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I just wanted to briefly remind
you of some of the periodic

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trends that we talked about.
As you go across the periodic

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table, both the electron
affinity and the ionization

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energy increase.
They increase because the

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nuclear charge increases.
Remember, the potential energy

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of interaction is Z times e,
where that is the nuclear

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charges, times e over 4 pi
epsilon nought r.

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Z increases as you go across
the periodic table here.

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As you go across,
r is remaining the same because

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you are essentially still in the
same shell.

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And so what increases is that
attractive interaction,

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meaning the electrons are more
strongly bound,

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meaning ionization energy and
electron affinity increases as

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you go across.
And this also means,

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as you go across,
r, the radius decreases.

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The radius decreases again
because Z increases.

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The nucleus is pulling the
electrons in closer.

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Since they are all in the same
shell, r is remaining the same.

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00:01:44,000 --> 00:01:49,000
And so, the overall effect is
that the radius of the atoms

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decreases.
As you go down the Periodic

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Table, the ionization energy and
the electron affinity decrease.

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00:02:00,000 --> 00:02:04,000
They decrease because it is the
r dependence,

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00:02:04,000 --> 00:02:07,000
here, that takes over.
Z is, of course,

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increasing, but not as fast as
r.

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As you go down the Periodic
Table, you are going to shells

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that, on the average,
are further out from the

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nucleus.
And that dependence takes over,

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causing EA and IE to decrease.
And then the radius,

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00:02:30,000 --> 00:02:34,000
of course, increases,
because, as you go down,

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you are putting the electrons
into shells which are on the

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average farther away from the
nucleus.

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00:02:44,000 --> 00:02:48,000
That is just a review of those
trends.

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00:02:48,000 --> 00:02:53,000
Then, finally,
I want to just define another

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term, and that is the
electronegativity.

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00:02:59,000 --> 00:03:01,000
Sometimes we give that the
symbol chi.

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The electronegativity is an
empirical quantity.

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00:03:05,000 --> 00:03:09,000
We are going to use Mulliken's
definition for the

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electronegativity.
There is a Pauling definition.

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Mulliken is a little bit more
straightforward.

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And that electronegativity is
defined as one-half times the

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quantity ionization energy plus
the electron affinity.

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The electronegativity is

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proportional to the average of
the ionization energy and the

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electron affinity.
The electronegativity is a

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00:03:42,000 --> 00:03:48,000
measure of the tendency of an
atom to accept or to donate an

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electron.
If you look at the Periodic

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Table, here, you have atoms in
the upper right-hand corner of

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the Periodic Table.
Well, they have high

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electronegativities.
They are good electron

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acceptors.
They have high

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00:04:09,000 --> 00:04:15,000
electronegativities because they
have high electron affinities.

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Adding an electron to them
means that there is a larger

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amount of energy release.
The anion is much more stable

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than the neutral.
And the electron affinity is

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minus that energy change,
remember from last time.

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These atoms here,
with their high electron

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affinities, are good electron
acceptors.

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They are also good electron
acceptors because their

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ionization energies are also
high, which means you have to

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put in a lot of energy to pull
an electron off.

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They don't like to donate
electrons, rather they are good

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electron acceptors.
And then, the elements that are

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in the bottom left-hand corner
of the Periodic Table have low

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electronegativities.
They are good electron donors

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because their ionization energy
is low in this part of the

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periodic table.
You don't have to put in so

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00:05:22,000 --> 00:05:26,000
much energy to pull an electron
off.

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They are also good electron
donors because their electron

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affinity is low.
You don't get as much energy

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back when you put an electron on
them.

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These are good electron donors.
High chi, here.

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These are good electron
acceptors.

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And one thing you already know
probably is that some of the

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strongest ionic bonds are made
between elements in these two

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corners of the periodic table.
An ionic bond,

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as we are going to talk about,
is one in which the electrons

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are not shared equally.
And so these strong ionic bonds

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occur between elements with high
electronegativity and low

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electronegativity.
So that's that concept.

