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PROFESSOR: So, our first
question here is about

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limiting reactants.
 

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So, that's something you will
encounter in your review

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reading for the sections, that
kind of review -- what we hope

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you have picked up from high
school or will pick up quickly

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by doing some review.
 

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So, how about we have everyone
take ten more seconds on the

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clicker question, get your
final answer in here.

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All right.
 

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So, let's see what we have.
 

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All right, so it looks like we
weren't showing the percentages

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here, but it looks like
hopefully most of you were able

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to get the correct answer of H2
being the limiting reactant.

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It looks like we're still
figuring out -- this room was

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just renovated, we're still
working out exactly how

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the electronics work.
 

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So, normally we'll see a
percentage of how many of you

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got it, but I'm going to say
it was probably about 95%

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got the answer right.
 

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So, good job there.
 

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If you didn't get the answer
right -- we'll send these

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questions to your TA, so any
time you get a clicker question

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wrong and you're confused,
bring it up in the next

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recitation section and you'll
be able to discuss it there.

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So, starting in, we can switch
over to the to the notes now.

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When we left off on Wednesday,
what we had really been doing

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is trying to give you an
overview of all of the

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different topics that
we're going to be going

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over this semester.
 

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And also, to make a couple of
those connections between the

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principles we're learning, and
some of the exciting research

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that's going on at MIT in the
Chemistry Department, and also,

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to give you the idea that we
are going to be trying to make

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these connections between the
chemistry and things like

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human health or medicine.
 

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So, now we get to actually take
a step back and start at the

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beginning, because before we
can talk about some of the more

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complex issues, which involve
interactions between molecules

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reacting or even when we're
talking about individual

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molecules -- the bonds that
form between individual atoms

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-- before any of that we
actually need to establish a

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way that we're going to
describe and think about how an

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individual atom behaves.
 

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And the way that we'll do this
is starting with talking about

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the discovery of the electron
and the nucleus here.

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Once we go through that, we
will be able to talk about

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describing an atom using
classical physics.

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So, once we have an atom and a
nucleus, what we'll try to do

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is apply the classical
mechanics to explain

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how that behaves.
 

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What we'll find is that this
fails, and once this fails

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we're going to need
another option.

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Luckily for us, we have quantum
mechanics, which we'll be

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talking about for the next few
lectures, and we'll

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dive into that.
 

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We might get a chance to
introduce it today, but

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certainly in next class we'll
be introducing this new kind

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of mechanics that's going to
allow to describe the

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behavior of atoms.
 

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So, I want to point out that it
makes a lot of sense for us to

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start with the discovery of the
electron and the nucleus,

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because it really highlights
one of the big issues that

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comes up in all chemistry
research that you do, and that

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is how do we actually study, or
in this case, how do we

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discover atoms or sub-particles
that we actually

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can't see at all.
 

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And there are lots of solutions
that chemists come up with --

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there's always new techniques
that allow us to do this, and

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these are just some of the
first, and we'll go through

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them in a little bit
of detail here.

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So, this all starts, in terms
of putting it in its historical

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context at the turn of the
Century, we said we'd start

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right in on the 20th Century
of where chemistry was.

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And where we where at the start
of the 20th Century in the late

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1890's is that we were at a
place where there was great

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confidence in our understanding
of the universe, and our

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understanding of how
all matter worked.

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So, people in the chemistry
community and in the physics

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community had this general
feeling that the theoretical

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structure of the entire
universe was pretty

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well understood.
 

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And they had this feeling
because there had just been

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this huge boon of discovery,
of scientific advances that

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included Newtonian mechanics,
it included Dalton's atomic

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theory of matter, also
thermodynamics and classical

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electromagnetism.
 

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So, you can understand they
really felt quite confident at

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this time that we could explain
everything that was going on,

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and in fact, a really telling
quote from the time was said by

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a professor at the University
of Chicago, and what he said

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is, "Our future discoveries
must be looked for in the

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sixth decimal place."
 

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So, basically what he's saying
here is we pretty much

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understand what's going on,
there's nothing new to really

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discover, all we need to do is
measure things more precisely.

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So, that's not exactly the
case, and we're going to start

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in at the point where right
around this time of great

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confidence of feeling all has
been conquered, there are some

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observations and discoveries
that are made that completely

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break down these theories.
 

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For example, in terms of the
atomic theory of matter, at the

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time at the turn of the
Century, the understanding was

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that atoms were the most basic
constituent of matter, meaning

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you couldn't break atoms up
into anything smaller --

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that was it, you're done.
 

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And with using Newtonian
mechanics, it was assumed since

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this type of mechanics worked
so well to describe everything

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we could see, it could even
describe the universe and

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planets, that, of course, we
could use Newtonian mechanics

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to describe how an electron --
actually, we didn't even know

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about an electron here, but how
atoms behaved, and it turns out

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this is not the case, and the
first step in discovering this

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is not the case, was
accomplished by J.J.

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Thomson, and J.J.
 

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Thomson is credited for
discovering the electron.

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He was a physicist in England,
and what his laboratory was

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studying is something called
cathode rays, and cathode rays

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are simply rays that are
emitted when you have a

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high voltage difference
between two electrodes.

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So, if you look at this set up,
what he did when he was

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studying these rays is he had
an evacuated tube, which is

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schematically shown here, where
it's evacuated of all it's air

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and filled instead just with
hydrogen gas, and he had this

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high voltage difference between
an anode and a cathode, and he

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actually put a little hole in
the anode here, so these

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cathode rays that were produced
could shoot out of the cathode

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and actually could be detected
as this luminescent spot

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on a detector screen.
 

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So, lots of people were
studying cathode rays at the

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time -- one reason is they
actually gave off this bright

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glow -- if you put them in an
evacuated glass tube, you got

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these crazy patterns
and glowing colors.

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So, for that reason it
was a very hot issue

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in terms of research.
 

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But also, no one really knew
what these were and Thomson was

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seeking to figure out some more
properties of them, and he had

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the theory that maybe they were
actually charged particles of

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some sort, and others had
proposed this in the past, but

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they didn't really have an
experimental set up to test it.

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And that's what Thomson did.
 

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And what we did was he put two
detection plates on either side

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of these cathode rays, and when
he put a voltage difference

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between these two plates, he
wanted to see if he could

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actually bend the rays and test
if they're actually

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charged or not.
 

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So, when the voltage difference
between the plates is zero, or

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when we just don't have the
plates there at all, the

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cathode rays are not bent, they
just go right in a straight

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line, and they can be
detected on this screen.

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When he actually cranked up the
voltage between these two

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plates, what he saw was really
amazing to him, which is that

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he actually was able to bend
these rays -- this had never

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been observed before in any
capacity, and he was able to

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detect on his screen that there
was this deflection, and he

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could even measure the degree
of the deflection that he had.

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So, we know now that we
have charged particles.

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Are these negatively or
positively charged,

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based on this evidence?
 

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STUDENT: Negatively.
 

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PROFESSOR: Yeah, that's right.
 

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So, what we have here,
cathode rays we now know are

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negatively charged particles.
 

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And, in fact, he named these
negatively charged particles.

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Does anyone know
what he named them?

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No, not electrons --
very good guess.

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He named them corpuscles.
 

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Has anyone heard of corpuscles?
 

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A little bit.
 

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Yeah, so it was later named
that these particles were,

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in fact, electrons, and
that's what they are.

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J.J.
 

