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SPEAKER: The following content
is provided under a Creative

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Commons License.

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PROFESSOR: OK.

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OK.

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Settle down.

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Settle down.

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Settle down.

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So the weekend doesn't begin
until after the 3.091 lecture.

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OK.

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A couple of announcements.

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Tuesday, Quiz 3 based
on Homework 3.

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The final exam has
been scheduled.

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In fact, all the finals are
scheduled now, so please

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consult the Registrar's
listing.

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The celebration of celebrations,
the 3.091 final

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exam, will be Tuesday, 15th of
December in the morning, 9:00

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am to 12:00 noon over in the
Johnson Athletic Center.

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So I urge you to go through the
final exam schedule and

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then make your travel plans when
you know what your last

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obligation is.

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And book them soon, because
we've got about a quarter of a

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million students in the Boston
area and the semesters all

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come to a close within a very
narrow time window, and

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everybody's trying to get
through a wormhole called

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Logan Airport.

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So you want to be ready.

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Do not try to leave town before
you've met all of your

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obligations.

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You can't leave before you've
finished all of your finals.

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But you know what they are now,
so call your travel agent

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or make your internet booking.

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And an announcement for
Professor Paul's section.

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Owing to the holiday on Monday,
he's going to have

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office hours from noon
to 1:30 today.

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So if you're in Professor Paul's
section, you'd like to

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catch up with him, noon
till 1:30 today.

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All right.

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Let's get to the lesson.

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The last day we started looking
at octet stability,

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and we looked at octet stability
and what it means in

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terms of shell filling and some
sweet spot in energy with

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respect to reactivity.

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And a filled shell leaves
us with this electron

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configuration, ns2np6 for
n greater than 1.

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In the case of n equals 1,
there's just ns2 for helium.

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Otherwise, ns2np6.

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2 plus 6 is 8.

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There's the octet stability.

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It's observed trivially
in noble gases.

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And then we saw that
it can also be

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observed in certain ions.

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And how do we get to
octet stability?

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Electron transfer.

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And here's the prototypical
reaction.

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I like this.

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This is very iconic.

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It puts it in broad terms. The
marriage of an electron donor

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with an electron acceptor leads
to the formation of a

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cation and an anion, thanks to
electron transfer from the

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donor to the acceptor.

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It doesn't end there, though.

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You have cations and anions in
the gas phase and they're

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attracted to one another
by coulombic forces, or

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electrostatic forces, and that
leads to ionic bonding.

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And today I want to go deeper
into it and study the

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energetics of ion-pair
formation.

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So let's do it.

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And what I'm going to do is
study this with reference to

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an example of sodium chloride.

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So we will go through the
energetics of sodium chloride,

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which we know is going
to exist as

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Na plus and Cl minus--

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sodium being the electron donor
and chlorine being the

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electron acceptor.

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So what I'm going to do is show
you a plot of energy as a

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function of separation.

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So you're going to have
to be pluralistic

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here in your ideas.

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So, for example, if I wrote this
word by itself you don't

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know if I'm saying lead or I'm
talking about the metal lead.

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The only way you know
is in context.

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And so you have to know
in context here.

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So r is not the radius
of the atom.

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In this case it's the symbol.

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And I'm using this symbol
not to confuse you.

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This is what professionals
use.

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So if you go to the text and the
literature you'll see r.

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This is the interionic
separation, and it's

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determined nucleus to nucleus.

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So I'm going to put a sodium
ion at the origin.

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This is the origin.

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Energy is on the ordinate.

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So I'm going to model this
as a hard sphere.

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So this is sodium ion,
Na plus, and it's

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got some finite radius.

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And its radius, I'm going
to call it r-plus.

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That's the radius
of the cation.

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And next to sodium I'm going
to put the chloride anion.

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And it's bigger.

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It's bigger.

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It's not to scale,
but it's bigger.

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So this is chloride, the
Cl minus, and it has

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its radius, rCL minus.

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And then the interionic
separation is measured from

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the sodium nucleus to the
chloride nucleus, and it's

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given the symbol r0.

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That's the interionic
separation.

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And we could we write that r0,
in fact, is strictly r-plus

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plus r-minus because we're using
a hard sphere model.

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So there's no shrinkage
when the two touch.

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So that makes sense.

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Now what I want to do is
calculate the energy here.

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The only energy that we have
here is electrostatic.

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So we're going to start and say,
imagine if we had these

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two ions separated by infinite
distance and we brought them

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to a separation of r0.

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How much electrostatic energy
would be stored there?

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So I can write that as E,
and I'm going to call it

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attractive.

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There's a force that attracts
these two ions together, and

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that's given by Coulomb's Law.

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So that's the product
q1 q2 over 4 pi

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epsilon0r, in general.

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I'm making this as a function
of r and then we're going to

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figure out how to get to r0.

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Let's put a little
ledge in here.

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So q1, I'm going to make
that the sodium just

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for grins and chuckles.

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So q1 is equal to the z, the
valence on the sodium, times

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the charge, the elementary
charge.

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So the charge on the sodium is
plus 1-- so it's plus 1e--

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and q2 is going to equal
the charge on the

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chloride times e.

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And in this case the chloride
ion is negative 1, so q2 is

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minus e, q1 is plus e.

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Now if instead I were doing
magnesium oxide, magnesium

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would be plus 2, oxide
would be minus 2.

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So that's where the charge on
the ion comes into play.

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So we can put that in here and
will make this z-plus times e,

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00:07:16,350 --> 00:07:18,520
z-minus times e.

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So there's q1 q2 over
4 pi epsilon0 r.

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And in this case, for sodium
chloride, this is plus 1 times

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minus 1 is minus 1 e squared
over 4 pi epsilon0 r.

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So this is a function of r.

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This e is 1/r.

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That's the hyperbole, and
I can draw that here.

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So it's going to look
something like this.

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All right?

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It's going to be a
right like this.

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Good.

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So that's the attractive
force.

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Now how do we avoid the ions
just blending together?

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Why do they stop at r0?

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What puts the brakes on
the coulombic force?

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Ah!

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For that we have to look at the
fine structure of sodium.

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So let's look at the fine
structure of sodium.

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So sodium is net
charge plus 1.

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But sodium more properly, if
I go to the next level of

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structure, is really 11 protons
in the nucleus and

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it's got electrons around it--

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in total, 10 electrons.

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So it's net charge is
plus 1, all right?

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Now if I'm way over here and
I look at sodium I just see

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something of charge plus 1.

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And, in fact, I could model
sodium as just a point charge,

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a plus 1, and do all the
electrostatics and I would be

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perfectly accurate
in my estimation.

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But as I get closer I see
there's fine structure.

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It's like so many other
things in life.

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You know, from a distance it
looks really good, and you get

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00:09:02,885 --> 00:09:05,190
up close you go, eww.

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00:09:05,190 --> 00:09:06,360
[LAUGHTER]

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PROFESSOR: I'm not going to
mention any names, all right?

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But it's Friday.

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Be careful.

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So as I get up closer I realize
that it's plus 1, but

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the plus 1 is plus 11 mediated
by minus 10.

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So when things start getting
close together this exterior

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of negative charge becomes
manifest, palpable.

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00:09:30,350 --> 00:09:32,090
So let's look at the chlorine.

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The chlorine's coming,
sees plus 1, plus 1.

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It starts getting closer
and closer.

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And now what happens?

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00:09:37,680 --> 00:09:41,360
The negative electronic
configuration on the outside

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00:09:41,360 --> 00:09:45,190
of sodium is interacting with
the negative electronic

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00:09:45,190 --> 00:09:48,270
configuration on chlorine, and
the result is you have

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00:09:48,270 --> 00:09:50,540
electron-electron repulsion.

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00:09:50,540 --> 00:09:55,200
And we've got an equation for
that, and that's given by E

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00:09:55,200 --> 00:10:02,240
repulsion is equal to some
constant b over r to the n.

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00:10:02,240 --> 00:10:07,890
And this n is called
the Born exponent.

197
00:10:07,890 --> 00:10:09,630
It's not the quantum number.

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00:10:09,630 --> 00:10:12,680
So r today means interionic
separation,

199
00:10:12,680 --> 00:10:14,450
n means Born exponent.

200
00:10:14,450 --> 00:10:17,800
And you have to determine it
by experiment and the value

201
00:10:17,800 --> 00:10:22,760
lies between 6 and 12.

202
00:10:22,760 --> 00:10:25,210
And we have to determine
b by experiment.

203
00:10:25,210 --> 00:10:26,750
So let's say this thing's
got a-- pick a

204
00:10:26,750 --> 00:10:27,410
number in the middle.

205
00:10:27,410 --> 00:10:29,520
Say it's 8.

206
00:10:29,520 --> 00:10:33,610
So let's plot r to the eighth.

207
00:10:33,610 --> 00:10:37,680
So that's going to hug the
abscissa, and it's going to

208
00:10:37,680 --> 00:10:39,890
come in really, really close.

209
00:10:39,890 --> 00:10:44,570
And then somewhere around this
distance here, where the

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00:10:44,570 --> 00:10:47,580
electron-electron repulsion
starts to be felt,

211
00:10:47,580 --> 00:10:49,000
this thing takes off.

212
00:10:49,000 --> 00:10:52,870
But 1 over r to the 8 goes way,
way up fast. So instead

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00:10:52,870 --> 00:10:54,890
of being a gentle curve
it's more like a

214
00:10:54,890 --> 00:10:56,900
hockey stick shape here.

215
00:10:56,900 --> 00:11:00,770
And so now the net energy is
the sum of the negative

216
00:11:00,770 --> 00:11:04,080
attractive energy and the
positive repulsive energy.

217
00:11:04,080 --> 00:11:08,840
And if we sum the two what
are we going to get?

218
00:11:08,840 --> 00:11:12,780
Well, way out here 1 over r
to the 8 is negligible.

219
00:11:12,780 --> 00:11:14,550
And the net value--

220
00:11:14,550 --> 00:11:17,960
so E net, in red--

221
00:11:17,960 --> 00:11:20,430
is essentially equal
to E attractive.

222
00:11:20,430 --> 00:11:25,820
And at very, very low values of
r, r to the 8 dominates r.

223
00:11:25,820 --> 00:11:28,770
So we have this as
the net value.

224
00:11:28,770 --> 00:11:30,840
And the two sum--

225
00:11:30,840 --> 00:11:33,650
and I can't quite do it because
of the way this is

226
00:11:33,650 --> 00:11:35,460
drawn, but I think
you can see.