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And then, finally,
one other kind of odd and end

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here.
That is this term

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isoelectronic.
I have listed here a bunch of

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atoms and ions that are
isoelectronic.

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Isoelectronic means having the
same electron structure.

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All of these atoms and ions
have the electron configuration

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1s 2 2s 2 2p 6.

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For example,
this nitrogen,

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N minus 3,
it has added three electrons to

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be nitrogen minus three.
It has added three electrons to

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get this electron configuration,
this rare gas configuration,

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this octet configuration which
is a very stable configuration.

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Aluminum has three electrons
removed to obtain this

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particular electron
configuration.

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The common ions,
ions that you see commonly in

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nature, are ions that,
in fact, do have this octet

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configuration,
this electron configuration of

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an inert gas.
For example,

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you will often see compounds
with nitrogen minus three.

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You won't very often see a

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compound with nitrogen minus two
or nitrogen minus one

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because those are not
as stable as nitrogen minus

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three,
given this rare gas or the

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octet configuration.
All right.

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That is just a little odd and
end.

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I just wanted to make sure that
everybody was on the same level

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with the understanding of the
word isoelectronic there.

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Well, now what I thought I
would do is talk a little bit

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about wave functions and the
usefulness of wave functions.

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This is going to be on the side
boards here.

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I wanted to just show you in
kind of simple terms how a wave

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function actually determines the
intensity of some transition.

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Many of you have asked me about
the intensities of transitions,

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00:08:47,000 --> 00:08:53,000
and so I thought I would show
you just a little bit about how

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these wave functions determine
the intensities of transitions.

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00:09:00,000 --> 00:09:03,000
First of all,
I have to explain this diagram

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to you.
This is going to be a diagram

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for a hydrogen atom.
That is what we are going to

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talk about here.
What we are going to start with

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is an energy level diagram for
the hydrogen atoms.

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That is what this axis is.
And so, I am plotting in that

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diagram, energy,
going up.

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And I plot the energy level for
n equals 1.

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I plot the energy level for n
equals 2, n equals 3,

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all the way up to n equals 235,
which is really very close to

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zero.
That is part of what is on this

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plot right here,
n equals 1, n equals 2,

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n equals 3.
But then, what is also

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00:10:00,000 --> 00:10:07,000
typically done on the same plot
is that the potential energy of

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interaction is plotted as a
function of r.

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00:10:11,000 --> 00:10:17,000
And so, on this axis here,
kind of superimposed,

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00:10:17,000 --> 00:10:22,000
is this distance r.
And we plot often the potential

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energy of interaction.
The potential energy of

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interaction kind of looks like
that.

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00:10:33,000 --> 00:10:37,000
This potential energy of
interaction is the Coulomb

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00:10:37,000 --> 00:10:43,000
interaction, minus e squared 4
pi epsilon nought times r.

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00:10:43,000 --> 00:10:48,000
That is what that line is on

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this plot.
Then what we do is we actually

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plot the form of the wave
function, kind of on top of the

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energy levels.
What we do is to say,

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00:11:01,000 --> 00:11:04,000
for example,
take the n equals 1 wave

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function, which starts at r
equals 0 at some finite value

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and it is just an exponential
decay.

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00:11:14,000 --> 00:11:19,000
And we plot it on this diagram,
but we use the n equals 1

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energy here as the value of Psi
equals 0.

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00:11:23,000 --> 00:11:28,000
In other words,
the n equals 1 wave function

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00:11:28,000 --> 00:11:34,000
looks kind of like that.
This level here is Psi equals

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00:00:00,000 --> 00:11:36,000
This is the value of Psi,

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00:11:36,000 --> 00:11:38,000
whatever it is,
at r equals 0,

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00:11:38,000 --> 00:11:41,000
and there is just an
exponential decay.

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We plot the wave function on
top of that energy level.

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In other words,
this is a complex diagram here.

