particles.
And what was known about alpha
particles at the time is that
they were these charged
particles and that they were
very heavy.
Does anyone know more than what
Rutherford knew at the
time, what alpha particles
actually are?
Yeah, good.
So, they're actually helium
atoms, helium ions.
And this wasn't really important
for the studies, it
didn't matter that didn't know
what they are, but it's nice
to kind of know now -- that we
do know what they were using.
And he was doing quite a
few studies with them.
One experiment that he was doing
is detecting the number
of particles that were being
emitted by this radium bromide
as a rate, so he would measure
the number of particles per
minute that the radium
bromide was emitting.
And what he used was a detector
here, so he here
could detect how many
particles were
hitting this detector.
He had actually developed this
detector with a postdoc by the
name of Hans Geiger.
Does that name ring a bell?
STUDENT: Geiger counter.
PROFESSOR: Um-hmm,
a Geiger counter.
So, this, in fact, is my very
schematic representation of a
Geiger counter.
For those of you don't know what
that is, it's simply an
instrument that counts
radioactive particles in the
air, and now that you're at MIT,
you'll all have a chance
to see one first hand, if you're
ever in any of the
labs, especially in the
chemistry or bio labs.
As carefully as people work with
radioactivity here, and
using often much, much safer
radioactive materials than
radium bromide, and using them,
and special hoods, and
having special procedures,
they still do a lot of
checking with these Geiger
counters to make sure
everything's safe.
You'll actually see a man
walking around with one,
sometimes in the halls, just
kind of like this -- you hear
that click, click, click.
That's a good sound, it means
low levels of radiation.
He'll walk by your hood, so
click by your hood --
I always get a little nervous
when he walked by my hood, I
don't know why, I never worked
with radioactive material.
But I was convinced
I'd hear the
click-click-click-click-click,
which is what tells you you're
in trouble.
So, I've never heard the
click-click-click-click-click,
and we might bring a Geiger
counter in here some time
later in the semester so we can
check all of you out, and
hopefully we won't hear any
when we do that either.
So, one thing that he discovered
with this detector
initially, and he was the first
to discover this, is
that radioactive material,
including radium bromide, have
a characteristic rate that they
emit, radioactive decay.
So basically they're decaying
at a constant rate, which
means, of course, that you can
figure out how old things are
by seeing how much
they've decayed.
So, he was really the first
person to discover you could
do this, which was used to make
the first somewhat close
approximation of the
age of the earth.
So that's a pretty exciting
set of experiments he did.
But one thing that he wanted
to do specific to
understanding the atom, and
using these alpha particles,
these heavy-charged particles,
was to test if this Plum
Pudding model actually fit
what he could observe.
So, what he did was he first
recorded the count rate of
radium bromide before it's going
through any kind of a
plum pudding atom, and he found
that it had a count rate
of 132,000 alpha particles per
minute were being detected by
this Geiger counter.
He then set up a situation where
he put a very, very thin
piece of gold foil right in what
would be in the stream of
the alpha particles.
So, it was only 10 to the
negative, 9 meters thick, so
about one nanometer, so that's
really thin, it's thinner than
a strand of hair.
So you can imagine, we actually
don't need to think
of it as a piece of gold foil,
it might be easier to think of
it as a couple of
layers of atoms.
So basically he's trying to put
some atoms in the way of
the alpha particle.
And what he would expect is if
this Plum Pudding model is
true, nothing's really going
to happen to the particles,
right, they should go straight
through, because if they hit
an electron, those
are so small.
We figured out the mass is so
tiny that it shouldn't really
deflect them very much.
And, of course, all that's left
is this positive pudding.
So that's not going to
do anything either.
And what he found when he did
this experiment, was that the
count rate with still 132,000
counts per minute.
So, what he could conclude thus
far was that this was
really consistent with the
Plum Pudding model.
All of his heavily-charged alpha
particles were going
right through this thin
layer of gold atoms.