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Thomson continued to call them
corpuscles for many, many, many

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years after everyone else
called them electrons, but I'm

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sure no one minded because he
did, in fact, discover them.

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And he was actually able to
find out more than just

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that these were charged.
 

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From classical
electromagnetism, he could

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actually relate the degree of
deflection that he saw to the

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charge and the mass of
the particles.

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So, using that he could say
that delta x, and we'll put

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sub-negative, because we know
now that these are negative

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particles, is proportional to
the charge on that particle

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over m, which is the mass.
 

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So, we have e being equal to
the charge of the negative

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particles, and m, of course,
is equal to the mass

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of those particles.
 

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So, Thomson didn't stop
here, he actually continued

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experimenting with
different voltages.

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And what he found was if he
really, really ramped the

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voltage up between those two
plates, he could actually

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detect something else.
 

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And what he could detect here
is that there was this little

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spot of luminescence that he
could see on the screen that

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was barely deflected at all --
certainly in comparison to

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how strongly this first
particle was deflected.

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The second particle was
deflected almost not at all.

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But what he could tell from the
fact that there was a second

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particle at all, and the fact
that it was in this direction,

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is that in addition to his
negative particle, he also, of

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course, had a positive particle
that was within this stream of

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rays that were coming out.
 

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So, of course, he can use the
same relationship for the

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positive particle, so delta x
now of the positive is

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proportional to the charge on
the positive particle all

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over the mass of the
positive particle.

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So, this is interesting
for several reasons.

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What did he manage to pull out
information-wise from using

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these two relationships?
 

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And actually to do this, he
made a few more observations.

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The first, which I just stated,
is that the deflection of that

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negative particle was just far
and away more extreme, much,

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much larger than that of
the positive particle.

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The other assumption that he
made here is that the charge on

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the two particles was equal.
 

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So, how could he know that
the charge on the two

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particles was equal?
 

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And actually he couldn't
exactly know it -- it was a

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very good assumption that he
made, and he could make the

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assumption because he, in fact,
did know that what he started

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with was this hydrogen gas.
 

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So, he was starting
with hydrogen.

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If some negative particle was
popping out from the hydrogen,

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then what he must be left with
is h-plus, and since hydrogen

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itself is neutral, the h-plus
and the electron had to add

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up to be a neutral charge.
 

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So, that means the charges of
the two pieces, the positive

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and negative particle, must be
equal in terms of

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absolute charge.
 

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So, using this relationship, he
could then actually figure out

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by knowing, which he knows how
much each of them were

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deflected, he could now try to
think about whether or not he

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could make some relationship
between the masses -- between

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the mass of the positive and
the negative particle.

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So, this relationship he was
looking at was starting with

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the deflection, and the
absolute distance that the

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particles were deflected.
 

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So, what he could set that
equal to is he knows what x is

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proportional to in terms of the
negative particle, so that's

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just the absolute value of the
charge over the mass of

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the negative particle.
 

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He could divide all of that by
the absolute value of the

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charge of the positive
particle, all over the mass of

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the positive particle.
 

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And as we said, he made the
assumption that those two

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charges were equal, so we
can go ahead and cross

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those right out.
 

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So, what that told him was if
he knew the relationship

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between how far they were each
displaced, he could also

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know something about the
relationship of the two masses.

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So essentially, there was
an inversely proportional

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relationship between how far
the particles were displaced,

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and what the mass of the two
particles turned out to be.

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So, because he, of course,
observed that the negative

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particle travelled -- it was
deflected much, much further by

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those plates, what he could
also assume and make the

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conclusion of is that the mass
of that negative particle is

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actually larger or smaller?
 

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STUDENT: Smaller.
 

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PROFESSOR: Much, much smaller,
exactly, then the mass of

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the positive particle.
 

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So essentially, what he found
here is the relationship

270
00:14:23 --> 00:14:28
between the mass of an electron
and the mass of the rest of the

271
00:14:28 --> 00:14:31
atom, the rest of the hydrogen
atom there, which is

272
00:14:31 --> 00:14:32
an ion in this case.
 

273
00:14:32 --> 00:14:36
And, in fact, it's so much
smaller, it's close to 2

274
00:14:36 --> 00:14:42
times smaller, that we can make
the assumption that essentially

275
00:14:42 --> 00:14:44
the electrons take up no mass.
 

276
00:14:44 --> 00:14:47
I mean they take up a teeny
bit, but essentially, when

277
00:14:47 --> 00:14:50
we're thinking about the set up
of the atom, we don't have to

278
00:14:50 --> 00:14:52
account for them as using up
a lot of the mass

279
00:14:52 --> 00:14:55
we're discussing.
 

280
00:14:55 --> 00:15:00
So, Thomson came up with a
model for the atom due to this,

281
00:15:00 --> 00:15:05
and this is called the Plum
Pudding model of the atom, and

282
00:15:05 --> 00:15:08
he was, as we said, English, so
plum pudding is kind

283
00:15:08 --> 00:15:10
of a British food.
 

284
00:15:10 --> 00:15:13
Has anyone here ever
had plum pudding?

285
00:15:13 --> 00:15:14
A couple of people.
 

286
00:15:14 --> 00:15:14
Okay.
 

287
00:15:14 --> 00:15:17
I've never even seen it, so
that's good -- you must be

288
00:15:17 --> 00:15:19
better travelled than I.
 

289
00:15:19 --> 00:15:23
So, the idea that he had here
was he treated the whole of the

290
00:15:23 --> 00:15:35
atom as sort of this positive
pudding, so the majority of the

291
00:15:35 --> 00:15:38
atom was just kind of this
goopy, positive stuff that you

292
00:15:38 --> 00:15:41
could think about, and within
the pudding, he had all these

293
00:15:41 --> 00:15:47
negative charges, which were
the electrons, and they were

294
00:15:47 --> 00:15:50
the raisins or the plums
that were in the pudding.

295
00:15:50 --> 00:15:54
So this was a revolutionary
model of an atom when we

296
00:15:54 --> 00:15:57
thought of the fact that before
this experiment, the

297
00:15:57 --> 00:15:59
understanding was an atom could
not be divisible into smaller

298
00:15:59 --> 00:16:03
parts, and now here we are with
subatomic particles with

299
00:16:03 --> 00:16:08
electrons, and this wonderful
Plum Pudding model.

300
00:16:08 --> 00:16:10
So, for those of you that
haven't actually had plum

301
00:16:10 --> 00:16:13
pudding, which myself is
included, I threw a

302
00:16:13 --> 00:16:15
picture up here.
 

303
00:16:15 --> 00:16:18
This was my first glance at
plum pudding, and I guess you

304
00:16:18 --> 00:16:22
can see that this must be that
positive part -- most of the

305
00:16:22 --> 00:16:25
plums are within that, and you
can see all these little

306
00:16:25 --> 00:16:29
raisins or plums in here, that
would be that negative charge.

307
00:16:29 --> 00:16:32
So, that already was a big
advancement from where the

308
00:16:32 --> 00:16:34
understanding was at the time.
 

309
00:16:34 --> 00:16:37
We already moved way forward
and completely revolutionizing

310
00:16:37 --> 00:16:40
the understanding of an atom in
that there's something in

311
00:16:40 --> 00:16:44
an atom -- it's not the
smallest thing there is.

312
00:16:44 --> 00:16:48
However, as you know, we didn't
stop at the plum pudding model,

313
00:16:48 --> 00:16:51
which is good, because it's a
little goofy, so it's nice

314
00:16:51 --> 00:16:53
to move on from that
and move on we did.