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You are going to see,
if you take any course beyond

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this, this diagram a lot,
with energy levels and wave

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functions plotted on top of
them.

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00:12:02,000 --> 00:12:07,000
And then, the n equals 2 wave
function is plotted on top of

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the n equals 2 energy level.
Again, at r equals 0,

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it is some finite value and
then it drops.

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At some value of r,
we have a node for n equals 2

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here.
The n equals 2 is the Psi

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00:12:21,000 --> 00:12:25,000
equals 0.
Right here, you have a radial

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node.
Then it goes up and then it

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comes back.
It goes down to a negative

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value and then comes back up.
That is n equals 2.

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00:12:37,000 --> 00:12:42,000
And so forth and so on.
n equals 3 looks like this.

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It has two radial nodes.
That is what that diagram is

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showing here.
And then we get to n equals

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Here is the wave function.

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Is this is a hydrogen atom and
you have n equals 235,

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how many radial nodes do you
have?

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This wave function is passing

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00:13:06,000 --> 00:13:11,000
through this origin 234 times.
That is the wave function.

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00:13:11,000 --> 00:13:16,000
And then it tails off.
There is always an exponential

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00:13:16,000 --> 00:13:20,000
dependence there.
That is what that wave function

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looks like.
Now, how do these relate to the

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intensity of some transition?
Well, the intensity of a

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transition is related to the
overlap between the wave

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function of the initial state
and the wave function of the

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final state.
What do I mean by overlap?

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00:13:42,000 --> 00:13:46,000
Well, by overlap,
I mean you take the wave

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function, here,
of the initial state,

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00:13:49,000 --> 00:13:54,000
so I am going to pretend we
have a hydrogen atom in the

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00:13:54,000 --> 00:13:57,000
state, this is its wave
function.

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00:13:57,000 --> 00:14:03,000
And that hydrogen atom is going
to be relaxing to the n equals 1

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state.
What I am going to do,

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to get the overlap,
is I'm going to take the

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00:14:09,000 --> 00:14:14,000
product of the wave function of
the initial state times that of

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00:14:14,000 --> 00:14:17,000
the final state,
and essentially I am going to

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00:14:17,000 --> 00:14:19,000
integrate that resulting
function.

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00:14:19,000 --> 00:14:23,000
I am going to multiply these
two wave functions together,

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00:14:23,000 --> 00:14:27,000
and I am going to integrate
over all r the resulting

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00:14:27,000 --> 00:14:31,000
function.
That is what I mean by overlap.

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00:14:31,000 --> 00:14:33,000
But there is another term here.
There is an r,

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00:14:33,000 --> 00:14:35,000
too.
That r is important.

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00:14:35,000 --> 00:14:38,000
It has to do with the
transition moment dipole.

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00:14:38,000 --> 00:14:41,000
And we won't go into that,
but it is there.

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00:14:41,000 --> 00:14:44,000
But it won't affect the
argument I am going to make for

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00:14:44,000 --> 00:14:47,000
you right now.
We take the wave function of

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00:14:47,000 --> 00:14:50,000
the initial state,
multiply it by the final state

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00:14:50,000 --> 00:14:54,000
times r, and then we integrate
this whole thing from r equals 0

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00:14:54,000 --> 00:15:00,000
to infinity and then square it.
That quantity is proportional

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00:15:00,000 --> 00:15:03,000
to the intensity of some
transition.

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00:15:03,000 --> 00:15:07,000
Let's do that.
Here is Psi n equals 235,

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00:15:07,000 --> 00:15:11,000
we are multiplying it by Psi of

208
00:15:11,000 --> 00:15:16,000
n equals 0 and
actually multiplying it by r.

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00:15:16,000 --> 00:15:22,000
And what we are going to see,
if we just look at this product

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00:15:22,000 --> 00:15:28,000
here, if we just looked at Psi n
equals 235 and

211
00:15:28,000 --> 00:15:33,000
Psi n equals 1,
if we just looked at that

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00:15:33,000 --> 00:15:39,000
product, we are going to
multiply this times that.