So, you might think that he
would stop his experiments
here, and maybe he would have,
but as I mentioned, he did
have a postdoc working with
him by the name of Geiger.
He also had an undergraduate, we
could say maybe even a UROP
working with him, and this was
by the name of Marsden was the
name of this UROP.
And Rutherford realized, you
know I have these two people
that are very excited to work on
this project, I don't need
to spend time doing it.
Maybe it's not the best way for
me to spend time looking
to see if I can find any
bounced-back particles since
all the particles are
accounted for.
But, you know, this
undergraduate's very eager to
do it, let's let
him have a try.
And something you might find in
your UROP experience is you
have a unique advantage as an
undergraduate, which is that
there's not a lot of pressure
to actually make a huge
discovery or necessarily
accomplish a great amount.
You have a little more pressure
in grad school, but
sometimes that means when
you're an undergrad your
advisor will decide to put you
on projects that maybe when
you look at them seem
a little bit silly.
So this project was, let's see
if we can detect any alpha
particles by making a detector
that swings around.
So, some people might say,
why are we doing this?
We know we started with a
132,000 alpha particles.
We detected a 132,000
alpha particles.
What are we even looking for?
We have to build this whole new
detector, is this really
the best use of my time?
As an undergrad, you don't have
to worry about it, you're
just worried about learning.
You can take these big risks of
time, and if at the end of
the day there's nothing to
detect, you still know how to
build a detector.
So, keep that in mind if
you're not over-the-top
excited about the prospects
of some of your research.
You might be surprised
at what you find out.
And this is exactly what
happened with Marsden who
discovered that when he shot
the alpha particles at the
gold foil, he detected something
on his detector that
click, click, click went
a little bit faster.
So, what he detected was that
there were 20 alpha particles
per minute.
Does that sound significant?
It depends, right?
So hopefully, the first
experiment he did, which I
know that they certainly did
do was maybe it's just
background noise, right?
So, they took away that gold
foil and said is just the
alpha particles hitting
it some other way?
And no, it wasn't.
When he took away the gold
foil, the count rate
went down to zero.
If he switched from gold to
let's say iron, he also tried
platinum, a number of different
foils, he found that
they count rate, it still was 20
alpha particles per minute.
So, this is an absolutely
outstanding discovery, even
though, if we think about it,
what is the probability that
this happened, how often
did this happen?
It actually almost happened
not at all.
We can figure out exactly what
the probability of this
backscattering was just by
dividing the count rate of the
number particle that were
backscattered divided by the
count rate of the incident
particles.
So essentially, we just
have 20, and our 20
is divided by 132,000.
So, we end up with a not so
large probability of 2 times
10 to the negative 4.
But still, we can't even
overstate how exciting this
discovery was.
Rutherford, the advisor here,
he had a lot of good things
happen in his life,
as I mentioned.
He was the person responsible
for being able to first date
the age of our earth.
That's a pretty nice thing.
He was also married, he had a
child, which I hear is very
nice, very exciting, also.
But yet, when he saw this one
single experiment from this
undergraduate, he described this
as the most incredible
event that had ever happened
to him in his life.
So, this was a pretty
big deal.
We won't tell his daughter.
And he gave a very good analogy
in saying, "It was
almost as incredible as if you'd
fired a 15 inch shell at
a piece of tissue paper, and
it came back and hit you."
And that really illustrates
what's happening here, because
if we think of the Plum
Pudding model, it's
essentially this very thin film,
right, there's nothing
that should hit if we send alpha
particles through it.
But what we actually
have is that
something's bouncing back.
So, what happened is Rutherford
needed to come up
with a new model for the atom
with several interpretations
that came out of these
experiments, and some of these
interpretations were that, of
course, we now know that these
gold atoms, they must be mostly
empty, and the reason
that we know that they must be
mostly empty is because all
but 20 of these 132,000
particles
went all the way through.
So they weren't hitting
anything, we're dealing with
mostly empty space.