315
00:16:53 --> 00:16:58
About 10 to 15 years later,
another physicist, Ernest

316
00:16:58 --> 00:17:03
Rutherford, actually put this
plum pudding model to test, and

317
00:17:03 --> 00:17:07
he did it through studies that
he'd been doing on radiation

318
00:17:07 --> 00:17:11
that was emitting something
called alpha particles.

319
00:17:11 --> 00:17:15
So, Rutherford, some of you may
recognize that name, is a very

320
00:17:15 --> 00:17:18
famous physicist who made a
lot of contributions in

321
00:17:18 --> 00:17:20
terms of radioactivity.
 

322
00:17:20 --> 00:17:23
When he was studying these
alpha particles, he was

323
00:17:23 --> 00:17:25
actually the first person to
identify the difference between

324
00:17:25 --> 00:17:28
different types of particles
that radioactive

325
00:17:28 --> 00:17:30
materials emit.
 

326
00:17:30 --> 00:17:34
And he got this particular
material that he was studying,

327
00:17:34 --> 00:17:37
radium bromide from his good
friend, Marie Curie, who,

328
00:17:37 --> 00:17:42
obviously, also was a leader,
really the leader in figuring

329
00:17:42 --> 00:17:45
out much of how radioactive
materials work.

330
00:17:45 --> 00:17:48
She has two Nobel
Prizes for her work in

331
00:17:48 --> 00:17:50
radioactive materials.
 

332
00:17:50 --> 00:17:53
And something that maybe many
of you think, which I know I

333
00:17:53 --> 00:17:57
always think when I hear about
radioactivity studies in the

334
00:17:57 --> 00:18:01
early 1900's, is oh, my gosh,
this sounds really dangerous,

335
00:18:01 --> 00:18:04
right, they're using radium
bromide, and this is pretty

336
00:18:04 --> 00:18:06
dangerous radioactive material.
 

337
00:18:06 --> 00:18:10
So, for those of you that don't
know radium is extremely

338
00:18:10 --> 00:18:14
radioactive, even in the range
of radioactivity, and one of

339
00:18:14 --> 00:18:17
the major problems with it is
that if it does get in your

340
00:18:17 --> 00:18:21
body, the radium is treated
as calcium in your body.

341
00:18:21 --> 00:18:23
So, you can imagine what
happens as it gets deposited

342
00:18:23 --> 00:18:28
into your bones, which is not
the ideal situation after

343
00:18:28 --> 00:18:30
a long day in the lab.
 

344
00:18:30 --> 00:18:33
So, this is really a pretty
dangerous situation that's

345
00:18:33 --> 00:18:35
always interesting
to point out.

346
00:18:35 --> 00:18:37
He got this from Marie Curie --
you can imagine they used the

347
00:18:37 --> 00:18:39
postal service, I'm not sure
how else they would have

348
00:18:39 --> 00:18:41
transferred it to each other.
 

349
00:18:41 --> 00:18:44
So, it really brings
up some issues.

350
00:18:44 --> 00:18:48
The first thing I did when I
heard that is actually look up

351
00:18:48 --> 00:18:53
to see how, in fact, Ernest
Rutherford did die in 1937, and

352
00:18:53 --> 00:18:55
you'll be happy to know, it
actually wasn't from radiation

353
00:18:55 --> 00:18:58
poisoning or from bone cancer,
so that's really good that that

354
00:18:58 --> 00:19:04
worked out okay for him, and
that he did get to, sort of

355
00:19:04 --> 00:19:08
safely, at least end his life
before the radiation ended it.

356
00:19:08 --> 00:19:11
But it's really interesting the
studies that he did do with

357
00:19:11 --> 00:19:15
radium bromide, and he was
studying the alpha particles.

358
00:19:15 --> 00:19:18
And what was known about alpha
particles at the time is that

359
00:19:18 --> 00:19:19
they were these charged
particles and that

360
00:19:19 --> 00:19:21
they were very heavy.
 

361
00:19:21 --> 00:19:24
Does anyone know more than what
Rutherford knew at the time,

362
00:19:24 --> 00:19:27
what alpha particles
actually are?

363
00:19:27 --> 00:19:28
Yeah, good.
 

364
00:19:28 --> 00:19:30
So, they're actually helium
atoms, helium ions.

365
00:19:30 --> 00:19:35
And this wasn't really
important for the studies, it

366
00:19:35 --> 00:19:37
didn't matter that didn't know
what they are, but it's nice to

367
00:19:37 --> 00:19:41
kind of know now -- that we do
know what they were using.

368
00:19:41 --> 00:19:44
And he was doing quite a
few studies with them.

369
00:19:44 --> 00:19:48
One experiment that he was
doing is detecting the number

370
00:19:48 --> 00:19:52
of particles that were being
emitted by this radium bromide

371
00:19:52 --> 00:19:54
as a rate, so he would measure
the number of particles per

372
00:19:54 --> 00:19:58
minute that the radium
bromide was emitting.

373
00:19:58 --> 00:20:03
And what he used was a detector
here, so he here could detect

374
00:20:03 --> 00:20:06
how many particles were
hitting this detector.

375
00:20:06 --> 00:20:10
He had actually developed this
detector with a postdoc by

376
00:20:10 --> 00:20:11
the name of Hans Geiger.
 

377
00:20:11 --> 00:20:14
Does that name ring a bell?
 

378
00:20:14 --> 00:20:15
STUDENT: Geiger counter.
 

379
00:20:15 --> 00:20:15
PROFESSOR: Um-hmm,
a Geiger counter.

380
00:20:15 --> 00:20:20
So, this, in fact, is my very
schematic representation

381
00:20:20 --> 00:20:21
of a Geiger counter.
 

382
00:20:21 --> 00:20:24
For those of you don't know
what that is, it's simply an

383
00:20:24 --> 00:20:29
instrument that counts
radioactive particles in the

384
00:20:29 --> 00:20:33
air, and now that you're at
MIT, you'll all have a chance

385
00:20:33 --> 00:20:35
to see one first hand, if
you're ever in any of the

386
00:20:35 --> 00:20:38
labs, especially in the
chemistry or bio labs.

387
00:20:38 --> 00:20:42
As carefully as people work
with radioactivity here, and

388
00:20:42 --> 00:20:45
using often much, much safer
radioactive materials than

389
00:20:45 --> 00:20:47
radium bromide, and using them,
and special hoods, and having

390
00:20:47 --> 00:20:50
special procedures, they still
do a lot of checking with these

391
00:20:50 --> 00:20:53
Geiger counters to make
sure everything's safe.

392
00:20:53 --> 00:20:55
You'll actually see a man
walking around with one,

393
00:20:55 --> 00:20:58
sometimes in the halls, just
kind of like this -- you hear

394
00:20:58 --> 00:21:01
that click, click, click.
 

395
00:21:01 --> 00:21:05
That's a good sound, it means
low levels of radiation.

396
00:21:05 --> 00:21:09
He'll walk by your hood, so
click by your hood -- I always

397
00:21:09 --> 00:21:11
get a little nervous when he
walked by my hood, I don't know

398
00:21:11 --> 00:21:14
why, I never worked with
radioactive material.

399
00:21:14 --> 00:21:16
But I was convinced
I'd hear the

400
00:21:16 --> 00:21:18
click-click-click-click-click,
which is what tells you

401
00:21:18 --> 00:21:20
you're in trouble.
 