227
00:11:35,460 --> 00:11:38,780
These two eventually
equilibrate and

228
00:11:38,780 --> 00:11:39,850
go through a minimum.

229
00:11:39,850 --> 00:11:42,410
So I'm going to cheat a little
bit here and I'm going to add

230
00:11:42,410 --> 00:11:45,900
these two in such a way as to go
through a minimum value of

231
00:11:45,900 --> 00:11:50,790
energy at r equals r0, which is
the sum of E attractive and

232
00:11:50,790 --> 00:11:52,500
E repulsive.

233
00:11:52,500 --> 00:12:00,730
So we can sum those two and
let's see what we get.

234
00:12:00,730 --> 00:12:12,980
At r equals r0, E net is equal
to its minimum value.

235
00:12:12,980 --> 00:12:15,070
So how do you find a minimum
in a function?

236
00:12:15,070 --> 00:12:16,650
You take the derivative.

237
00:12:16,650 --> 00:12:18,180
I'm going to put some
math to work here.

238
00:12:18,180 --> 00:12:23,890
So we'll take dE by dr and
set it equal to 0.

239
00:12:23,890 --> 00:12:30,820
And the value of r at which
it equals 0 is termed r0.

240
00:12:30,820 --> 00:12:31,500
OK?

241
00:12:31,500 --> 00:12:34,020
So we'll just go through
and take the

242
00:12:34,020 --> 00:12:35,450
derivative of that thing.

243
00:12:35,450 --> 00:12:37,940
And I'm not going to go through
all the math but just

244
00:12:37,940 --> 00:12:39,120
show you the set-up here.

245
00:12:39,120 --> 00:12:40,830
What's the other thing
that we know?

246
00:12:40,830 --> 00:12:43,200
dE by dr represents what?

247
00:12:43,200 --> 00:12:44,700
That's force.

248
00:12:44,700 --> 00:12:50,520
So I could say that at r equals
r0 the net force is 0,

249
00:12:50,520 --> 00:12:51,540
which is what you'd expect.

250
00:12:51,540 --> 00:12:54,390
Because if the net force isn't
0 it's going to either push

251
00:12:54,390 --> 00:12:57,240
the ions farther apart or draw
them closer together.

252
00:12:57,240 --> 00:13:00,060
So this is mathematics
imitating reality.

253
00:13:00,060 --> 00:13:01,300
What a concept.

254
00:13:01,300 --> 00:13:04,610
Math working for you instead
of you working for math.

255
00:13:04,610 --> 00:13:06,070
So what do I have?

256
00:13:06,070 --> 00:13:08,270
I have everything in these
equations except

257
00:13:08,270 --> 00:13:09,540
the value of b.

258
00:13:09,540 --> 00:13:12,400
I'm assuming we know the value
of n from experiment.

259
00:13:12,400 --> 00:13:13,860
We don't know the value of b.

260
00:13:13,860 --> 00:13:20,420
And so you can solve to get
the value of b, and once

261
00:13:20,420 --> 00:13:23,500
you've got that you can put
everything together and give

262
00:13:23,500 --> 00:13:28,350
an expression for the energy of
the system at r equals r0.

263
00:13:28,350 --> 00:13:32,920
When you plug everything in you
get this: z-plus, which is

264
00:13:32,920 --> 00:13:36,465
the net charge on the cation,
times z-minus, which is the

265
00:13:36,465 --> 00:13:42,890
net charge on anion, divided
by 4 pi epsilon0 r0.

266
00:13:42,890 --> 00:13:47,310
1 minus 1/n, where n is
the Born exponent.

267
00:13:47,310 --> 00:13:50,060
And this is valid at
r equals r0 only.

268
00:13:54,870 --> 00:13:58,850
If you're not at r equals r0
then you can get the value of

269
00:13:58,850 --> 00:14:02,460
b and then put it into this
expression, where E net will

270
00:14:02,460 --> 00:14:05,630
equal E attractive
plus E repulsive.

271
00:14:05,630 --> 00:14:06,890
So there it is.

272
00:14:06,890 --> 00:14:08,150
And so this represents--

273
00:14:08,150 --> 00:14:16,370
this is the energy of a single
ionic bond, because that's all

274
00:14:16,370 --> 00:14:17,320
the energy that's there.

275
00:14:17,320 --> 00:14:18,840
It's the single ionic bond.

276
00:14:18,840 --> 00:14:25,360
And the second thing that we
realize is plus times minus is

277
00:14:25,360 --> 00:14:29,080
net minus, so this means that
it's negative quantity,

278
00:14:29,080 --> 00:14:29,980
as it should be.

279
00:14:29,980 --> 00:14:32,790
It has to be a negative
quantity.

280
00:14:32,790 --> 00:14:33,080
All right.

281
00:14:33,080 --> 00:14:34,020
So what do we have here?

282
00:14:34,020 --> 00:14:36,800
What we've seen by going through
this derivation is the

283
00:14:36,800 --> 00:14:42,880
recognition that the ionic
bond is electrostatic

284
00:14:42,880 --> 00:14:46,980
attraction mediated by
electronic repulsion.

285
00:14:46,980 --> 00:14:48,800
It's the balance of the two.

286
00:14:48,800 --> 00:14:50,745
And those words sound so good
to me that I'm going

287
00:14:50,745 --> 00:14:52,070
to write them down.

288
00:14:52,070 --> 00:14:59,140
Electrostatic attraction
mediated--

289
00:14:59,140 --> 00:15:00,420
another lovely word--

290
00:15:00,420 --> 00:15:06,170
mediated by electronic
repulsion.

291
00:15:10,750 --> 00:15:16,040
So that's how you get to the
final setting here of the

292
00:15:16,040 --> 00:15:18,410
interionic separation.

293
00:15:18,410 --> 00:15:20,110
So what are the characteristics?

294
00:15:20,110 --> 00:15:22,380
What does this lead
to in terms of

295
00:15:22,380 --> 00:15:25,280
characteristics of this bond?

296
00:15:25,280 --> 00:15:31,020
Characteristics of
the ionic bond.

297
00:15:31,020 --> 00:15:32,750
First of all, it's
omnidirectional.

298
00:15:39,100 --> 00:15:41,270
This is a concept based on the
fact that the electric field

299
00:15:41,270 --> 00:15:43,950
radiates in all directions
uniformly.

300
00:15:43,950 --> 00:15:48,060
So the negative field coming
from the chloride ion is

301
00:15:48,060 --> 00:15:49,630
uniform in all directions.

302
00:15:49,630 --> 00:15:52,200
There's no preferred
direction.

303
00:15:52,200 --> 00:15:53,660
Omnidirectional.

304
00:15:53,660 --> 00:15:54,470
OK?

305
00:15:54,470 --> 00:15:56,160
E field--

306
00:15:56,160 --> 00:15:57,170
oh, I better not say that.

307
00:15:57,170 --> 00:16:07,230
Electric field, not the energy
field, radiates in all

308
00:16:07,230 --> 00:16:10,380
directions uniformly.

309
00:16:17,740 --> 00:16:19,180
And that's going to
have consequences.

310
00:16:19,180 --> 00:16:20,640
I'm not just telling
you this because we

311
00:16:20,640 --> 00:16:22,600
like cataloguing things.

312
00:16:22,600 --> 00:16:25,070
This isn't a bookkeeping
class.

313
00:16:25,070 --> 00:16:27,820
So we're going to come
back, use this fact.

314
00:16:27,820 --> 00:16:33,720
And the second thing is that the
bond is unsaturated, which

315
00:16:33,720 --> 00:16:38,110
is a chemical way of saying that
a given ion can bond to

316
00:16:38,110 --> 00:16:40,510
more than one other ion.

317
00:16:40,510 --> 00:16:43,430
In other types of bonds
that's not the case.

318
00:16:43,430 --> 00:16:47,430
A given atom can only bond
once and then it's done.

319
00:16:47,430 --> 00:16:52,050
Whereas in this case the ion
can bond to a plurality of

320
00:16:52,050 --> 00:16:53,240
other ions.

321
00:16:53,240 --> 00:16:58,440
So ions bond to more than one.

322
00:17:02,460 --> 00:17:03,000
OK?

323
00:17:03,000 --> 00:17:05,560
Plurality of bonds is formed.

324
00:17:05,560 --> 00:17:09,300
They're polygamous,
if you like.

325
00:17:09,300 --> 00:17:11,000
So what does that mean?

326
00:17:11,000 --> 00:17:14,270
That means that here
is what happens.

327
00:17:14,270 --> 00:17:17,600
We've got the blues as the
sodiums, and for any given

328
00:17:17,600 --> 00:17:22,240
sodium it forms bonds without
limit until the number of

329
00:17:22,240 --> 00:17:27,800
bonds is stopped by physical
limitations--

330
00:17:27,800 --> 00:17:30,020
not because the E field
was saturated.

331
00:17:30,020 --> 00:17:31,310
It's unsaturated.

332
00:17:31,310 --> 00:17:35,140
You just can't jam any more
chlorides physically around

333
00:17:35,140 --> 00:17:35,740
the sodium.

334
00:17:35,740 --> 00:17:38,930
That's why the sodium is only
bonding to the number of

335
00:17:38,930 --> 00:17:40,205
chlorides that it bonds to.

336
00:17:40,205 --> 00:17:42,605
There's no intrinsic
limitation.

337
00:17:46,930 --> 00:17:51,140
So what happens when you get
to this situation where you

338
00:17:51,140 --> 00:17:56,090
have omnidirectional forces,
unsaturated bonds, and ions

339
00:17:56,090 --> 00:18:00,280
that you can model as hard
spheres of constant radius?

340
00:18:00,280 --> 00:18:03,190
All the sodiums have the same
radius, all the chlorides have

341
00:18:03,190 --> 00:18:03,950
the same radius.

342
00:18:03,950 --> 00:18:08,270
You make a 3-dimensional
ordered array.

343
00:18:08,270 --> 00:18:19,500
So you can make an infinite
atomic ordered array, which we

344
00:18:19,500 --> 00:18:21,650
use the simple Anglo-Saxon
word last day

345
00:18:21,650 --> 00:18:23,145
to describe: crystal.

346
00:18:23,145 --> 00:18:25,670
You form a crystal.