But he also realized that when
they did hit something, what
they hit what unbelievably
massive, but also that that
mass was concentrated into this
very, very small space.
So eventually, this is what we
have come to call the nucleus
of an atom.
And the nucleus name was used
as an analogy to the nucleus
of a cell, so in some ways that
makes it easier to see
the connection, but I think it
can also be a little bit
confusing for maybe 7th graders
that are learning both
at the same time, that this
nucleus acts very different
from a nucleus in a cell,
although, of course, there
many of them in the
nucleus of a cell.
There are some other things that
Rutherford was able to
figure out.
One is the diameter of the
nucleus, and that turns out to
be 10 to the negative
14 meters.
If we think about the size of
a typical cell -- excuse me,
now I'm getting confused
about nuclei.
If we think of the size of a
typical atom, we would say
that would be about 10 to
the negative 10 meters.
So, we can see the diameter
of a nucleus is absolutely
smaller, really concentrating
that mass into
a very small space.
So, you might be asking
how did he
actually figure that out?
We'll do the calculation
ourselves.
In fact, we'll do the whole
experiment ourselves, minus
the radioactivity in just a
minute, so we'll be able to
answer that question for you.
He also figured out that
the charge of the
nucleus was a plus ze.
This makes sense intuitively as
well, because z is just the
atomic number.
So, let's say we have an atomic
number of 3, that means
we have 3 electrons, so we
better hope to get our neutral
atom that we have a charge
of plus 3 in the nucleus.
So, I mentioned at the
beginning, while he was
working with this radium
bromide, that I was very
relieved to see that it did
not kill him to do these
experiments.
However, I think I will share
with you that the cause of his
death was, in fact, related to
his research here, even though
it was a little more
tangled up.
So, what happened, of course,
after he discovered the
nucleus, not surprising, he won
a Nobel Prize for this --
I would hope that he would.
And in addition to winning a
Nobel Prize, he was also
knighted, which was a nice
bonus for someone born in
England, that's a great thing
to happen to them.
The problem that he ran into is
at some point a little bit
later in his life, he had a
hernia which was a pretty
standard case, but what he
was going to need was an
operation on it.
And the glitch came that at
least at the time, if you were
a knight, you could only be
operated on by a doctor that
was also titled.
So, Rutherford had a little bit
of waiting to do for that
doctor to show up, and it turns
out the wait was too
long, and he actually passed
away because he discovered the
nucleus and got a Noble Prize
and became knighted.
So, it's still dangerous.
If that opportunity comes up
for you, maybe you want to
check into the policies of how
that works with the doctor
situation now.
Hopefully they've cleared
it up a little bit.
So, what we want to do now is
see if we can understand how
this backscattering
experiment worked.
So, we will do our own
backscattering experiment.
And we'll ask you to imagine
a few things.
First is that we have this mono
layer of gold particles.
So let's see if Professor
Drennan is able
to help us out here.
Oh, great.
So, that is her daughter, Sam
that you see strapped to the
chest, and Dr. Patti Christie
helping us out here.
All right.
So, we'll move this up to the
front in just a minute, but
I'm going to explain how this
experiment works, and we'll do
the calculation first before
the excitement breaks out.
But I'm sure you can easily see
how these styrofoam balls
could, in fact, be a mono
layer of gold nuclei.
We have 266, as some of you
might know who saw me counting
ping-pong balls the other
day in office hours.
We have 266 ping-pong balls, and
we need someone, hopefully
you, to be some radioactive
material that are going to be
emitting these ping-pong
balls.
And when the time comes, in just
a minute, I'll ask the
TAs to come down and hand these
out very quickly to you,
so we can do this experiment.
But first, let's go through how
we're going to determine
what Rutherford determined,
which was he was interested in
knowing, which we said
what the diameter
of the nuclei were.
So, we're going to do the same
thing and figure out the
diameter of these styrofoam
balls here, and we can do it
by using the relationship
of how many backscatter.