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00:15:39,000 --> 00:15:42,000
In a graphical form,
it is going to look like this.

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00:15:42,000 --> 00:15:44,000
It is going to go up,
down, up, down,

215
00:15:44,000 --> 00:15:47,000
up, down.
It is going to oscillate and

216
00:15:47,000 --> 00:15:51,000
then tail off in an exponential
way because we are multiply this

217
00:15:51,000 --> 00:15:53,000
up, down, up,
down, up down times this

218
00:15:53,000 --> 00:15:56,000
exponential decay.
It is going to look something

219
00:15:56,000 --> 00:16:00,000
like that.
But now, we are going to

220
00:16:00,000 --> 00:16:04,000
integrate this resulting curve.
What you can see is that the

221
00:16:04,000 --> 00:16:09,000
area above this curve is equal
to the area below this curve,

222
00:16:09,000 --> 00:16:12,000
approximately.
And, when we integrate

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00:16:12,000 --> 00:16:17,000
something, we are calculating
the area underneath the curve.

224
00:16:17,000 --> 00:16:23,000
These positive areas are going
to cancel these negative areas.

225
00:16:23,000 --> 00:16:27,000
The result is that this
integral is going to be very

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00:16:27,000 --> 00:16:31,000
small.
And the result is that the

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00:16:31,000 --> 00:16:34,000
intensity of that line is very
low.

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00:16:34,000 --> 00:16:38,000
The intensities are
proportional to this overlap,

229
00:16:38,000 --> 00:16:42,000
the overlap of the initial
state wave function and the

230
00:16:42,000 --> 00:16:46,000
final state wave function.
And you can see,

231
00:16:46,000 --> 00:16:49,000
here, graphically,
how if you integrate that

232
00:16:49,000 --> 00:16:53,000
product in this case,
the positive areas cancel the

233
00:16:53,000 --> 00:16:57,000
negative areas,
and you don't have a very

234
00:16:57,000 --> 00:17:02,000
intense transition.
However, suppose we look at the

235
00:17:02,000 --> 00:17:06,000
transition from n equals 3 to n
equals 2.

236
00:17:06,000 --> 00:17:10,000
Well, here is the n equals 3
wave function,

237
00:17:10,000 --> 00:17:13,000
here is the n equals 2 wave
function.

238
00:17:13,000 --> 00:17:19,000
And our intensity expression
says that we have to multiply

239
00:17:19,000 --> 00:17:21,000
these two.
Let's do that.

240
00:17:21,000 --> 00:17:25,000
Let's multiply n equals 3 times
n equals 2, here.

241
00:17:25,000 --> 00:17:30,000
Well, the result,
if you excuse my not so great

242
00:17:30,000 --> 00:17:37,000
drawing, is we start out with a
very positive function here.

243
00:17:37,000 --> 00:17:42,000
But then we have two negatives
here, which make it a little bit

244
00:17:42,000 --> 00:17:45,000
less negative.
But then, we have a positive,

245
00:17:45,000 --> 00:17:50,000
here, times a negative,
and what that makes is a large

246
00:17:50,000 --> 00:17:54,000
area that is negative.
And, if we go and integrate

247
00:17:54,000 --> 00:17:59,000
that, now we don't have the same
cancellation of positive and

248
00:17:59,000 --> 00:18:03,000
negative areas.
We integrate that,

249
00:18:03,000 --> 00:18:06,000
and that transition energy is
large.

250
00:18:06,000 --> 00:18:10,000
Or, that area is large,
therefore the intensity of that

251
00:18:10,000 --> 00:18:12,000
transition is large.
Bottom line,

252
00:18:12,000 --> 00:18:17,000
that is one of the elements
that dictates the intensity of a

253
00:18:17,000 --> 00:18:20,000
transition.
It is also one of the elements

254
00:18:20,000 --> 00:18:24,000
that dictates the intensity of
your photoelectron spectra.