347
00:18:25,670 --> 00:18:33,650
And as a result ionics have to
be solid at room temperature,

348
00:18:33,650 --> 00:18:38,240
because if you've got thousands
and thousands of

349
00:18:38,240 --> 00:18:40,490
atoms together in one
aggregate they're

350
00:18:40,490 --> 00:18:41,560
not going to float.

351
00:18:41,560 --> 00:18:42,980
They're going to settle.

352
00:18:42,980 --> 00:18:45,690
Put another way, the strength
of the bond, the amount of

353
00:18:45,690 --> 00:18:48,900
energy in here, is so great that
the thermal energy of the

354
00:18:48,900 --> 00:18:52,763
room isn't great enough
to disrupt this bond.

355
00:18:52,763 --> 00:18:57,420
It's a combination of
unsaturated, omnidirectional,

356
00:18:57,420 --> 00:18:59,310
and high energy.

357
00:18:59,310 --> 00:19:02,470
So we form solids at
room temperature.

358
00:19:02,470 --> 00:19:03,470
OK.

359
00:19:03,470 --> 00:19:05,860
Now I want to show the
energetics of that one because

360
00:19:05,860 --> 00:19:06,850
this is good.

361
00:19:06,850 --> 00:19:09,320
You know, I promised you I
wouldn't do derivations, so

362
00:19:09,320 --> 00:19:11,300
I'm not going in
detail on this.

363
00:19:11,300 --> 00:19:13,710
I'm giving you just enough so
that I can introduce the

364
00:19:13,710 --> 00:19:15,040
characters here.

365
00:19:15,040 --> 00:19:16,100
You know, how else
am I going to

366
00:19:16,100 --> 00:19:17,860
introduce the Born exponent?

367
00:19:17,860 --> 00:19:20,510
Am I'm just going to say,
there's this exponent n, the

368
00:19:20,510 --> 00:19:21,330
Born exponent.

369
00:19:21,330 --> 00:19:22,850
We're going to introduce
it in context.

370
00:19:22,850 --> 00:19:24,630
So now you know what
the energetics are.

371
00:19:24,630 --> 00:19:27,980
So now I want to prove to you
energetically along this line

372
00:19:27,980 --> 00:19:29,830
that crystals will form.

373
00:19:32,540 --> 00:19:35,010
So let's imagine--

374
00:19:35,010 --> 00:19:36,520
we're going to do this
thought experiment.

375
00:19:36,520 --> 00:19:47,100
We're going to take three
ion-pairs of sodium chloride.

376
00:19:47,100 --> 00:19:50,090
So here's three ion-pairs
of sodium chloride.

377
00:19:50,090 --> 00:19:52,850
And I want to compare these
three ion-pairs.

378
00:19:52,850 --> 00:19:57,240
So this is an ion gas.

379
00:19:57,240 --> 00:20:03,430
And the distance between
ion-pairs is great enough that

380
00:20:03,430 --> 00:20:05,100
one pair doesn't affect
the other.

381
00:20:05,100 --> 00:20:08,350
The electrostatics are only
strong within the pair.

382
00:20:08,350 --> 00:20:12,530
So we'll just label this
infinity with quotation

383
00:20:12,530 --> 00:20:13,690
marks around it.

384
00:20:13,690 --> 00:20:15,260
They're very far apart.

385
00:20:15,260 --> 00:20:18,860
When a physicist says they're
very far apart, very is code

386
00:20:18,860 --> 00:20:20,370
for infinity.

387
00:20:20,370 --> 00:20:22,820
So this one doesn't interact
with this one, which doesn't

388
00:20:22,820 --> 00:20:23,900
interact with this one.

389
00:20:23,900 --> 00:20:27,530
And I want to compare the
energetic state of the ion

390
00:20:27,530 --> 00:20:33,820
dispersion to what would happen
if I were to put all of

391
00:20:33,820 --> 00:20:37,600
those in a single line.

392
00:20:37,600 --> 00:20:40,830
Plus, minus, plus, minus,
plus, minus.

393
00:20:40,830 --> 00:20:43,320
So then this has a certain
energy state, it's the energy

394
00:20:43,320 --> 00:20:44,642
of the ion line.

395
00:20:44,642 --> 00:20:49,300
And I want to show you that
there's an energy decrease in

396
00:20:49,300 --> 00:20:54,312
collecting all of these and
ordering them into a line.

397
00:20:54,312 --> 00:20:56,250
So there's more energy
in a line dance

398
00:20:56,250 --> 00:20:57,520
than in ballroom dancing.

399
00:20:57,520 --> 00:20:59,150
That's what we're going
to say ultimately.

400
00:20:59,150 --> 00:20:59,450
OK?

401
00:20:59,450 --> 00:21:01,300
So let's compare the energies.

402
00:21:01,300 --> 00:21:02,930
That's all we're going to do.

403
00:21:02,930 --> 00:21:05,060
So what's the energy of this?

404
00:21:05,060 --> 00:21:08,720
Well, we're not going to do 3
versus 3 Let's think big.

405
00:21:08,720 --> 00:21:09,170
It's Friday.

406
00:21:09,170 --> 00:21:12,690
So let's take Avogadro's number
of pairs, shall we?

407
00:21:12,690 --> 00:21:22,350
So the energy of the ion
dispersion would then equal--

408
00:21:22,350 --> 00:21:25,610
that's the energy of one pair,
and they're infinite distance

409
00:21:25,610 --> 00:21:28,450
apart, so there's nothing to be
gained by putting them in

410
00:21:28,450 --> 00:21:31,220
the same chamber.

411
00:21:31,220 --> 00:21:33,330
So it's just going to be N
Avogadro, if that's the

412
00:21:33,330 --> 00:21:38,100
number, times the energy
evaluated at r equals r0.

413
00:21:38,100 --> 00:21:39,160
So we're done.

414
00:21:39,160 --> 00:21:40,550
And we know what that is.

415
00:21:40,550 --> 00:21:42,300
I don't have to rewrite
it for you.

416
00:21:42,300 --> 00:21:42,620
OK.

417
00:21:42,620 --> 00:21:46,640
So now what I have to do is get
an estimate of the energy

418
00:21:46,640 --> 00:21:49,040
of the line and show you
that the line is at a

419
00:21:49,040 --> 00:21:50,165
lower energy state.

420
00:21:50,165 --> 00:21:52,420
Well, let's see.

421
00:21:52,420 --> 00:21:56,240
Jocelyn, take the top one and
the middle one, please, but

422
00:21:56,240 --> 00:21:57,360
not the bottom one.

423
00:21:57,360 --> 00:21:58,090
Thanks.

424
00:21:58,090 --> 00:21:58,380
OK.

425
00:21:58,380 --> 00:22:00,960
So now let's look at the
energy of a line.

426
00:22:00,960 --> 00:22:03,270
So we're going to do--
here's my line.

427
00:22:03,270 --> 00:22:06,950
I'm going to get the
colored chalk.

428
00:22:06,950 --> 00:22:08,720
Green and blue.

429
00:22:08,720 --> 00:22:10,880
You know, some people think
being a professor is so cool

430
00:22:10,880 --> 00:22:14,540
because you get to travel, you
get to research, and so on.

431
00:22:14,540 --> 00:22:15,580
It's the colored chalk.

432
00:22:15,580 --> 00:22:16,855
[LAUGHTER]

433
00:22:16,855 --> 00:22:19,280
PROFESSOR: It's the
colored chalk.

434
00:22:19,280 --> 00:22:20,400
All right.

435
00:22:20,400 --> 00:22:22,100
So there's a sodium.

436
00:22:22,100 --> 00:22:24,860
And on each side of the sodium
we'll put a chloride.

437
00:22:24,860 --> 00:22:25,470
All right?

438
00:22:25,470 --> 00:22:27,450
And I'm going to just
keep going this way.

439
00:22:27,450 --> 00:22:30,690
Here's a sodium and
here's a chloride.

440
00:22:30,690 --> 00:22:31,530
All right.

441
00:22:31,530 --> 00:22:33,960
And now what I'm going to do,
I'm going to start here at

442
00:22:33,960 --> 00:22:38,120
this sodium and I'm going
to count the energy,

443
00:22:38,120 --> 00:22:41,610
electrostatic energy, that's
in this system.

444
00:22:41,610 --> 00:22:44,090
So we're going to count to the
left, we're going to count to

445
00:22:44,090 --> 00:22:46,060
the right, and then we're going
to multiply it by the

446
00:22:46,060 --> 00:22:47,780
total number of ion-pairs.

447
00:22:47,780 --> 00:22:50,540
And I know that the ones on the
end aren't the same, but

448
00:22:50,540 --> 00:22:53,650
the number of ends over N
Avogadro, that's peanuts.

449
00:22:53,650 --> 00:22:56,390
The edge effects are negligible
because there's

450
00:22:56,390 --> 00:22:57,670
such a giant middle.

451
00:22:57,670 --> 00:22:58,760
That's how you model
this stuff.

452
00:22:58,760 --> 00:23:01,960
You don't obsess over the fact
that the last ion doesn't see

453
00:23:01,960 --> 00:23:03,080
anything on that side.

454
00:23:03,080 --> 00:23:05,960
You just do it and forget about
it, because you know you

455
00:23:05,960 --> 00:23:07,060
wouldn't do it for 5.

456
00:23:07,060 --> 00:23:08,300
This would be a big problem.

457
00:23:08,300 --> 00:23:12,130
But if you have Avogadro's
number, who cares?

458
00:23:12,130 --> 00:23:13,280
It's called risk assessment.

459
00:23:13,280 --> 00:23:13,610
All right.

460
00:23:13,610 --> 00:23:17,050
So let's look at the
energetics here.

461
00:23:17,050 --> 00:23:24,820
So what we've got is the
energy of the ion line.

462
00:23:24,820 --> 00:23:25,470
OK?

463
00:23:25,470 --> 00:23:27,970
So let's start with
this central one.

464
00:23:27,970 --> 00:23:32,380
And separated by distance r0 is
the chloride, and there's

465
00:23:32,380 --> 00:23:33,950
an attractive energy here.

466
00:23:33,950 --> 00:23:38,190
So that's going to equal
minus e squared over

467
00:23:38,190 --> 00:23:42,400
4 pi epsilon0 r0.

468
00:23:42,400 --> 00:23:44,290
Now I'm going to keep going,
because the field is

469
00:23:44,290 --> 00:23:46,710
unsaturated and goes
in all directions.