So, if we think about the
probability of backscattering,
which is the exact same thing
that we saw Rutherford
calculate, using the 20
divided by 132,000.
But in our case, the probability
of backscattering
is going to be the number of
balls that backscatter, and
that's going to be divided
by the total number
of ping-pong balls.
So, do you remember
what that was?
STUDENT: 266.
PROFESSOR: 266.
Good information retention.
All right.
So, we have the probability
here.
So, in terms of the number of
balls scattered over the
total, we can also relate the
probability to the area of all
of those nuclei divided
by the total area that
the atoms take up.
Right, this makes a lot of
sense, because if the entire
atom was made up of nuclei,
then we would have 100%
probability of hitting one of
these nuclei and having things
bounce back.
So, here we have the area of
the nuclei we'll figure out
adding those all together versus
the space of all of the
atoms put together.
So, not only did Professor
Sayer, who's in the Chemistry
Department who put together this
contraption for all of
you, not only did she magnify
the size of these gold nuclei,
but she actually had to smoosh
all of these atoms closer
together then they normally
would be.
If, in fact, a gold nucleus was
this size here, we would
need to use another lecture hall
in order to find a place
to put this nucleus
right here.
This is a little bit of a
tricky experiment, so we
decided we'll just smoosh it all
in, and we'll actually be
able to account for it, because
we'll take into
account the area of all
of those atoms.
I think this board does not
like to go by itself.
All right.
So we can figure out what that
is, the area of all of the
nuclei is going to be the number
of nuclei times the
area per nucleus, and we're
going to talk about the
cross-section here to
keep it simple.
And all of that is divided
by the area of the
atoms, which is 1 .
39 meters squared, measuring
that space there.
So, the number of nuclei, if we
were to sit and count these
as well, is 119.
So, we'll multiply that by just
pi, r squared, to get
that cross-section, and divide
all of that by 1 .
39 meters squared.
So, what we have here is a
relationship that can tell us
what the probability of
backscattering is, but what we
want to pull out, since we can
experimentally measure what
the probability is, what we need
to pull out is the radius
or the diameter of these
nuclei, so we can just,
instead of solving for p, we can
switch it around and solve
for the radius.
So, that's going to be equal to
the probability raised to
the 1/2 times 6 .
098 times 10 to the
negative 2 meters.
So, actually, just for
discussion sake, it makes a
little more sense for us to talk
about the diameter, so
that's just twice the radius.
So, once we figure out what
our probability of
backscattering is, we'll just
raise that to the 1/2, and
we'll multiply that by 12 .
20 centimeters.
All right.
So now all we have to do is
figure out this probability of
backscattering.
We know we need to divide by
266, but what we need you to
help us with is to figure out
this top number here and see
how many particles are
going to backscatter.
So, if the TAs can come up
and quickly hand out
1 particle to everyone.
And a few people will need to
throw 2, if you feel like you
have particularly good aim.
PROFESSOR: So, as you're getting
your ping-pong balls
-- do not throw them yet.
Let me explain to you
what constitutes
a backscatter event.
So, it'll be considered a
backscatter event if your
ping-pong ball hits
one of the nuclei.
It's not going to be a
backscatter event if your
ping-pong ball hits
the frame or these
strings, or the top part.
So, in a few minutes, not now,
we're going to ask you to
stand up, and you can kind of
come over more toward the
center of the room if you want,
and aim your ping-pong
ball at the lattice here, follow
the ping-pong ball with
your eye, and discover, watching
it, whether it's a
backscatter -- it hits one of
the nuclei and bounces back
towards you, or if it goes
through, and also if your
ping-pong ball doesn't land
anywhere in the vicinity of
this at all, then keep
that in mind.
And then at the end of the
experiment we'll ask you what
happened to your ping-pong ball,
and you'll let us know,
and we can calculate the number
of backscatter events.
Are there any questions
before we get started?
Raise your hand if you don't
if you don't have a
ping-pong ball yet.
Any questions before
we get started?