402
00:21:20 --> 00:21:22
So, I've never heard the
click-click-click-click-click,

403
00:21:22 --> 00:21:25
and we might bring a Geiger
counter in here some time later

404
00:21:25 --> 00:21:28
in the semester so we can check
all of you out, and hopefully

405
00:21:28 --> 00:21:31
we won't hear any when
we do that either.

406
00:21:31 --> 00:21:33
So, one thing that he
discovered with this detector

407
00:21:33 --> 00:21:37
initially, and he was the first
to discover this, is that

408
00:21:37 --> 00:21:40
radioactive material, including
radium bromide, have a

409
00:21:40 --> 00:21:45
characteristic rate that they
emit, radioactive decay.

410
00:21:45 --> 00:21:48
So basically they're decaying
at a constant rate, which

411
00:21:48 --> 00:21:53
means, of course, that you can
figure out how old things are

412
00:21:53 --> 00:21:56
by seeing how much
they've decayed.

413
00:21:56 --> 00:21:58
So, he was really the first
person to discover you could do

414
00:21:58 --> 00:22:02
this, which was used to make
the first somewhat close

415
00:22:02 --> 00:22:04
approximation of the
age of the earth.

416
00:22:04 --> 00:22:07
So that's a pretty exciting
set of experiments he did.

417
00:22:07 --> 00:22:10
But one thing that he wanted to
do specific to understanding

418
00:22:10 --> 00:22:14
the atom, and using these alpha
particles, these heavy-charged

419
00:22:14 --> 00:22:18
particles, was to test if this
Plum Pudding model actually

420
00:22:18 --> 00:22:21
fit what he could observe.
 

421
00:22:21 --> 00:22:24
So, what he did was he first
recorded the count rate of

422
00:22:24 --> 00:22:28
radium bromide before it's
going through any kind of a

423
00:22:28 --> 00:22:31
plum pudding atom, and he found
that it had a count rate of

424
00:22:31 --> 00:22:36
132,000 alpha particles per
minute were being detected

425
00:22:36 --> 00:22:39
by this Geiger counter.
 

426
00:22:39 --> 00:22:43
He then set up a situation
where he put a very, very thin

427
00:22:43 --> 00:22:47
piece of gold foil right in
what would be in the stream

428
00:22:47 --> 00:22:49
of the alpha particles.
 

429
00:22:49 --> 00:22:53
So, it was only 10 to the
negative, 9 meters thick, so

430
00:22:53 --> 00:22:56
about one nanometer, so that's
really thin, it's thinner

431
00:22:56 --> 00:22:57
than a strand of hair.
 

432
00:22:57 --> 00:23:00
So you can imagine, we actually
don't need to think of it as a

433
00:23:00 --> 00:23:03
piece of gold foil, it might be
easier to think of it as a

434
00:23:03 --> 00:23:05
couple of layers of atoms.
 

435
00:23:05 --> 00:23:09
So basically he's trying to
put some atoms in the way

436
00:23:09 --> 00:23:12
of the alpha particle.
 

437
00:23:12 --> 00:23:17
And what he would expect is if
this Plum Pudding model is

438
00:23:17 --> 00:23:20
true, nothing's really going to
happen to the particles, right,

439
00:23:20 --> 00:23:22
they should go straight
through, because if they hit an

440
00:23:22 --> 00:23:24
electron, those are so small.
 

441
00:23:24 --> 00:23:27
We figured out the mass is so
tiny that it shouldn't really

442
00:23:27 --> 00:23:29
deflect them very much.
 

443
00:23:29 --> 00:23:33
And, of course, all that's left
is this positive pudding.

444
00:23:33 --> 00:23:35
So that's not going to
do anything either.

445
00:23:35 --> 00:23:38
And what he found when he did
this experiment, was that

446
00:23:38 --> 00:23:45
the count rate with still
132,000 counts per minute.

447
00:23:45 --> 00:23:49
So, what he could conclude thus
far was that this was really

448
00:23:49 --> 00:23:52
consistent with the
Plum Pudding model.

449
00:23:52 --> 00:23:56
All of his heavily-charged
alpha particles were going

450
00:23:56 --> 00:24:00
right through this thin
layer of gold atoms.

451
00:24:00 --> 00:24:02
So, you might think that he
would stop his experiments

452
00:24:02 --> 00:24:05
here, and maybe he would have,
but as I mentioned, he did have

453
00:24:05 --> 00:24:08
a postdoc working with him
by the name of Geiger.

454
00:24:08 --> 00:24:13
He also had an undergraduate,
we could say maybe even a UROP

455
00:24:13 --> 00:24:18
working with him, and this was
by the name of Marsden was

456
00:24:18 --> 00:24:19
the name of this UROP.
 

457
00:24:19 --> 00:24:23
And Rutherford realized, you
know I have these two people

458
00:24:23 --> 00:24:26
that are very excited to work
on this project, I don't need

459
00:24:26 --> 00:24:27
to spend time doing it.
 

460
00:24:27 --> 00:24:30
Maybe it's not the best way for
me to spend time looking to see

461
00:24:30 --> 00:24:34
if I can find any bounced-back
particles since all the

462
00:24:34 --> 00:24:35
particles are accounted for.
 

463
00:24:35 --> 00:24:38
But, you know, this
undergraduate's very eager

464
00:24:38 --> 00:24:41
to do it, let's let
him have a try.

465
00:24:41 --> 00:24:45
And something you might find in
your UROP experience is you

466
00:24:45 --> 00:24:47
have a unique advantage as an
undergraduate, which is that

467
00:24:47 --> 00:24:50
there's not a lot of pressure
to actually make a huge

468
00:24:50 --> 00:24:53
discovery or necessarily
accomplish a great amount.

469
00:24:53 --> 00:24:56
You have a little more pressure
in grad school, but sometimes

470
00:24:56 --> 00:24:59
that means when you're an
undergrad your advisor will

471
00:24:59 --> 00:25:02
decide to put you on projects
that maybe when you look at

472
00:25:02 --> 00:25:03
them seem a little bit silly.
 

473
00:25:03 --> 00:25:08
So this project was, let's see
if we can detect any alpha

474
00:25:08 --> 00:25:11
particles by making a
detector that swings around.

475
00:25:11 --> 00:25:14
So, some people might say,
why are we doing this?

476
00:25:14 --> 00:25:17
We know we started with a
132,000 alpha particles.

477
00:25:17 --> 00:25:21
We detected a 132
alpha particles.

478
00:25:21 --> 00:25:23
What are we even looking for?
 

479
00:25:23 --> 00:25:25
We have to build this whole
new detector, is this really

480
00:25:25 --> 00:25:26
the best use of my time?
 

481
00:25:26 --> 00:25:29
As an undergrad, you don't have
to worry about it, you're

482
00:25:29 --> 00:25:30
just worried about learning.
 

483
00:25:30 --> 00:25:33
You can take these big risks of
time, and if at the end of the

484
00:25:33 --> 00:25:35
day there's nothing to detect,
you still know how to

485
00:25:35 --> 00:25:37
build a detector.
 

486
00:25:37 --> 00:25:40
So, keep that in mind if you're
not over-the-top excited about

487
00:25:40 --> 00:25:42
the prospects of some
of your research.

488
00:25:42 --> 00:25:43
You might be surprised
at what you find out.