470
00:23:46,710 --> 00:23:51,490
So this sodium, that's
a distance 2r0 away.

471
00:23:51,490 --> 00:23:55,920
It's got a repulsive force
exerted on this sodium.

472
00:23:55,920 --> 00:23:56,920
So let's add that.

473
00:23:56,920 --> 00:23:58,040
So that's going to be plus.

474
00:23:58,040 --> 00:24:01,020
A repulsive force raises
the energy of a system.

475
00:24:01,020 --> 00:24:07,180
That's e squared over 4pi
epsilon0 times 2r0.

476
00:24:07,180 --> 00:24:08,620
And let's keep going.

477
00:24:08,620 --> 00:24:10,940
So now let's go 3r0 away.

478
00:24:10,940 --> 00:24:15,330
So 3 times r0, that gets me out
to the chloride over here.

479
00:24:15,330 --> 00:24:17,040
Let's put 3r0.

480
00:24:17,040 --> 00:24:20,570
Now that will take me from the
center of the sodium to the

481
00:24:20,570 --> 00:24:22,610
center of the next chloride.

482
00:24:22,610 --> 00:24:24,540
And that's going to
be attractive.

483
00:24:24,540 --> 00:24:30,180
So that'll be minus e squared
over 4pi epsilon0 times 3r0

484
00:24:30,180 --> 00:24:31,180
plus, et cetera.

485
00:24:31,180 --> 00:24:32,820
So you see how this goes.

486
00:24:32,820 --> 00:24:34,560
So you go all the way out, you
add them all up, and you go

487
00:24:34,560 --> 00:24:35,610
the other way.

488
00:24:35,610 --> 00:24:37,670
And so on and so forth.

489
00:24:37,670 --> 00:24:39,400
So that's how the
derivation goes.

490
00:24:39,400 --> 00:24:40,370
You might say, hey
wait a minute.

491
00:24:40,370 --> 00:24:43,520
What happened to the Born
exponent and the repulsive

492
00:24:43,520 --> 00:24:44,870
energy term?

493
00:24:44,870 --> 00:24:48,190
Well, where's the repulsive
energy term going to be felt?

494
00:24:48,190 --> 00:24:51,960
It's called electron-electron
repulsion.

495
00:24:51,960 --> 00:24:54,980
Axiomatically, the electrons
here are

496
00:24:54,980 --> 00:24:56,980
nowhere near these electrons.

497
00:24:56,980 --> 00:25:00,130
See, you only have to count it
for the nearest neighbor.

498
00:25:00,130 --> 00:25:02,530
So we can patch that
in at the end.

499
00:25:02,530 --> 00:25:04,130
And we do.

500
00:25:04,130 --> 00:25:05,610
I haven't forgotten.

501
00:25:05,610 --> 00:25:08,390
But I'm not going to spend a
whole day trying to derive

502
00:25:08,390 --> 00:25:08,940
this thing.

503
00:25:08,940 --> 00:25:10,720
I'll show you how it
starts to evolve.

504
00:25:10,720 --> 00:25:12,290
At some point you end
up with something

505
00:25:12,290 --> 00:25:13,490
that looks like this.

506
00:25:13,490 --> 00:25:15,450
e squared over--

507
00:25:15,450 --> 00:25:17,310
in fact, I'll put the
minus sign up here.

508
00:25:17,310 --> 00:25:22,210
Minus e squared over
4 pi epsilon0 r0.

509
00:25:22,210 --> 00:25:24,450
And you're going to double it,
because you're going to go one

510
00:25:24,450 --> 00:25:26,710
side and the other side, and
you're going to get a series

511
00:25:26,710 --> 00:25:33,830
that looks like this: 1 minus
1/2 plus 1/3 minus 1/4 plus

512
00:25:33,830 --> 00:25:35,150
blah, blah, blah.

513
00:25:35,150 --> 00:25:36,090
Yeah.

514
00:25:36,090 --> 00:25:36,760
OK.

515
00:25:36,760 --> 00:25:39,800
So what does this look like?

516
00:25:39,800 --> 00:25:44,660
I've really broken this
into two pieces.

517
00:25:44,660 --> 00:25:49,570
So this coefficient out in front
here, you should now be

518
00:25:49,570 --> 00:25:52,500
able to repeat this in your
sleep: e squared over 4 pi

519
00:25:52,500 --> 00:25:53,740
epsilon0 r.

520
00:25:53,740 --> 00:25:58,170
This is electrostatics,
isn't it?

521
00:25:58,170 --> 00:25:59,000
Electrostatics.

522
00:25:59,000 --> 00:26:01,580
This is the consequence
of Coulomb's law.

523
00:26:01,580 --> 00:26:03,830
What's this second term here?

524
00:26:03,830 --> 00:26:06,000
What's this all about?

525
00:26:06,000 --> 00:26:07,440
Geometry.

526
00:26:07,440 --> 00:26:10,450
This is dictated by atomic
arrangement.

527
00:26:17,060 --> 00:26:20,810
So I could calculate this if I
took, instead of a line, what

528
00:26:20,810 --> 00:26:24,960
if I put them in a sheet subject
to the constraints of

529
00:26:24,960 --> 00:26:28,400
those sizes and plus
1 and minus 1?

530
00:26:28,400 --> 00:26:29,150
So what would be?

531
00:26:29,150 --> 00:26:31,900
I'd start at the sodium and
count how many chlorides?

532
00:26:31,900 --> 00:26:35,710
If I'm on a plane there'd be
one, two, three, four.

533
00:26:35,710 --> 00:26:36,820
And then how many sodiums?

534
00:26:36,820 --> 00:26:38,810
Well, they'd be on the backside

535
00:26:38,810 --> 00:26:40,090
of each of the chlorides.

536
00:26:40,090 --> 00:26:43,430
And I'd add them all up in
2-space and I'd end up with

537
00:26:43,430 --> 00:26:45,045
another coefficient here.

538
00:26:45,045 --> 00:26:46,070
All right?

539
00:26:46,070 --> 00:26:50,490
And we compress all of this into
a coefficient which we

540
00:26:50,490 --> 00:26:52,170
call the Madelung constant.

541
00:26:55,700 --> 00:26:57,890
And it's a function of the
atomic arrangements.

542
00:26:57,890 --> 00:27:00,320
So different crystal structures
have different

543
00:27:00,320 --> 00:27:02,450
Madelung constants.

544
00:27:02,450 --> 00:27:06,302
It's named after a German
professor, Madelung.

545
00:27:06,302 --> 00:27:10,630
In 1910, he published
calculations for the energy of

546
00:27:10,630 --> 00:27:12,230
a system of point charges--

547
00:27:12,230 --> 00:27:14,510
just abstract theoretical
paper.

548
00:27:14,510 --> 00:27:18,925
And then about 10 years later
another German professor by

549
00:27:18,925 --> 00:27:20,970
the name of Paul Ewald--

550
00:27:20,970 --> 00:27:22,970
he did his PhD for
Sommerfeld--

551
00:27:22,970 --> 00:27:25,770
he published a paper in which
he actually made the

552
00:27:25,770 --> 00:27:30,310
calculation for ion crystals,
and he came

553
00:27:30,310 --> 00:27:31,390
up with this constant.

554
00:27:31,390 --> 00:27:34,380
And to show you the class of the
guy, instead of naming the

555
00:27:34,380 --> 00:27:37,790
constant after himself he
named it after Madelung.

556
00:27:37,790 --> 00:27:38,870
Now that's class.

557
00:27:38,870 --> 00:27:42,190
So Madelung did the first
calculation so he gets named.

558
00:27:42,190 --> 00:27:45,620
So now what we're going to do is
we're going to multiply by

559
00:27:45,620 --> 00:27:48,970
the N Avogadro, because I've
got N Avogadro of these

560
00:27:48,970 --> 00:27:52,510
things, and we're going to
put in the Born exponent

561
00:27:52,510 --> 00:27:53,690
patch and so on.

562
00:27:53,690 --> 00:27:56,260
And here's what the final
expression looks

563
00:27:56,260 --> 00:27:59,220
like for the line.

564
00:27:59,220 --> 00:28:02,620
There are a few algebraic tricks
that I'm not willing to

565
00:28:02,620 --> 00:28:05,140
do in class because I don't
think that's a profitable use

566
00:28:05,140 --> 00:28:06,930
of our time in a chemistry
class.

567
00:28:06,930 --> 00:28:08,940
But if you want to try the
derivation I have it in full

568
00:28:08,940 --> 00:28:10,450
and we can compare notes.

569
00:28:10,450 --> 00:28:13,350
So once we get the patch in it's
going to look like this.

570
00:28:13,350 --> 00:28:14,490
It'll be minus.

571
00:28:14,490 --> 00:28:17,060
There'll be the Madelung
constant times

572
00:28:17,060 --> 00:28:19,750
N Avogadro e squared--

573
00:28:19,750 --> 00:28:22,020
and this is already assuming
it's plus 1, minus 1.

574
00:28:22,020 --> 00:28:25,100
If this were magnesium oxide
there'd be a 4 in here.

575
00:28:25,100 --> 00:28:32,170
4 pi epsilon0 r0 times
1 minus 1/n, where

576
00:28:32,170 --> 00:28:33,870
n is the Born exponent.

577
00:28:33,870 --> 00:28:38,730
So compare this to
this one here.

578
00:28:38,730 --> 00:28:40,060
What's the only difference?

579
00:28:40,060 --> 00:28:42,870
The only difference is the
Madelung constant, right?

580
00:28:42,870 --> 00:28:44,160
It's the only difference.

581
00:28:44,160 --> 00:28:56,480
So E of the pair dispersion is
really equal to E of the line

582
00:28:56,480 --> 00:28:58,240
divided by the Madelung
constant.

583
00:28:58,240 --> 00:29:01,670
So what I'm trying to prove to
you is that E line is more

584
00:29:01,670 --> 00:29:03,860
negative than E of
the dispersion.

585
00:29:03,860 --> 00:29:06,140
So it all hinges on the
magnitude of M.

586
00:29:06,140 --> 00:29:08,240
If M is greater than 1 we win.

587
00:29:08,240 --> 00:29:12,050
If M is less than 1 I've just
proved to you that water runs

588
00:29:12,050 --> 00:29:13,390
uphill, so that's a bad day.

589
00:29:13,390 --> 00:29:14,240
All right?