255
00:18:24,000 --> 00:18:29,000
Somebody asked me about it the
other day.

256
00:18:29,000 --> 00:18:32,000
I had drawn lines in the
photoelectronic spectra that

257
00:18:32,000 --> 00:18:36,000
were of the same intensity,
1s, 2s, 2p 6.

258
00:18:36,000 --> 00:18:40,000
Somebody said,
well, you have more electrons

259
00:18:40,000 --> 00:18:43,000
in the 2p state.
Why don't you have a larger

260
00:18:43,000 --> 00:18:46,000
number of electrons coming off?
The answer is,

261
00:18:46,000 --> 00:18:51,000
that is part of what goes into
determining the intensity of the

262
00:18:51,000 --> 00:18:54,000
transition, but there is more to
it.

263
00:18:54,000 --> 00:18:57,000
It is not just the number of
electrons.

264
00:18:57,000 --> 00:19:01,000
Here is one of the elements
that goes into determining the

265
00:19:01,000 --> 00:19:07,000
intensity of some transition.
It is the wave functions and

266
00:19:07,000 --> 00:19:13,000
the overlap between the final
and the initial state.

267
00:19:13,000 --> 00:19:17,000
And then, I just wanted to also
show you, here,

268
00:19:17,000 --> 00:19:23,000
for this atom in the n equals
235 state, I plotted just for

269
00:19:23,000 --> 00:19:29,000
fun, kind of schematically,
what the radial probability

270
00:19:29,000 --> 00:19:35,000
distribution would look like.
That is just r squared times

271
00:19:35,000 --> 00:19:38,000
the radial part squared.
And, of course,

272
00:19:38,000 --> 00:19:41,000
since the wave function goes
like this, oscillates,

273
00:19:41,000 --> 00:19:45,000
that is what the radial
probability distribution is

274
00:19:45,000 --> 00:19:48,000
going to do.
And you are going to see

275
00:19:48,000 --> 00:19:52,000
nodes here, 234 values of r,
that is going to make the wave

276
00:19:52,000 --> 00:19:56,000
function be equal to zero.
And then way out here,

277
00:19:56,000 --> 00:20:00,000
you are going to have a
feature.

278
00:20:00,000 --> 00:20:04,000
That last feature,
here, is going to have the

279
00:20:04,000 --> 00:20:09,000
maximum probability,
and that is your value of r

280
00:20:09,000 --> 00:20:15,000
that is most probable.
It turns out for n equals

281
00:20:15,000 --> 00:20:21,000
that the most probable value of
r is 43,800 angstroms.

282
00:20:21,000 --> 00:20:24,000
That is about 4.38x10^-6
meters.

283
00:20:24,000 --> 00:20:31,000
This is a really large hydrogen
atom, n equals 235.

284
00:20:31,000 --> 00:20:33,000
Do they exist?
The answer is yes,

285
00:20:33,000 --> 00:20:37,000
they do exist.
They exist, particularly in

286
00:20:37,000 --> 00:20:41,000
outer space, where there is lots
of UV radiation to get these

287
00:20:41,000 --> 00:20:45,000
hydrogen atoms up into these
very excited states.

288
00:20:45,000 --> 00:20:50,000
And they exist in deep outer
space, where the temperatures

289
00:20:50,000 --> 00:20:53,000
are pretty cold.
And you need those cold

290
00:20:53,000 --> 00:20:58,000
temperatures because this
hydrogen atom is not very stable

291
00:20:58,000 --> 00:21:06,000
in n equals 235.
And, if you went and calculated

292
00:21:06,000 --> 00:21:12,000
here, I am going to draw a line,
here.

293
00:21:12,000 --> 00:21:21,000
This is going to be n equals
235, and this is the zero of

294
00:21:21,000 --> 00:21:27,000
energy.
This energy difference here is

295
00:21:27,000 --> 00:21:34,000
about 4x10^-23 joules.
Whereas, at room temperature,

296
00:21:34,000 --> 00:21:38,000
we will just talk about the
thermal energy,

297
00:21:38,000 --> 00:21:41,000
thermal energy is about
4x10^-21 joules.