All right.
So, we'll come around and
get ping-pong balls
to the rest of you.
Those of you who have your
ping-pong balls can now begin
the experiment.
[EXPERIMENTING]
PROFESSOR: All right.
Any last shots?
There we go.
All right.
So, it looks like we were a
little bit successful, I saw
some backbouncing.
We were going to have a clicker
slide on how many
bounced back, but it looks like
we're having a little
technical difficulty
with that.
So, what I'll ask is can you
stand up if you had your
particle bounce back?
All right, so let's count
how many we have here.
So, 13 backscattered.
TAs, if you can maybe pick up
these ping-pong balls for me.
I'm sure it would be very
amusing if I fell, but I'd
rather not.
All right, so, we have
13 divided by 266.
All right, MIT students, who
has a calculator on them?
Actually, I should probably do
it as well, so I know I'm
hearing correctly.
So, are you getting 0 .
0489 or so?
All right.
So, we've got our probability.
We can go ahead and plug that
in, take the square root of
it, multiply it by 12 .
2.
What are you getting
for your diameters?
Yup, that's what I got, too.
All right.
So, we have 2 .
70 for our diameter, and
that's in centimeters.
So, we actually did a pretty
good job here.
It turns out that the diameter
is actually 2 .
5 centimeters.
So, good job, experiment well
done, plus we were not exposed
to radioactivity, which
is a bonus.
So, this is exactly how
Rutherford did discover that
these particles were present
and made this new model for
the atom that we now know has
both a nucleus, and we know
the size, and also
has electrons.
So, to finish up today, we won't
get through all of it.
But the next thing we can
actually talk about is now
that we know we have an atom
that has a nucleus, let's say
somewhere in the center, and
it has electrons around it,
thinking on our most simple
example, which is hydrogen, we
have a nucleus and an electron
that have to hang together in
the atom in some way, and we
need to think about well how
can we describe how atoms
behave, and specifically, how
do we describe how any single
atom stays together where the
two are associated, but at
the same time they don't
immediately collapse
into themselves.
So, what we can do is try
using the classical
description of the atom and
see where this takes us.
So, if we think about the force
that occurs between a
positively and a negatively
charged particle, what we have
is essentially a Coulomb force,
so we can describe this
as a force of attraction.
We can use the Coulomb force law
to explain this where we
can describe the force
as a function of r.
So, let's think about what
we're saying here.
We're describing the force
that's holding these two
particles together, and it's
related to the charge of each
of the particles, where e is
the absolute value of an
electron's charge.
So, an electron has a charge of
negative e, we've written
here, and the nucleus has
a charge of positive e.
And then we have r, which is
simply the distance between
the two charges.
And what we see is that the
force is inversely related to
the distance between
the two charges.
And we can simplify this
expression as saying negative
e squared over 4 pi, epsilon
nought r squared.
Epsilon nought is a constant,
it's something you might see
in physics as well.
Essentially for our purposes
here, you can just think of it
as a conversion factor.
What we need to do is get rid
of the Coulomb tag that we
have -- that's how we measure
our electron charges --
charge, and so we use this
epsilon nought quite often,
this permativity constant
of a vacuum to make that
conversion.
And I'll just point out here
also, this is a conversion
factor you'll use quite
frequently -- many of you,
quite on accident, will memorize
it as you use it over
and over again.
But I do want to point out
that you don't have to
memorize it for any exams in
this class, we will give you a
sheet that has all the needed
constants that you're going to
use on there, so save up that
brain space for other
information. ah
So, we can use Coulomb's force
law, and we can think about
these different scenarios.
So, when you come in on Monday,
we're going to start
off, you can think for the
weekend -- you probably only
need to think for a second about
what happens when r goes
to infinity, but that's where
we'll start on Monday.
And let me just suggest to all
of you also, that you get
those problem sets started
this weekend.
You should absolutely finish,
at least through part a this
weekend, and save part
b for next week.
So, have a great weekend.