590
00:29:14,240 --> 00:29:16,600
So let's calculate
the value of M.

591
00:29:16,600 --> 00:29:21,020
And you can go to your
algebra books.

592
00:29:21,020 --> 00:29:24,680
And you've got this series
natural log-- and engineers

593
00:29:24,680 --> 00:29:27,160
write natural log "ln." I know
the mathematicians write

594
00:29:27,160 --> 00:29:28,770
"log." Uh-uh.

595
00:29:28,770 --> 00:29:29,650
Engineers--

596
00:29:29,650 --> 00:29:30,320
uh.

597
00:29:30,320 --> 00:29:31,620
That's 1 plus x.

598
00:29:31,620 --> 00:29:32,240
OK?

599
00:29:32,240 --> 00:29:34,070
Natural log, 1 plus x.

600
00:29:34,070 --> 00:29:43,120
You can expand this as x minus
x squared over 2 plus x cubed

601
00:29:43,120 --> 00:29:44,510
over 3, dah, dah, dah, dah.

602
00:29:44,510 --> 00:29:46,080
You know, look that one up.

603
00:29:46,080 --> 00:29:50,250
Set x equal to 1, which is
what we've got, right?

604
00:29:50,250 --> 00:29:54,510
Because we've got 1 minus 1/2,
1/3, dah, dah, dah, dah.

605
00:29:54,510 --> 00:29:57,920
Go through it and you'll get the
value that M, according to

606
00:29:57,920 --> 00:30:01,740
this, will give you 2 times the
natural logarithm of 2,

607
00:30:01,740 --> 00:30:03,990
which is 1.386--

608
00:30:03,990 --> 00:30:06,330
which is greater than 1.

609
00:30:06,330 --> 00:30:08,170
And so we're golden.

610
00:30:08,170 --> 00:30:12,840
That means that the energy of
the line is lower, more

611
00:30:12,840 --> 00:30:15,800
negative, than the energy
of the dispersion.

612
00:30:15,800 --> 00:30:17,400
So I'm going to do
this pictorially.

613
00:30:17,400 --> 00:30:19,780
Let's make an energy
level diagram.

614
00:30:19,780 --> 00:30:22,370
And the energy level diagram
will look like this.

615
00:30:22,370 --> 00:30:28,010
So up here the energy is 0 and
everything is negative.

616
00:30:28,010 --> 00:30:31,595
So if I put this as
minus 1 unit.

617
00:30:31,595 --> 00:30:32,340
All right?

618
00:30:32,340 --> 00:30:35,980
These are all negative values
increasing in this direction.

619
00:30:35,980 --> 00:30:45,370
So this is the dispersion
of ion-pairs.

620
00:30:45,370 --> 00:30:47,070
So all we've done is
take a cation and

621
00:30:47,070 --> 00:30:48,270
put it to the anion.

622
00:30:48,270 --> 00:30:52,670
We've just seen that if we do
the calculation for the line

623
00:30:52,670 --> 00:30:56,580
it's 1.386 times whatever
this is.

624
00:30:56,580 --> 00:31:01,695
So that gives us-- this is for
the ion line, which I'm going

625
00:31:01,695 --> 00:31:05,650
to take the liberty of calling
a 1-dimensional crystal.

626
00:31:05,650 --> 00:31:07,250
It's a 1-dimensional
ordered array.

627
00:31:09,750 --> 00:31:15,580
And what I can do is go to the
3-dimensional array, start at

628
00:31:15,580 --> 00:31:18,690
the lower right-hand corner
with that chloride.

629
00:31:18,690 --> 00:31:21,630
Calculate the distance to each
of the nearest neighbor

630
00:31:21,630 --> 00:31:23,860
sodiums. Go through
the geometry.

631
00:31:23,860 --> 00:31:26,440
The next nearest neighbor
chlorides, the next nearest

632
00:31:26,440 --> 00:31:29,570
neighbor sodiums. And you'll
build an infinite series and

633
00:31:29,570 --> 00:31:30,570
you'll evaluate it.

634
00:31:30,570 --> 00:31:33,880
And in three dimensions
it's even lower.

635
00:31:33,880 --> 00:31:38,140
It's 1.7476.

636
00:31:38,140 --> 00:31:41,230
So this is for the 3-dimensional
crystal.

637
00:31:41,230 --> 00:31:44,760
This is for the ionic crystal.

638
00:31:44,760 --> 00:31:45,410
All right?

639
00:31:45,410 --> 00:31:48,390
3-D crystal.

640
00:31:48,390 --> 00:31:52,400
So what this is showing is that
the system keeps making

641
00:31:52,400 --> 00:31:53,660
more and more bonds.

642
00:31:53,660 --> 00:31:55,110
Why does it make bonds?

643
00:31:55,110 --> 00:31:58,590
Because the more nearest
neighbors it has the lower the

644
00:31:58,590 --> 00:32:01,510
energy goes.

645
00:32:01,510 --> 00:32:03,630
So making a 3-dimensional
crystal is

646
00:32:03,630 --> 00:32:04,820
energetically favored.

647
00:32:04,820 --> 00:32:07,400
Now there are different
Madelung constants for

648
00:32:07,400 --> 00:32:08,550
different crystal structures.

649
00:32:08,550 --> 00:32:09,340
You say, well wait a minute.

650
00:32:09,340 --> 00:32:11,020
How do you get different
crystal structures?

651
00:32:11,020 --> 00:32:13,780
Suppose instead of sodium
it's potassium.

652
00:32:13,780 --> 00:32:14,850
What's the only difference?

653
00:32:14,850 --> 00:32:16,940
Potassium is plus 1.

654
00:32:16,940 --> 00:32:18,300
What's the difference?

655
00:32:18,300 --> 00:32:19,650
Size.

656
00:32:19,650 --> 00:32:21,080
Potassium is larger.

657
00:32:21,080 --> 00:32:24,470
They're not going to pack
quite the same.

658
00:32:24,470 --> 00:32:26,800
And so depending on the
relative ion sizes--

659
00:32:26,800 --> 00:32:31,440
I mean what if I have something
like silver iodide?

660
00:32:31,440 --> 00:32:33,000
Iodide is huge.

661
00:32:33,000 --> 00:32:37,630
Silver is so small it'll fit
into the interstices between

662
00:32:37,630 --> 00:32:39,980
touching iodines.

663
00:32:39,980 --> 00:32:41,720
So it's going to have a
different crystal structure,

664
00:32:41,720 --> 00:32:43,860
and the different crystal
structure will give us a

665
00:32:43,860 --> 00:32:46,370
different Madelung constant.

666
00:32:46,370 --> 00:32:48,130
And there it is.

667
00:32:48,130 --> 00:32:52,210
So we've come a long way with
that little assumption of

668
00:32:52,210 --> 00:32:53,660
octet stability.

669
00:32:53,660 --> 00:32:56,490
So now let's take a look at
what the properties are of

670
00:32:56,490 --> 00:32:57,540
these things.

671
00:32:57,540 --> 00:32:59,400
They're solid at room
temperature because we've got

672
00:32:59,400 --> 00:33:01,070
strong bonds.

673
00:33:01,070 --> 00:33:02,400
High melting points.

674
00:33:02,400 --> 00:33:05,390
Bonding is related
to melting point.

675
00:33:05,390 --> 00:33:07,640
Now think point is dictated by
bonding, because now you're

676
00:33:07,640 --> 00:33:11,240
comparing thermal energy versus
the cohesive energy of

677
00:33:11,240 --> 00:33:12,180
the crystal.

678
00:33:12,180 --> 00:33:15,720
So tightly bonded substances
melt at high temperatures,

679
00:33:15,720 --> 00:33:18,710
weakly bonded substances melt
at low temperatures.

680
00:33:18,710 --> 00:33:21,010
Transparent to visible light.

681
00:33:21,010 --> 00:33:23,690
How do I know that?

682
00:33:23,690 --> 00:33:24,970
Because I'm the professor.

683
00:33:24,970 --> 00:33:25,570
No.

684
00:33:25,570 --> 00:33:26,840
How do I know that?

685
00:33:26,840 --> 00:33:28,970
How do we think about it when
someone says to you is

686
00:33:28,970 --> 00:33:32,490
something transparent, in this
case to visible light.

687
00:33:32,490 --> 00:33:37,310
Well, what I do is I say,
here's the solid.

688
00:33:37,310 --> 00:33:41,780
This is the ionic solid and here
is visible light, h nu.

689
00:33:41,780 --> 00:33:46,700
And I'm going to write 2 to 3
electron volts per photon.

690
00:33:46,700 --> 00:33:49,730
And what happens when I want
to decide whether this is

691
00:33:49,730 --> 00:33:51,000
transparent to visible light?

692
00:33:51,000 --> 00:33:52,690
Now look at the modeling here.

693
00:33:52,690 --> 00:33:54,140
Photon is a squiggle.

694
00:33:54,140 --> 00:33:55,960
I don't know if that's
Cartesian space.

695
00:33:55,960 --> 00:33:58,425
This is like a crystal, right?

696
00:33:58,425 --> 00:33:59,700
I'm speaking California.

697
00:33:59,700 --> 00:34:00,860
It's like a crystal.

698
00:34:00,860 --> 00:34:05,080
So now if I go inside I want
to make the energy diagram.

699
00:34:05,080 --> 00:34:07,360
So what's the energy
diagram look like?

700
00:34:07,360 --> 00:34:09,260
All right?

701
00:34:09,260 --> 00:34:12,270
So now the question
is how does--

702
00:34:12,270 --> 00:34:17,510
if this is the energy diagram of
the crystal and I make this

703
00:34:17,510 --> 00:34:21,960
the energy of the photon of
visible light, I'm going to

704
00:34:21,960 --> 00:34:25,460
compare how much energy the
photon has versus how much

705
00:34:25,460 --> 00:34:28,780
energy it takes to excite
electrons all the

706
00:34:28,780 --> 00:34:30,710
way to a new state.

707
00:34:30,710 --> 00:34:31,980
Because if you don't
excite them all the

708
00:34:31,980 --> 00:34:33,140
way to a new state--

709
00:34:33,140 --> 00:34:35,720
they can't go part way,
so nothing happens.

710
00:34:35,720 --> 00:34:38,270
And if nothing happens the
photon goes through and that's

711
00:34:38,270 --> 00:34:40,440
transparent.