489
00:25:43 --> 00:25:47
And this is exactly what
happened with Marsden who

490
00:25:47 --> 00:25:50
discovered that when he shot
the alpha particles at the gold

491
00:25:50 --> 00:25:55
foil, he detected something on
his detector that click, click,

492
00:25:55 --> 00:25:59
click went a little bit faster.
 

493
00:25:59 --> 00:26:01
So, what he detected was
that there were 20 alpha

494
00:26:01 --> 00:26:03
particles per minute.
 

495
00:26:03 --> 00:26:05
Does that sound significant?
 

496
00:26:05 --> 00:26:08
It depends, right?
 

497
00:26:08 --> 00:26:11
So hopefully, the first
experiment he did, which I

498
00:26:11 --> 00:26:13
know that they certainly
did do was maybe it's just

499
00:26:13 --> 00:26:15
background noise, right?
 

500
00:26:15 --> 00:26:18
So, they took away that gold
foil and said is just the

501
00:26:18 --> 00:26:20
alpha particles hitting
it some other way?

502
00:26:20 --> 00:26:21
And no, it wasn't.
 

503
00:26:21 --> 00:26:24
When he took away the gold
foil, the count rate

504
00:26:24 --> 00:26:26
went down to zero.
 

505
00:26:26 --> 00:26:31
If he switched from gold to
let's say iron, he also tried

506
00:26:31 --> 00:26:34
platinum, a number of different
foils, he found that they count

507
00:26:34 --> 00:26:38
rate, it still was 20 alpha
particles per minute.

508
00:26:38 --> 00:26:41
So, this is an absolutely
outstanding discovery, even

509
00:26:41 --> 00:26:44
though, if we think about
it, what is the probability

510
00:26:44 --> 00:26:46
that this happened, how
often did this happen?

511
00:26:46 --> 00:26:48
It actually almost
happened not at all.

512
00:26:48 --> 00:26:51
We can figure out exactly what
the probability of this

513
00:26:51 --> 00:26:54
backscattering was just by
dividing the count rate of the

514
00:26:54 --> 00:26:57
number particle that were
backscattered divided by

515
00:26:57 --> 00:27:00
the count rate of the
incident particles.

516
00:27:00 --> 00:27:03
So essentially, we just
have 20, and our 20 is

517
00:27:03 --> 00:27:06
divided by 132,000.
 

518
00:27:06 --> 00:27:10
So, we end up with a not so
large probability of 2 times

519
00:27:10 --> 00:27:14
10 to the negative 4.
 

520
00:27:14 --> 00:27:17
But still, we can't even
overstate how exciting

521
00:27:17 --> 00:27:19
this discovery was.
 

522
00:27:19 --> 00:27:22
Rutherford, the advisor here,
he had a lot of good things

523
00:27:22 --> 00:27:25
happen in his life,
as I mentioned.

524
00:27:25 --> 00:27:28
He was the person responsible
for being able to first

525
00:27:28 --> 00:27:29
date the age of our earth.
 

526
00:27:29 --> 00:27:31
That's a pretty nice thing.
 

527
00:27:31 --> 00:27:34
He was also married, he had a
child, which I hear is very

528
00:27:34 --> 00:27:36
nice, very exciting, also.
 

529
00:27:36 --> 00:27:41
But yet, when he saw this one
single experiment from this

530
00:27:41 --> 00:27:46
undergraduate, he described
this as the most incredible

531
00:27:46 --> 00:27:50
event that had ever happened
to him in his life.

532
00:27:50 --> 00:27:54
So, this was a pretty big deal.
 

533
00:27:54 --> 00:27:57
We won't tell his daughter.
 

534
00:27:57 --> 00:28:01
And he gave a very good analogy
in saying, "It was almost as

535
00:28:01 --> 00:28:05
incredible as if you'd fired a
15 inch shell at a piece

536
00:28:05 --> 00:28:09
of tissue paper, and it
came back and hit you."

537
00:28:09 --> 00:28:11
And that really illustrates
what's happening here, because

538
00:28:11 --> 00:28:19
if we think of the Plum Pudding
model, it's essentially this

539
00:28:19 --> 00:28:22
very thin film, right, there's
nothing that should hit if we

540
00:28:22 --> 00:28:24
send alpha particles
through it.

541
00:28:24 --> 00:28:27
But what we actually have is
that something's bouncing back.

542
00:28:27 --> 00:28:30
So, what happened is Rutherford
needed to come up with a new

543
00:28:30 --> 00:28:35
model for the atom with several
interpretations that came out

544
00:28:35 --> 00:28:39
of these experiments, and some
of these interpretations were

545
00:28:39 --> 00:28:42
that, of course, we now know
that these gold atoms, they

546
00:28:42 --> 00:28:45
must be mostly empty, and the
reason that we know that they

547
00:28:45 --> 00:28:50
must be mostly empty is because
all but 20 of these 132

548
00:28:50 --> 00:28:53
particles went all
the way through.

549
00:28:53 --> 00:28:55
So they weren't hitting
anything, we're dealing

550
00:28:55 --> 00:28:57
with mostly empty space.
 

551
00:28:57 --> 00:29:02
But he also realized that when
they did hit something, what

552
00:29:02 --> 00:29:07
they hit what unbelievably
massive, but also that that

553
00:29:07 --> 00:29:11
mass was concentrated into
this very, very small space.

554
00:29:11 --> 00:29:13
So eventually, this is
what we have come to call

555
00:29:13 --> 00:29:15
the nucleus of an atom.
 

556
00:29:15 --> 00:29:18
And the nucleus name was used
as an analogy to the nucleus of

557
00:29:18 --> 00:29:22
a cell, so in some ways that
makes it easier to see the

558
00:29:22 --> 00:29:24
connection, but I think it can
also be a little bit confusing

559
00:29:24 --> 00:29:28
for maybe 7th graders that are
learning both at the same time,

560
00:29:28 --> 00:29:31
that this nucleus acts very
different from a nucleus in a

561
00:29:31 --> 00:29:33
cell, although, of course,
there many of them in

562
00:29:33 --> 00:29:36
the nucleus of a cell.
 

563
00:29:36 --> 00:29:39
There are some other things
that Rutherford was

564
00:29:39 --> 00:29:40
able to figure out.
 

565
00:29:40 --> 00:29:43
One is the diameter of the
nucleus, and that turns

566
00:29:43 --> 00:29:47
out to be 10 to the
negative 14 meters.

567
00:29:47 --> 00:29:51
If we think about the size of a
typical cell -- excuse me, now

568
00:29:51 --> 00:29:52
I'm getting confused
about nuclei.

569
00:29:52 --> 00:29:55
If we think of the size of a
typical atom, we would say

570
00:29:55 --> 00:29:58
that would be about 10 to
the negative 10 meters.

571
00:29:58 --> 00:30:02
So, we can see the diameter
of a nucleus is absolutely

572
00:30:02 --> 00:30:05
smaller, really concentrating
that mass into a

573
00:30:05 --> 00:30:06
very small space.
 

574
00:30:06 --> 00:30:09
So, you might be asking how did
he actually figure that out?

575
00:30:09 --> 00:30:11
We'll do the
calculation ourselves.

576
00:30:11 --> 00:30:14
In fact, we'll do the whole
experiment ourselves, minus the

577
00:30:14 --> 00:30:17
radioactivity in just a minute,
so we'll be able to answer

578
00:30:17 --> 00:30:19
that question for you.
 

579
00:30:19 --> 00:30:21
He also figured out
that the charge of the

580
00:30:21 --> 00:30:24
nucleus was a plus ze.
 