298
00:21:41,000 --> 00:21:46,000
You can see that any little
fluctuation at room temperature,

299
00:21:46,000 --> 00:21:52,000
since this is two orders of
magnitude larger than what this

300
00:21:52,000 --> 00:21:57,000
bound by, any little fluctuation
would kick this very weakly

301
00:21:57,000 --> 00:22:02,000
bound electron up and ionize it.
And it would.

302
00:22:02,000 --> 00:22:07,000
You really only see these in
environments that are very cold,

303
00:22:07,000 --> 00:22:12,000
where you don't perturb what
are called Rydberg atoms

304
00:22:12,000 --> 00:22:16,000
sometimes.
I think in the laboratory the

305
00:22:16,000 --> 00:22:22,000
largest Rydberg atom that has
been made is n equals 180 or n

306
00:22:22,000 --> 00:22:26,000
equals 200 or so.
Anyway, that was really just

307
00:22:26,000 --> 00:22:32,000
for fun that I wanted to tell
you about that.

308
00:22:32,000 --> 00:22:38,000
Now, there is another little
tidbit that I want to talk to

309
00:22:38,000 --> 00:22:44,000
you about that has to do with
how knowing something about the

310
00:22:44,000 --> 00:22:51,000
energy levels in an atom leads
to a nice practical device,

311
00:22:51,000 --> 00:22:57,000
like a helium neon laser.
We have to take a look at the

312
00:22:57,000 --> 00:23:02,000
neon energy levels.
And so we have another

313
00:23:02,000 --> 00:23:07,000
discharge lamp here,
and we have some more of these

314
00:23:07,000 --> 00:23:12,000
glasses, here,
so that you can resolve the

315
00:23:12,000 --> 00:23:16,000
neon lines here.
The TAs will get them out.

316
00:23:16,000 --> 00:23:21,000
Here is our neon discharge
lamp.

317
00:23:27,000 --> 00:23:30,000
You can resolve,
here, the neon spectrum.

318
00:23:30,000 --> 00:23:34,000
The spectrum that you should
see should be what is shown on

319
00:23:34,000 --> 00:23:38,000
the side walls here.
Let me turn off the lights so

320
00:23:38,000 --> 00:23:43,000
that you can see it a little bit
better, hopefully.

321
00:23:52,000 --> 00:23:57,000
You can see lots of lines in
the case of neon because we have

322
00:23:57,000 --> 00:24:00,000
lots of different occupied
states.

323
00:24:00,000 --> 00:24:05,000
The glasses that I have
actually are doing a phenomenal

324
00:24:05,000 --> 00:24:10,000
job in resolving those very
closely spaced lines.

325
00:24:10,000 --> 00:24:15,000
I must have a better quality
glass today.

326
00:24:35,000 --> 00:24:40,000
And, if you look at the side
walls, you can see that I drew

327
00:24:40,000 --> 00:24:44,000
one of those lines.
One of those emission lines is

328
00:24:44,000 --> 00:24:48,000
at 632 nanometers,
which is the emission line of a

329
00:24:48,000 --> 00:24:52,000
helium neon laser.
But it is really a neon

330
00:24:52,000 --> 00:24:56,000
transition that we will talk
about in a moment.

331
00:24:56,000 --> 00:25:01,000
I drew it as very thick on the
board.

332
00:25:01,000 --> 00:25:05,000
Because when I looked at the
discharge lamp and drew that

333
00:25:05,000 --> 00:25:10,000
picture, my glasses did not
resolve those lines so very

334
00:25:10,000 --> 00:25:13,000
well.
And so that one looked really

335
00:25:13,000 --> 00:25:16,000
thick to me.
At least my glasses,

336
00:25:16,000 --> 00:25:20,000
I can really see lots and lots
of discrete lines.