712
00:34:40,440 --> 00:34:43,830
Now what do I know about the
binding energy and the energy

713
00:34:43,830 --> 00:34:46,240
level diagram of Na plus?

714
00:34:46,240 --> 00:34:49,560
Well, it's isoelectronic
with neon.

715
00:34:49,560 --> 00:34:51,960
And I know that neon has an
average valence electron

716
00:34:51,960 --> 00:34:55,490
energy of about 20
electron volts.

717
00:34:55,490 --> 00:34:57,660
So my guess is the
visible light is

718
00:34:57,660 --> 00:34:59,550
not going to do anything.

719
00:34:59,550 --> 00:35:03,160
And so it just passes
right on through.

720
00:35:03,160 --> 00:35:04,940
See, we got all that.

721
00:35:04,940 --> 00:35:06,090
Electrical insulator.

722
00:35:06,090 --> 00:35:06,840
How do I know that?

723
00:35:06,840 --> 00:35:09,160
Well, all that glitters
is not gold, but it

724
00:35:09,160 --> 00:35:11,040
must have free electrons.

725
00:35:11,040 --> 00:35:13,510
And these electrons
are all bound, and

726
00:35:13,510 --> 00:35:16,490
they're tightly bound.

727
00:35:16,490 --> 00:35:18,532
Hard and brittle.

728
00:35:18,532 --> 00:35:22,350
If it's going to be ductile the
atoms need to be able to

729
00:35:22,350 --> 00:35:24,260
slide over one another.

730
00:35:24,260 --> 00:35:26,890
Well, there's no way these can
slide over one another because

731
00:35:26,890 --> 00:35:29,900
to slide over one another
requires that at some point

732
00:35:29,900 --> 00:35:32,160
the two sodiums are going to be
nearest neighbors, and the

733
00:35:32,160 --> 00:35:35,570
repulsive forces are so high
the crystal fractures.

734
00:35:35,570 --> 00:35:39,890
So if you try to deform an ionic
solid you will get it

735
00:35:39,890 --> 00:35:43,660
moving in accordance
to the elasticity.

736
00:35:43,660 --> 00:35:46,790
So force will be proportional
to the extension--

737
00:35:46,790 --> 00:35:49,270
Hooke's Law-- but if you try
to plastically deform

738
00:35:49,270 --> 00:35:52,270
it, you shear it.

739
00:35:52,270 --> 00:35:53,170
Soluble in water.

740
00:35:53,170 --> 00:35:54,580
We'll come back to that later.

741
00:35:54,580 --> 00:35:56,530
Melt to form ionic liquids.

742
00:35:56,530 --> 00:36:00,150
And good for electrolytic
extraction of metals.

743
00:36:00,150 --> 00:36:01,580
I showed you magnesium
last day.

744
00:36:01,580 --> 00:36:04,700
Today I'll talk a little
bit about aluminum.

745
00:36:04,700 --> 00:36:06,640
But that comes later.

746
00:36:06,640 --> 00:36:07,120
OK.

747
00:36:07,120 --> 00:36:11,520
So where do we find elements
that are going

748
00:36:11,520 --> 00:36:13,510
to form ionic solids?

749
00:36:13,510 --> 00:36:14,920
Well, you go back to the
beginning of the lecture.

750
00:36:14,920 --> 00:36:15,930
What do you look for?

751
00:36:15,930 --> 00:36:19,580
You've got to find the box of
really good electron donors

752
00:36:19,580 --> 00:36:22,130
and the box of really good
electron acceptors.

753
00:36:22,130 --> 00:36:24,220
That's where you go.

754
00:36:24,220 --> 00:36:28,340
So the good electron donors are
at the left side and the

755
00:36:28,340 --> 00:36:30,990
good electron acceptors
are at the right side.

756
00:36:30,990 --> 00:36:33,220
So if you take sodium
plus chlorine

757
00:36:33,220 --> 00:36:34,360
you get sodium chloride.

758
00:36:34,360 --> 00:36:36,750
If you get calcium plus
fluorine, calcium fluoride.

759
00:36:36,750 --> 00:36:39,332
Magnesium plus oxygen,
and so on.

760
00:36:39,332 --> 00:36:41,300
OK?

761
00:36:41,300 --> 00:36:43,330
Yeah, this shows.

762
00:36:43,330 --> 00:36:45,030
Yeah.

763
00:36:45,030 --> 00:36:48,850
Aluminum plus oxygen, yeah.

764
00:36:48,850 --> 00:36:50,780
There's Max Born.

765
00:36:50,780 --> 00:36:54,180
Max Born, he got
a Nobel Prize.

766
00:36:54,180 --> 00:36:56,070
And so did Fritz Haber,
but we're going to

767
00:36:56,070 --> 00:36:57,420
come to him in a minute.

768
00:36:57,420 --> 00:36:57,770
All right.

769
00:36:57,770 --> 00:37:04,820
So now I want to do this
energetic calculation one more

770
00:37:04,820 --> 00:37:08,340
way, because right now we've
been operating with ion gas

771
00:37:08,340 --> 00:37:11,130
but sodium isn't found
normally in the

772
00:37:11,130 --> 00:37:12,250
form of an ion gas.

773
00:37:12,250 --> 00:37:15,320
So let's do something
that starts with

774
00:37:15,320 --> 00:37:16,810
elements found in nature.

775
00:37:16,810 --> 00:37:26,670
So we want to form an ionic
crystal from elements in their

776
00:37:26,670 --> 00:37:27,920
natural state.

777
00:37:31,060 --> 00:37:33,660
And what's going to happen is
en route we're going to be

778
00:37:33,660 --> 00:37:36,870
able to define a few more terms.
So that's going to make

779
00:37:36,870 --> 00:37:39,090
everybody happy because we
get more definitions.

780
00:37:39,090 --> 00:37:44,900
And this is called the
Born-Haber Cycle, named after

781
00:37:44,900 --> 00:37:48,070
Born and Haber.

782
00:37:48,070 --> 00:37:50,880
And what we're going to
do is we're going to--

783
00:37:50,880 --> 00:37:53,360
pardon me, there's a C in
there-- we're going to invoke

784
00:37:53,360 --> 00:37:56,570
Hess's Law.

785
00:37:56,570 --> 00:37:59,710
And Hess's Law is sort of
like Kirchhoff's law

786
00:37:59,710 --> 00:38:00,740
for electric circuits.

787
00:38:00,740 --> 00:38:05,050
Hess's law says that the energy
of a chemical change is

788
00:38:05,050 --> 00:38:06,650
path independent.

789
00:38:06,650 --> 00:38:18,380
So energy change in a chemical
reaction is path independent.

790
00:38:18,380 --> 00:38:23,950
It's sort of like potential
energy in Newtonian mechanics.

791
00:38:23,950 --> 00:38:26,090
It doesn't matter if you take
the elevator to the top of the

792
00:38:26,090 --> 00:38:29,420
Hancock Tower or if you walk up
the stairs, the change in

793
00:38:29,420 --> 00:38:33,320
potential energy is the same
when you express it from the

794
00:38:33,320 --> 00:38:36,850
top of the Hancock Tower,
although you might be somewhat

795
00:38:36,850 --> 00:38:39,920
more exhausted having walked
the steps instead of taking

796
00:38:39,920 --> 00:38:40,720
the elevator.

797
00:38:40,720 --> 00:38:42,240
But you don't get any
credit in terms of

798
00:38:42,240 --> 00:38:45,000
the potential energy.

799
00:38:45,000 --> 00:38:52,070
So let's use Hess's Law in
order to describe the

800
00:38:52,070 --> 00:38:53,250
formation of sodium chloride.

801
00:38:53,250 --> 00:38:56,940
So I'm going to start with
sodium as it's found in

802
00:38:56,940 --> 00:38:58,980
nature, and I'm going to talk
about room temperature.

803
00:38:58,980 --> 00:39:02,480
So sodium is a solid at room
temperature, and I'm going to

804
00:39:02,480 --> 00:39:07,010
react it with chlorine gas.

805
00:39:07,010 --> 00:39:08,755
Chlorine's a gas at room
temperature and it's a

806
00:39:08,755 --> 00:39:11,090
diatomic molecule.

807
00:39:11,090 --> 00:39:16,640
And we're going to react it to
form sodium chloride, which is

808
00:39:16,640 --> 00:39:18,810
a solid and a crystal.

809
00:39:18,810 --> 00:39:20,590
Now you might say, well isn't
that kind of redundant?

810
00:39:20,590 --> 00:39:23,230
No, because later on I'm going
to teach you about a form of

811
00:39:23,230 --> 00:39:26,980
solid matter that does
not consist of atoms

812
00:39:26,980 --> 00:39:28,310
in a regular array--

813
00:39:28,310 --> 00:39:29,580
disordered solids.

814
00:39:29,580 --> 00:39:33,300
So we're specifying, I want to
form crystal and solid sodium

815
00:39:33,300 --> 00:39:35,775
chloride, because that's the
reaction that would occur if

816
00:39:35,775 --> 00:39:37,540
we were to do it in the lab.

817
00:39:37,540 --> 00:39:39,700
And what have we calculated
so far?

818
00:39:39,700 --> 00:39:42,490
What we've calculated
so far is this.

819
00:39:42,490 --> 00:39:48,630
We've calculated chloride ion
in the gas phase plus sodium

820
00:39:48,630 --> 00:39:52,560
ion in the gas phase reacting
to form the crystal.

821
00:39:52,560 --> 00:39:57,720
And we've called this the energy
of crystallization.

822
00:39:57,720 --> 00:39:59,960
That's this Madelung stuff.

823
00:39:59,960 --> 00:40:01,860
This is the Madelung
energy here.

824
00:40:01,860 --> 00:40:02,430
All right?

825
00:40:02,430 --> 00:40:04,370
I'll even put M here.

826
00:40:04,370 --> 00:40:05,280
Madelung energy.

827
00:40:05,280 --> 00:40:06,320
And why am I using H?

828
00:40:06,320 --> 00:40:07,850
Because that's what
the books use.

829
00:40:07,850 --> 00:40:10,580
H is enthalpy, and for
condensed matter the

830
00:40:10,580 --> 00:40:12,060
difference between enthalpy
and energy

831
00:40:12,060 --> 00:40:13,660
doesn't amount to much.

832
00:40:13,660 --> 00:40:17,870
So H, just for the record,
is enthalpy.