581
00:30:24 --> 00:30:27
This makes sense intuitively
as well, because z is

582
00:30:27 --> 00:30:29
just the atomic number.
 

583
00:30:29 --> 00:30:32
So, let's say we have an atomic
number of 3, that means we have

584
00:30:32 --> 00:30:36
3 electrons, so we better hope
to get our neutral atom that we

585
00:30:36 --> 00:30:40
have a charge of plus
3 in the nucleus.

586
00:30:40 --> 00:30:42
So, I mentioned at the
beginning, while he was working

587
00:30:42 --> 00:30:47
with this radium bromide, that
I was very relieved to see that

588
00:30:47 --> 00:30:50
it did not kill him to
do these experiments.

589
00:30:50 --> 00:30:53
However, I think I will share
with you that the cause of his

590
00:30:53 --> 00:30:57
death was, in fact, related to
his research here, even

591
00:30:57 --> 00:30:58
though it was a little
more tangled up.

592
00:30:58 --> 00:31:01
So, what happened, of course,
after he discovered the

593
00:31:01 --> 00:31:04
nucleus, not surprising, he won
a Nobel Prize for this -- I

594
00:31:04 --> 00:31:06
would hope that he would.
 

595
00:31:06 --> 00:31:09
And in addition to winning a
Nobel Prize, he was also

596
00:31:09 --> 00:31:12
knighted, which was a nice
bonus for someone born in

597
00:31:12 --> 00:31:14
England, that's a great
thing to happen to them.

598
00:31:14 --> 00:31:17
The problem that he ran into is
at some point a little bit

599
00:31:17 --> 00:31:20
later in his life, he had a
hernia which was a pretty

600
00:31:20 --> 00:31:23
standard case, but what he was
going to need was an

601
00:31:23 --> 00:31:24
operation on it.
 

602
00:31:24 --> 00:31:28
And the glitch came that at
least at the time, if you were

603
00:31:28 --> 00:31:34
a knight, you could only be
operated on by a doctor

604
00:31:34 --> 00:31:36
that was also titled.
 

605
00:31:36 --> 00:31:39
So, Rutherford had a little bit
of waiting to do for that

606
00:31:39 --> 00:31:43
doctor to show up, and it turns
out the wait was too long, and

607
00:31:43 --> 00:31:46
he actually passed away because
he discovered the nucleus and

608
00:31:46 --> 00:31:48
got a Noble Prize and
became knighted.

609
00:31:48 --> 00:31:51
So, it's still dangerous.
 

610
00:31:51 --> 00:31:54
If that opportunity comes up
for you, maybe you want to

611
00:31:54 --> 00:31:56
check into the policies of
how that works with the

612
00:31:56 --> 00:31:58
doctor situation now.
 

613
00:31:58 --> 00:32:01
Hopefully they've cleared
it up a little bit.

614
00:32:01 --> 00:32:04
So, what we want to do now is
see if we can understand how

615
00:32:04 --> 00:32:06
this backscattering
experiment worked.

616
00:32:06 --> 00:32:10
So, we will do our own
backscattering experiment.

617
00:32:10 --> 00:32:12
And we'll ask you to
imagine a few things.

618
00:32:12 --> 00:32:18
First is that we have this
mono layer of gold particles.

619
00:32:18 --> 00:32:23
So let's see if Professor
Drennan is able to

620
00:32:23 --> 00:32:24
help us out here.
 

621
00:32:24 --> 00:32:32
Oh, great.
 

622
00:32:32 --> 00:32:35
So, that is her daughter, Sam
that you see strapped to the

623
00:32:35 --> 00:32:45
chest, and Dr. Patti Christie
helping us out here.

624
00:32:45 --> 00:32:45
All right.
 

625
00:32:45 --> 00:32:48
So, we'll move this up to the
front in just a minute, but I'm

626
00:32:48 --> 00:32:50
going to explain how this
experiment works, and we'll do

627
00:32:50 --> 00:32:54
the calculation first before
the excitement breaks out.

628
00:32:54 --> 00:32:57
But I'm sure you can easily see
how these styrofoam balls

629
00:32:57 --> 00:33:01
could, in fact, be a mono
layer of gold nuclei.

630
00:33:01 --> 00:33:07
We have 266, as some of you
might know who saw me counting

631
00:33:07 --> 00:33:09
ping-pong balls the other
day in office hours.

632
00:33:09 --> 00:33:13
We have 266 ping-pong balls,
and we need someone, hopefully

633
00:33:13 --> 00:33:16
you, to be some radioactive
material that are going to be

634
00:33:16 --> 00:33:19
emitting these ping-pong balls.
 

635
00:33:19 --> 00:33:21
And when the time comes, in
just a minute, I'll ask the TAs

636
00:33:21 --> 00:33:26
to come down and hand these out
very quickly to you, so we

637
00:33:26 --> 00:33:27
can do this experiment.
 

638
00:33:27 --> 00:33:31
But first, let's go through how
we're going to determine what

639
00:33:31 --> 00:33:34
Rutherford determined, which
was he was interested in

640
00:33:34 --> 00:33:38
knowing, which we said what the
diameter of the nuclei were.

641
00:33:38 --> 00:33:40
So, we're going to do the same
thing and figure out the

642
00:33:40 --> 00:33:51
diameter of these styrofoam
balls here, and we can do it

643
00:33:51 --> 00:33:57
by using the relationship
of how many backscatter.

644
00:33:57 --> 00:34:00
So, if we think about the
probability of backscattering,

645
00:34:00 --> 00:34:04
which is the exact same thing
that we saw Rutherford

646
00:34:04 --> 00:34:08
calculate, using the 20
divided by 132,000.

647
00:34:08 --> 00:34:11
But in our case, the
probability of backscattering

648
00:34:11 --> 00:34:20
is going to be the number of
balls that backscatter, and

649
00:34:20 --> 00:34:26
that's going to be divided by
the total number of

650
00:34:26 --> 00:34:26
ping-pong balls.
 

651
00:34:26 --> 00:34:28
So, do you remember
what that was?

652
00:34:28 --> 00:34:30
STUDENT: 266.
 

653
00:34:30 --> 00:34:31
PROFESSOR: 266.
 

654
00:34:31 --> 00:34:32
Good information retention.
 

655
00:34:32 --> 00:34:33
All right.
 

656
00:34:33 --> 00:34:36
So, we have the
probability here.

657
00:34:36 --> 00:34:41
So, in terms of the number of
balls scattered over the total,

658
00:34:41 --> 00:34:47
we can also relate the
probability to the area of all

659
00:34:47 --> 00:34:56
of those nuclei divided by the
total area that the

660
00:34:56 --> 00:34:59
atoms take up.
 

661
00:34:59 --> 00:35:02
Right, this makes a lot of
sense, because if the entire

662
00:35:02 --> 00:35:05
atom was made up of nuclei,
then we would have 100%

663
00:35:05 --> 00:35:09
probability of hitting one of
these nuclei and having

664
00:35:09 --> 00:35:10
things bounce back.
 

665
00:35:10 --> 00:35:14
So, here we have the area of
the nuclei we'll figure out

666
00:35:14 --> 00:35:17
adding those all together
versus the space of all of

667
00:35:17 --> 00:35:18
the atoms put together.
 