833
00:40:17,870 --> 00:40:20,750
And we've been operating
with E as energy.

834
00:40:20,750 --> 00:40:24,930
It's almost equal to
E, which is energy

835
00:40:24,930 --> 00:40:26,250
for condensed matter.

836
00:40:29,590 --> 00:40:31,090
For the gas phase
it gets hairy.

837
00:40:35,630 --> 00:40:36,710
OK.

838
00:40:36,710 --> 00:40:41,320
So I want to get us from sodium
solid, chloride solid

839
00:40:41,320 --> 00:40:42,440
over to here.

840
00:40:42,440 --> 00:40:43,410
So how am I going to do that?

841
00:40:43,410 --> 00:40:47,090
Well, first of all, I know how
to make sodium ion gas.

842
00:40:47,090 --> 00:40:52,630
I start with sodium gas and then
by ionization I make the

843
00:40:52,630 --> 00:40:55,280
electron plus sodium ion.

844
00:40:55,280 --> 00:40:58,730
So this is called the ionization
energy, isn't it?

845
00:40:58,730 --> 00:41:00,170
This is the ionization energy.

846
00:41:00,170 --> 00:41:02,060
Sodium gas goes to that.

847
00:41:02,060 --> 00:41:04,090
And now how do I get sodium
gas from sodium?

848
00:41:04,090 --> 00:41:06,310
Well that's just called
sublimation.

849
00:41:06,310 --> 00:41:09,050
So this I'm going to need
delta H of sublimation.

850
00:41:09,050 --> 00:41:12,560
Sublimation is the conversion
of solid to vapor.

851
00:41:12,560 --> 00:41:16,640
And you can look that up
on the Periodic Table.

852
00:41:16,640 --> 00:41:18,310
I'll show you how to get
that in a second.

853
00:41:18,310 --> 00:41:19,780
And now how do I get
chloride gas?

854
00:41:19,780 --> 00:41:23,370
Well chloride gas is going to
start with atomic chlorine

855
00:41:23,370 --> 00:41:27,320
gas, but instead of losing an
electron I've got to acquire

856
00:41:27,320 --> 00:41:29,420
an electron.

857
00:41:29,420 --> 00:41:33,720
And this action of adding an
electron is sort of an inverse

858
00:41:33,720 --> 00:41:38,860
ionization, and this is called
electron affinity.

859
00:41:38,860 --> 00:41:41,230
And there are tables of
electron affinity.

860
00:41:41,230 --> 00:41:44,620
So each element has the ability
to lose an electron,

861
00:41:44,620 --> 00:41:45,950
it has the ability to
gain an electron.

862
00:41:45,950 --> 00:41:48,485
Losing an electron is ionization
energy, acquiring

863
00:41:48,485 --> 00:41:50,000
an electron is electron
affinity.

864
00:41:50,000 --> 00:41:53,100
And just as with ionization
energies, if you have multiple

865
00:41:53,100 --> 00:41:55,730
electrons you have a first
electron affinity, second

866
00:41:55,730 --> 00:41:57,580
electron affinity, and so on.

867
00:41:57,580 --> 00:42:00,270
And now how do I get
to atomic chlorine?

868
00:42:00,270 --> 00:42:02,760
I've got to dissociate
diatomic chlorine.

869
00:42:02,760 --> 00:42:04,120
So this is called
dissociation.

870
00:42:07,820 --> 00:42:08,790
So that's the whole thing.

871
00:42:08,790 --> 00:42:11,000
And I'm going to now put
some numbers on here.

872
00:42:11,000 --> 00:42:11,200
Let's see.

873
00:42:11,200 --> 00:42:16,120
I'm going to call sublimation
step one, dissociation step

874
00:42:16,120 --> 00:42:22,280
two, ionization I've got here
is step three, electron

875
00:42:22,280 --> 00:42:25,810
affinity is step four, and
crystallization or

876
00:42:25,810 --> 00:42:27,630
Madelung is step five.

877
00:42:27,630 --> 00:42:32,390
And so working off of Hess's law
we can say that the total

878
00:42:32,390 --> 00:42:36,380
energy required for the
formation of the crystal--

879
00:42:36,380 --> 00:42:38,930
delta H for the reaction.

880
00:42:38,930 --> 00:42:39,560
What's the reaction?

881
00:42:39,560 --> 00:42:41,260
The reaction of sodium
plus chlorine

882
00:42:41,260 --> 00:42:42,470
to make sodium chloride--

883
00:42:42,470 --> 00:42:47,210
is going to be the sum of all of
the constituent components.

884
00:42:47,210 --> 00:42:49,870
The sum of all the delta's H.

885
00:42:49,870 --> 00:42:51,160
Not delta H's.

886
00:42:51,160 --> 00:42:52,990
delta's H, like attorneys
general.

887
00:42:52,990 --> 00:42:53,660
All right?

888
00:42:53,660 --> 00:42:54,850
So now let's add these up.

889
00:42:54,850 --> 00:42:56,500
So we go number one.

890
00:42:56,500 --> 00:43:01,120
Number one I can look up
on the Periodic Table.

891
00:43:01,120 --> 00:43:01,510
Where is it?

892
00:43:01,510 --> 00:43:03,810
There's Fritz Haber.

893
00:43:03,810 --> 00:43:05,310
So that's given here.

894
00:43:05,310 --> 00:43:06,630
If you look on the Periodic
Table that'll

895
00:43:06,630 --> 00:43:07,770
give you the number.

896
00:43:07,770 --> 00:43:12,640
And for sodium it's 108
kilojoules per mole.

897
00:43:12,640 --> 00:43:14,990
Number two, get that
from tables.

898
00:43:14,990 --> 00:43:16,660
It's 122.

899
00:43:16,660 --> 00:43:20,310
Number three is just the first
ionization energy.

900
00:43:20,310 --> 00:43:22,250
You look it up on the
Periodic Table.

901
00:43:22,250 --> 00:43:25,220
First ionization energy of
sodium is about 5.3 electron

902
00:43:25,220 --> 00:43:29,320
volts, which turns out to be
496 kilojoules per mole.

903
00:43:29,320 --> 00:43:31,230
But look, these are all positive
energies and we're

904
00:43:31,230 --> 00:43:33,140
trying to make a net
negative energy.

905
00:43:33,140 --> 00:43:35,340
So these three steps
are all raising the

906
00:43:35,340 --> 00:43:36,600
energy of the system.

907
00:43:36,600 --> 00:43:40,820
Finally, acquiring an electron
by chlorine is going to

908
00:43:40,820 --> 00:43:43,190
decrease the energy of the
system, because chlorine is a

909
00:43:43,190 --> 00:43:44,655
good electron acceptor.

910
00:43:44,655 --> 00:43:46,430
So that's minus 349.

911
00:43:46,430 --> 00:43:47,900
But watch this people.

912
00:43:47,900 --> 00:43:51,550
The energy in forming the
crystal from the discrete

913
00:43:51,550 --> 00:43:57,220
ion-pairs is 787 kilojoules per
mole, which gives us a net

914
00:43:57,220 --> 00:44:02,690
value of minus 410 kilojoules
per mole.

915
00:44:02,690 --> 00:44:05,580
So what this is showing you
is what the relative

916
00:44:05,580 --> 00:44:07,830
contributions are
of the different

917
00:44:07,830 --> 00:44:10,630
components of that thing.

918
00:44:10,630 --> 00:44:12,450
So here it is in
graphical form.

919
00:44:12,450 --> 00:44:15,350
There's the vaporization
of sodium.

920
00:44:15,350 --> 00:44:18,390
This is the dissociation
of chlorine.

921
00:44:18,390 --> 00:44:20,500
This is the ionization
of sodium.

922
00:44:20,500 --> 00:44:21,810
All positive energies.

923
00:44:21,810 --> 00:44:23,110
And now electron affinity.

924
00:44:23,110 --> 00:44:25,870
And look at this contribution
from the Madelung energy.

925
00:44:25,870 --> 00:44:28,970
So when things crystallize a
lot of heat's given off.

926
00:44:28,970 --> 00:44:35,160
In fact, we can use that in
cooling and moderating climate

927
00:44:35,160 --> 00:44:36,700
if we're clever about it.

928
00:44:36,700 --> 00:44:37,400
All right.

929
00:44:37,400 --> 00:44:41,960
Now just to show you what the
different values are here that

930
00:44:41,960 --> 00:44:44,500
you're going to go in and get
the lattice energies, you need

931
00:44:44,500 --> 00:44:47,750
to know the various
r values, you see.

932
00:44:47,750 --> 00:44:50,970
The r0 is simply going to be
the r-plus and the r-minus.

933
00:44:50,970 --> 00:44:53,440
So lithium fluoride,
there it is.

934
00:44:53,440 --> 00:44:57,600
There's the lattice energy and
it's based on the combination

935
00:44:57,600 --> 00:45:00,090
of lithium cation and
fluoride anion.

936
00:45:00,090 --> 00:45:02,710
So they've gone through and
calculated these values.

937
00:45:02,710 --> 00:45:05,090
So there's sodium
chloride is 787.

938
00:45:05,090 --> 00:45:07,020
And, you know, you even get
things like the boiling

939
00:45:07,020 --> 00:45:08,020
points, melting points.

940
00:45:08,020 --> 00:45:11,920
So sodium chloride, for example,
melts at about 800

941
00:45:11,920 --> 00:45:13,290
degrees Celsius.

942
00:45:13,290 --> 00:45:17,310
Now if you take magnesium oxide,
magnesium oxide is,

943
00:45:17,310 --> 00:45:19,860
look, 3,700 versus 700.

944
00:45:19,860 --> 00:45:22,170
And the melting point of
magnesium oxide is

945
00:45:22,170 --> 00:45:24,480
2,800 degrees C.

946
00:45:24,480 --> 00:45:25,250
Look at aluminum.

947
00:45:25,250 --> 00:45:29,340
Aluminum plus oxygen, look at
the end binding energy there.

948
00:45:29,340 --> 00:45:33,200
It's phenomenal, which means
it might be useful for--

949
00:45:33,200 --> 00:45:34,820
I'm standing underneath
the shuttle here.

950
00:45:34,820 --> 00:45:37,800
This is the tiles underneath the
shuttle, and they're made

951
00:45:37,800 --> 00:45:40,730
of aluminum oxide because the
Madelung energy is so high so

952
00:45:40,730 --> 00:45:43,120
it's got the thermal
shock resistance.

953
00:45:43,120 --> 00:45:46,810
So now you know how to go and
design things for thermal

954
00:45:46,810 --> 00:45:48,340
ablation resistance.

955
00:45:48,340 --> 00:45:49,990
All you need is this table.

956
00:45:49,990 --> 00:45:50,800
That's all.

957
00:45:50,800 --> 00:45:52,650
No, you need a little more than
that, but this is a good

958
00:45:52,650 --> 00:45:53,740
place to start.

959
00:45:53,740 --> 00:45:56,320
If you don't understand this
table I don't want you working

960
00:45:56,320 --> 00:45:57,080
on the project.

961
00:45:57,080 --> 00:45:58,980
OK?

962
00:45:58,980 --> 00:45:59,700
What else?

963
00:45:59,700 --> 00:46:01,850
All this shows you-- yeah,
we're going skip that.

964
00:46:01,850 --> 00:46:02,160
All right.

965
00:46:02,160 --> 00:46:03,390
So now we've got a
few minutes here.

966
00:46:03,390 --> 00:46:06,360
What I want to do is last day
I talked about magnesium,

967
00:46:06,360 --> 00:46:08,020
today I want to talk
about aluminum.

968
00:46:08,020 --> 00:46:11,510
And it is also made in an
electrochemical process.

969
00:46:11,510 --> 00:46:14,370
In this case the electrodes
are horizontal.

970
00:46:14,370 --> 00:46:16,980
We feed aluminum oxide in
and we pass current--

971
00:46:16,980 --> 00:46:17,870
and huge currents.

972
00:46:17,870 --> 00:46:22,615
This thing typically runs at
300,000, 400,000 amperes and

973
00:46:22,615 --> 00:46:24,770
about 4 volts.

974
00:46:24,770 --> 00:46:27,250
So with the cathode we are
running-- remember, we're

975
00:46:27,250 --> 00:46:28,910
running nature in reverse.

976
00:46:28,910 --> 00:46:31,720
Instead of the electron donor
that aluminum is, we're

977
00:46:31,720 --> 00:46:34,370
shoving electrons onto aluminum
ion and converting it

978
00:46:34,370 --> 00:46:35,460
back to aluminum.

979
00:46:35,460 --> 00:46:39,090
Unfortunately, on the anode side
we have to use carbon,

980
00:46:39,090 --> 00:46:41,330
and the carbon itself
is consumed.

981
00:46:41,330 --> 00:46:43,320
So we consume about a half
a ton of carbon to

982
00:46:43,320 --> 00:46:44,910
make a ton of aluminum.

983
00:46:44,910 --> 00:46:47,820
So aluminum smelters generate
a lot of greenhouse gases.

984
00:46:50,640 --> 00:46:53,730
So you can see this is like
a drafting pencil: it's

985
00:46:53,730 --> 00:46:54,810
constantly being fed.

986
00:46:54,810 --> 00:46:56,340
And to give you a sense of scale
this is probably about

987
00:46:56,340 --> 00:47:00,520
10 feet across, and this gap is
about 2 inches, and this is

988
00:47:00,520 --> 00:47:02,780
about, I don't know, a
foot and a half deep.

989
00:47:02,780 --> 00:47:04,720
It's going to get about 1,000
degrees Centigrade--

990
00:47:04,720 --> 00:47:07,710
liquid aluminum and
liquid salt.

991
00:47:07,710 --> 00:47:09,660
So this is what a smelter
looks like.

992
00:47:09,660 --> 00:47:13,232
What's the sound of
electric current?

993
00:47:13,232 --> 00:47:13,650
Yeah.

994
00:47:13,650 --> 00:47:16,810
The only sound you hear is the
fans on the top that keep the

995
00:47:16,810 --> 00:47:17,470
place clean.

996
00:47:17,470 --> 00:47:19,450
There's the busbars that are
bringing in the current.

997
00:47:19,450 --> 00:47:23,410
And all of these various
posts are these things.

998
00:47:23,410 --> 00:47:25,710
So all of the magic
is occurring

999
00:47:25,710 --> 00:47:26,940
below the floor here.

1000
00:47:26,940 --> 00:47:29,780
It was invented simultaneously
in the United States by

1001
00:47:29,780 --> 00:47:32,700
Charles Martin Hall and in
France by Paul Heroult.

1002
00:47:32,700 --> 00:47:35,390
In the same year they filed
patents independently and

1003
00:47:35,390 --> 00:47:38,080
eventually crossed license
when they collided at the

1004
00:47:38,080 --> 00:47:40,260
World Court.

1005
00:47:40,260 --> 00:47:41,450
So this is what happens.

1006
00:47:41,450 --> 00:47:44,820
We dissolve aluminum oxide in
a molten fluoride called

1007
00:47:44,820 --> 00:47:48,000
cryolite, which originally
came from Greenland, make

1008
00:47:48,000 --> 00:47:49,530
liquid aluminum carbon
dioxide.

1009
00:47:49,530 --> 00:47:52,330
Now if we wanted to make this
truly green, we want to

1010
00:47:52,330 --> 00:47:55,100
eliminate greenhouse gas
emissions, you need to find an

1011
00:47:55,100 --> 00:47:56,490
inert anode.

1012
00:47:56,490 --> 00:47:59,970
So on an inert anode aluminum
oxide would be converted into

1013
00:47:59,970 --> 00:48:01,560
aluminum and oxygen.

1014
00:48:01,560 --> 00:48:06,540
So not only would you not
produce greenhouse gases but

1015
00:48:06,540 --> 00:48:10,760
you'd produce tonnage oxygen,
which is marketable.

1016
00:48:10,760 --> 00:48:14,520
So some of the work that goes
on in my lab is in advanced

1017
00:48:14,520 --> 00:48:18,380
materials with a view to trying
to find an inert anode

1018
00:48:18,380 --> 00:48:21,660
that would then make this
process very, very clean and

1019
00:48:21,660 --> 00:48:25,700
justify substituting aluminum
for steel in cars.

1020
00:48:25,700 --> 00:48:32,680
By the way, when you have the
field, even though it's a DC

1021
00:48:32,680 --> 00:48:34,980
current it's a divergent
field.

1022
00:48:34,980 --> 00:48:39,580
And this is me in a magnesium
smelter just in Utah.

1023
00:48:39,580 --> 00:48:41,690
There is the busbar for
the magnesium cell.

1024
00:48:41,690 --> 00:48:44,360
So I'm about, oh, two
meters away from

1025
00:48:44,360 --> 00:48:46,240
the edge of the busbars.

1026
00:48:46,240 --> 00:48:49,180
The magnetic field is so high
I've got one, two, three,

1027
00:48:49,180 --> 00:48:54,560
four, five paper clips standing
against gravity.

1028
00:48:54,560 --> 00:48:57,720
And I asked them for paper
clips and there

1029
00:48:57,720 --> 00:48:58,560
was no office there.

1030
00:48:58,560 --> 00:48:59,920
They managed to find a few.

1031
00:48:59,920 --> 00:49:01,540
I wanted to see how
many would go.

1032
00:49:01,540 --> 00:49:04,520
I'm willing to bet I could
probably have about seven or

1033
00:49:04,520 --> 00:49:07,510
eight paper clips up before the
gravity would cause them

1034
00:49:07,510 --> 00:49:07,970
to collapse.

1035
00:49:07,970 --> 00:49:09,290
That's the intensity
of magnetic

1036
00:49:09,290 --> 00:49:10,770
fields in these smelters.

1037
00:49:10,770 --> 00:49:14,230
So when you drive up to the
smelter for the tour you park

1038
00:49:14,230 --> 00:49:16,940
a fair distance away, you leave
your wallet with the

1039
00:49:16,940 --> 00:49:19,940
credit cards in it, because
this is the biggest bulk

1040
00:49:19,940 --> 00:49:22,410
demagnetizer you can imagine.

1041
00:49:22,410 --> 00:49:25,630
If you've got a watch that's
got hands that move they're

1042
00:49:25,630 --> 00:49:26,655
going to be going like this.

1043
00:49:26,655 --> 00:49:28,590
[GESTURING]

1044
00:49:28,590 --> 00:49:30,640
PROFESSOR: Yeah.

1045
00:49:30,640 --> 00:49:32,430
This is the shuttle.

1046
00:49:32,430 --> 00:49:34,870
This is forged aluminum
wheels.

1047
00:49:34,870 --> 00:49:37,410
The shuttle lands on Centerline
racing wheels.

1048
00:49:37,410 --> 00:49:39,140
They're forged at a place
in California.

1049
00:49:39,140 --> 00:49:40,810
They're made of aluminum
alloy.

1050
00:49:40,810 --> 00:49:42,870
And I don't know if you can read
on the side here, it's a

1051
00:49:42,870 --> 00:49:45,340
little bit light, but these
are special tires.

1052
00:49:45,340 --> 00:49:48,800
They're made by Michelin

1053
00:49:48,800 --> 00:49:54,880
So, anyways, the whole message
here is learn the lessons here

1054
00:49:54,880 --> 00:49:59,760
in 3.091 and then we can work
together to make metal in an

1055
00:49:59,760 --> 00:50:01,230
environmentally acceptable
way.

1056
00:50:01,230 --> 00:50:04,050
And just before I send you on
your way for the weekend I

1057
00:50:04,050 --> 00:50:06,890
thought I'd tell a little
joke related to

1058
00:50:06,890 --> 00:50:08,400
the uncertainty principle.

1059
00:50:08,400 --> 00:50:09,380
So the joke goes like this.

1060
00:50:09,380 --> 00:50:13,740
Heisenberg is racing down the
Autobahn and he gets pulled

1061
00:50:13,740 --> 00:50:18,410
over by the state trooper who
comes to the car and says,

1062
00:50:18,410 --> 00:50:20,610
where's the fire buddy?

1063
00:50:20,610 --> 00:50:22,560
Do you know how fast
you were going?

1064
00:50:22,560 --> 00:50:25,860
And Heisenberg looks at
him he says, no, but I

1065
00:50:25,860 --> 00:50:27,122
know where I am.

1066
00:50:27,122 --> 00:50:28,300
[LAUGHTER]

1067
00:50:28,300 --> 00:50:28,670
PROFESSOR: All right.

1068
00:50:28,670 --> 00:50:29,270
Get out of here.

1069
00:50:29,270 --> 00:50:30,890
Have a good weekend.