668
00:35:18 --> 00:35:22
So, not only did Professor
Sayer, who's in the Chemistry

669
00:35:22 --> 00:35:25
Department who put together
this contraption for all of

670
00:35:25 --> 00:35:31
you, not only did she magnify
the size of these gold nuclei,

671
00:35:31 --> 00:35:34
but she actually had to smoosh
all of these atoms closer

672
00:35:34 --> 00:35:35
together then they
normally would be.

673
00:35:35 --> 00:35:39
If, in fact, a gold nucleus was
this size here, we would need

674
00:35:39 --> 00:35:42
to use another lecture hall in
order to find a place to put

675
00:35:42 --> 00:35:45
this nucleus right here.
 

676
00:35:45 --> 00:35:47
This is a little bit of a
tricky experiment, so we

677
00:35:47 --> 00:35:49
decided we'll just smoosh it
all in, and we'll actually be

678
00:35:49 --> 00:35:52
able to account for it, because
we'll take into account the

679
00:35:52 --> 00:35:56
area of all of those atoms.
 

680
00:35:56 --> 00:35:58
I think this board does
not like to go by itself.

681
00:35:58 --> 00:35:59
All right.
 

682
00:35:59 --> 00:36:04
So we can figure out what that
is, the area of all of the

683
00:36:04 --> 00:36:12
nuclei is going to be the
number of nuclei times the area

684
00:36:12 --> 00:36:16
per nucleus, and we're going to
talk about the cross-section

685
00:36:16 --> 00:36:20
here to keep it simple.
 

686
00:36:20 --> 00:36:25
And all of that is divided
by the area of the

687
00:36:25 --> 00:36:26
atoms, which is 1 .
 

688
00:36:26 --> 00:36:33
39 meters squared, measuring
that space there.

689
00:36:33 --> 00:36:36
So, the number of nuclei, if
we were to sit and count

690
00:36:36 --> 00:36:41
these as well, is 119.
 

691
00:36:41 --> 00:36:47
So, we'll multiply that by just
pi, r squared, to get that

692
00:36:47 --> 00:36:50
cross-section, and divide
all of that by 1 .

693
00:36:50 --> 00:36:54
39 meters squared.
 

694
00:36:54 --> 00:36:58
So, what we have here is a
relationship that can tell us

695
00:36:58 --> 00:37:01
what the probability of
backscattering is, but what we

696
00:37:01 --> 00:37:05
want to pull out, since we can
experimentally measure what the

697
00:37:05 --> 00:37:08
probability is, what we need to
pull out is the radius or the

698
00:37:08 --> 00:37:15
diameter of these nuclei, so we
can just, instead of solving

699
00:37:15 --> 00:37:19
for p, we can switch it around
and solve for the radius.

700
00:37:19 --> 00:37:21
So, that's going to be equal
to the probability raised

701
00:37:21 --> 00:37:21
to the 1/2 times 6 .
 

702
00:37:21 --> 00:37:28
098 times 10 to the
negative 2 meters.

703
00:37:28 --> 00:37:35
So, actually, just for
discussion sake, it makes a

704
00:37:35 --> 00:37:39
little more sense for us to
talk about the diameter, so

705
00:37:39 --> 00:37:41
that's just twice the radius.
 

706
00:37:41 --> 00:37:44
So, once we figure out what our
probability of backscattering

707
00:37:44 --> 00:37:48
is, we'll just raise that
to the 1/2, and we'll

708
00:37:48 --> 00:37:50
multiply that by 12 .
 

709
00:37:50 --> 00:37:54
20 centimeters.
 

710
00:37:54 --> 00:37:54
All right.
 

711
00:37:54 --> 00:37:57
So now all we have to do is
figure out this probability

712
00:37:57 --> 00:37:58
of backscattering.
 

713
00:37:58 --> 00:38:02
We know we need to divide by
266, but what we need you to

714
00:38:02 --> 00:38:06
help us with is to figure out
this top number here and see

715
00:38:06 --> 00:38:08
how many particles are
going to backscatter.

716
00:38:08 --> 00:38:14
So, if the TAs can come up
and quickly hand out 1

717
00:38:14 --> 00:38:21
particle to everyone.
 

718
00:38:21 --> 00:38:25
And a few people will need to
throw 2, if you feel like you

719
00:38:25 --> 00:38:31
have particularly good aim.
 

720
00:38:31 --> 00:38:43
PROFESSOR: So, as you're
getting your ping-pong balls

721
00:38:43 --> 00:38:46
-- do not throw them yet.
 

722
00:38:46 --> 00:38:49
Let me explain to you
what constitutes a

723
00:38:49 --> 00:38:49
backscatter event.
 

724
00:38:49 --> 00:38:54
So, it'll be considered a
backscatter event if your

725
00:38:54 --> 00:38:58
ping-pong ball hits
one of the nuclei.

726
00:38:58 --> 00:39:00
It's not going to be a
backscatter event if your

727
00:39:00 --> 00:39:04
ping-pong ball hits the
frame or these strings,

728
00:39:04 --> 00:39:05
or the top part.
 

729
00:39:05 --> 00:39:09
So, in a few minutes, not now,
we're going to ask you to stand

730
00:39:09 --> 00:39:12
up, and you can kind of come
over more toward the center of

731
00:39:12 --> 00:39:16
the room if you want, and aim
your ping-pong ball at the

732
00:39:16 --> 00:39:20
lattice here, follow the
ping-pong ball with your eye,

733
00:39:20 --> 00:39:24
and discover, watching it,
whether it's a backscatter --

734
00:39:24 --> 00:39:28
it hits one of the nuclei and
bounces back towards you, or if

735
00:39:28 --> 00:39:31
it goes through, and also if
your ping-pong ball doesn't

736
00:39:31 --> 00:39:36
land anywhere in the vicinity
of this at all, then

737
00:39:36 --> 00:39:37
keep that in mind.
 

738
00:39:37 --> 00:39:40
And then at the end of the
experiment we'll ask you what

739
00:39:40 --> 00:39:42
happened to your ping-pong
ball, and you'll let us know,

740
00:39:42 --> 00:39:46
and we can calculate the
number of backscatter events.

741
00:39:46 --> 00:39:50
Are there any questions
before we get started?

742
00:39:50 --> 00:39:52
Raise your hand if you
don't if you don't have

743
00:39:52 --> 00:40:12
a ping-pong ball yet.
 

744
00:40:12 --> 00:40:20
Any questions before
we get started?

745
00:40:20 --> 00:40:21
All right.
 

746
00:40:21 --> 00:40:23
So, we'll come around
and get ping-pong balls

747
00:40:23 --> 00:40:24
to the rest of you.
 

748
00:40:24 --> 00:40:26
Those of you who have your
ping-pong balls can now

749
00:40:26 --> 00:41:25
begin the experiment.
 

750
00:41:25 --> 00:41:25
[EXPERIMENTING]
 

751
00:41:25 --> 00:41:25
PROFESSOR: All right.
 

752
00:41:25 --> 00:41:26
Any last shots?
 

753
00:41:26 --> 00:41:36
There we go.
 

754
00:41:36 --> 00:41:37
All right.
 

755
00:41:37 --> 00:41:39
So, it looks like we were a
little bit successful, I

756
00:41:39 --> 00:41:42
saw some backbouncing.
 

757
00:41:42 --> 00:41:46
We were going to have a clicker
slide on how many bounced back,

758
00:41:46 --> 00:41:48
but it looks like we're
having a little technical

759
00:41:48 --> 00:41:49
difficulty with that.
 

760
00:41:49 --> 00:41:51
So, what I'll ask is can you
stand up if you had your

761
00:41:51 --> 00:41:58
particle bounce back?
 

762
00:41:58 --> 00:42:01
All right, so let's count
how many we have here.

763
00:42:01 --> 00:42:04
So, 13 backscattered.
 

764
00:42:04 --> 00:42:24
TAs, if you can maybe pick up
these ping-pong balls for me.

765
00:42:24 --> 00:42:25
I'm sure it would be
very amusing if I fell,

766
00:42:25 --> 00:42:27
but I'd rather not.
 

767
00:42:27 --> 00:42:32
All right, so, we have
13 divided by 266.

768
00:42:32 --> 00:42:40
All right, MIT students, who
has a calculator on them?

769
00:42:40 --> 00:42:42
Actually, I should probably
do it as well, so I know

770
00:42:42 --> 00:42:49
I'm hearing correctly.
 

771
00:42:49 --> 00:42:51
So, are you getting 0 .
 

772
00:42:51 --> 00:42:56
0489 or so?
 

773
00:42:56 --> 00:42:57
All right.
 

774
00:42:57 --> 00:42:59
So, we've got our probability.
 

775
00:42:59 --> 00:43:02
We can go ahead and plug that
in, take the square root

776
00:43:02 --> 00:43:06
of it, multiply it by 12 .
 

777
00:43:06 --> 00:43:08
2.
 

778
00:43:08 --> 00:43:15
What are you getting
for your diameters?

779
00:43:15 --> 00:43:16
Yup, that's what I got, too.
 

780
00:43:16 --> 00:43:16
All right.
 

781
00:43:16 --> 00:43:20
So, we have 2 .
 

782
00:43:20 --> 00:43:26
70 for our diameter, and
that's in centimeters.

783
00:43:26 --> 00:43:28
So, we actually did a
pretty good job here.

784
00:43:28 --> 00:43:31
It turns out that the
diameter is actually 2 .

785
00:43:31 --> 00:43:33
5 centimeters.
 

786
00:43:33 --> 00:43:37
So, good job, experiment well
done, plus we were not exposed

787
00:43:37 --> 00:43:41
to radioactivity,
which is a bonus.

788
00:43:41 --> 00:43:45
So, this is exactly how
Rutherford did discover that

789
00:43:45 --> 00:43:52
these particles were present
and made this new model for the

790
00:43:52 --> 00:43:56
atom that we now know has both
a nucleus, and we know the

791
00:43:56 --> 00:43:58
size, and also has electrons.
 

792
00:43:58 --> 00:44:01
So, to finish up today, we
won't get through all of it.

793
00:44:01 --> 00:44:05
But the next thing we can
actually talk about is now that

794
00:44:05 --> 00:44:09
we know we have an atom that
has a nucleus, let's say

795
00:44:09 --> 00:44:12
somewhere in the center, and it
has electrons around it,

796
00:44:12 --> 00:44:16
thinking on our most simple
example, which is hydrogen, we

797
00:44:16 --> 00:44:20
have a nucleus and an electron
that have to hang together in

798
00:44:20 --> 00:44:23
the atom in some way, and we
need to think about well how

799
00:44:23 --> 00:44:25
can we describe how atoms
behave, and specifically, how

800
00:44:25 --> 00:44:32
do we describe how any single
atom stays together where the

801
00:44:32 --> 00:44:34
two are associated, but at the
same time they don't

802
00:44:34 --> 00:44:37
immediately collapse
into themselves.

803
00:44:37 --> 00:44:41
So, what we can do is try using
the classical description

804
00:44:41 --> 00:44:44
of the atom and see
where this takes us.

805
00:44:44 --> 00:44:48
So, if we think about the force
that occurs between a

806
00:44:48 --> 00:44:52
positively and a negatively
charged particle, what we have

807
00:44:52 --> 00:44:56
is essentially a Coulomb force,
so we can describe this as

808
00:44:56 --> 00:44:59
a force of attraction.
 

809
00:44:59 --> 00:45:03
We can use the Coulomb force
law to explain this where we

810
00:45:03 --> 00:45:06
can describe the force
as a function of r.

811
00:45:06 --> 00:45:08
So, let's think about
what we're saying here.

812
00:45:08 --> 00:45:11
We're describing the force
that's holding these two

813
00:45:11 --> 00:45:16
particles together, and it's
related to the charge of each

814
00:45:16 --> 00:45:20
of the particles, where e is
the absolute value of

815
00:45:20 --> 00:45:22
an electron's charge.
 

816
00:45:22 --> 00:45:25
So, an electron has a charge of
negative e, we've written here,

817
00:45:25 --> 00:45:28
and the nucleus has a
charge of positive e.

818
00:45:28 --> 00:45:32
And then we have r, which
is simply the distance

819
00:45:32 --> 00:45:33
between the two charges.
 

820
00:45:33 --> 00:45:37
And what we see is that the
force is inversely related

821
00:45:37 --> 00:45:41
to the distance between
the two charges.

822
00:45:41 --> 00:45:43
And we can simplify this
expression as saying negative

823
00:45:43 --> 00:45:47
e squared over 4 pi,
epsilon nought r squared.

824
00:45:47 --> 00:45:51
Epsilon nought is a constant,
it's something you might

825
00:45:51 --> 00:45:52
see in physics as well.
 

826
00:45:52 --> 00:45:55
Essentially for our purposes
here, you can just think of

827
00:45:55 --> 00:45:57
it as a conversion factor.
 

828
00:45:57 --> 00:46:00
What we need to do is get rid
of the Coulomb tag that we have

829
00:46:00 --> 00:46:04
-- that's how we measure our
electron charges -- charge, and

830
00:46:04 --> 00:46:09
so we use this epsilon nought
quite often, this permativity

831
00:46:09 --> 00:46:12
constant of a vacuum to
make that conversion.

832
00:46:12 --> 00:46:18
And I'll just point out here
also, this is a conversion

833
00:46:18 --> 00:46:21
factor you'll use quite
frequently -- many of you,

834
00:46:21 --> 00:46:23
quite on accident, will
memorize it as you use

835
00:46:23 --> 00:46:25
it over and over again.
 

836
00:46:25 --> 00:46:27
But I do want to point out that
you don't have to memorize it

837
00:46:27 --> 00:46:31
for any exams in this class, we
will give you a sheet that has

838
00:46:31 --> 00:46:33
all the needed constants that
you're going to use on there,

839
00:46:33 --> 00:46:38
so save up that brain space
for other information. ah

840
00:46:38 --> 00:46:42
So, we can use Coulomb's force
law, and we can think about

841
00:46:42 --> 00:46:43
these different scenarios.
 

842
00:46:43 --> 00:46:46
So, when you come in on Monday,
we're going to start off, you

843
00:46:46 --> 00:46:48
can think for the weekend --
you probably only need to think

844
00:46:48 --> 00:46:52
for a second about what happens
when r goes to infinity, but

845
00:46:52 --> 00:46:54
that's where we'll
start on Monday.

846
00:46:54 --> 00:46:58
And let me just suggest to all
of you also, that you get those

847
00:46:58 --> 00:46:59
problem sets started
this weekend.

848
00:46:59 --> 00:47:03
You should absolutely finish,
at least through part a this

849
00:47:03 --> 00:47:06
weekend, and save part
b for next week.

850
00:47:06 --> 00:47:08
So, have a great weekend.
 

851
00:47:08 --> 00:47:09