337
00:25:20,000 --> 00:25:23,000
But it is this transition,
632 nanometers,

338
00:25:23,000 --> 00:25:27,000
that is the output of the
helium neon laser,

339
00:25:27,000 --> 00:25:32,000
which is the red laser that I
use sometimes in the lecture,

340
00:25:32,000 --> 00:25:37,000
here, to point.
It is the basis of the laser

341
00:25:37,000 --> 00:25:43,000
that is used in the grocery
stores to scan the prices on

342
00:25:43,000 --> 00:25:46,000
your items.
And it turns out that what is

343
00:25:46,000 --> 00:25:50,000
going on, here,
is the following.

344
00:25:50,000 --> 00:25:55,000
If you look on the side walls,
we have neon in the ground

345
00:25:55,000 --> 00:26:00,000
state before we turn the
discharge on.

346
00:26:00,000 --> 00:26:04,000
And then, when we turn the
discharge on,

347
00:26:04,000 --> 00:26:11,000
that pumps energy into the neon
atoms such that one of those

348
00:26:11,000 --> 00:26:17,000
electrons, the 2p electron,
gets promoted into the 5s

349
00:26:17,000 --> 00:26:20,000
state.
And then, of course,

350
00:26:20,000 --> 00:26:26,000
that atom wants to relax.
And so here it comes again.

351
00:26:26,000 --> 00:26:33,000
That 5s state relaxes.
That electron relaxes to the 3p

352
00:26:33,000 --> 00:26:35,000
state.
And it is actually that

353
00:26:35,000 --> 00:26:41,000
transition that occurs at 632.8
nanometers, the basis of the

354
00:26:41,000 --> 00:26:45,000
helium neon laser.
It is that transition,

355
00:26:45,000 --> 00:26:50,000
from the 5s to the 3p.
It is not all the way down,

356
00:26:50,000 --> 00:26:54,000
but ultimately,
of course, that state relaxes.

357
00:26:54,000 --> 00:27:00,000
But what is going on in the
helium neon laser?

358
00:27:00,000 --> 00:27:05,000
Well, in the helium neon laser,
we have a discharge ignited

359
00:27:05,000 --> 00:27:10,000
where we have a lot of neon
atoms here in this excited

360
00:27:10,000 --> 00:27:16,000
state, with the one electron in
the 5s state right as I show

361
00:27:16,000 --> 00:27:18,000
you.
And that is emitting,

362
00:27:18,000 --> 00:27:24,000
a photon comes out.
But what is happening here is

363
00:27:24,000 --> 00:27:30,000
that the photon that is emitted
is able to, because of the

364
00:27:30,000 --> 00:27:36,000
construction of this laser,
contact or to interact with

365
00:27:36,000 --> 00:27:41,000
another neon atom in this same
excited state,

366
00:27:41,000 --> 00:27:48,000
that 2p 5 5s state.
That photon interacts with this

367
00:27:48,000 --> 00:27:53,000
excited atom.
When it interacts with that

368
00:27:53,000 --> 00:27:58,000
excited atom,
what happens is that the photon

369
00:27:58,000 --> 00:28:04,000
stimulates that excited atom to
actually emit a photon of the

370
00:28:04,000 --> 00:28:10,000
same energy.
This photon stimulates this

371
00:28:10,000 --> 00:28:14,000
excited atom to release its
energy right at that time.

372
00:28:14,000 --> 00:28:18,000
The result is that you have two
photons coming out.

373
00:28:18,000 --> 00:28:23,000
They are going to come out in
the same direction and they are

374
00:28:23,000 --> 00:28:26,000
going to be what is called
coherent.

375
00:28:26,000 --> 00:28:31,000
That is, their phases are going
to match.

376
00:28:31,000 --> 00:28:36,000
If you think now of the photon
as a wave, they are going to be

377
00:28:36,000 --> 00:28:39,000
coherent.
And the result is that you are

378
00:28:39,000 --> 00:28:44,000
going to have some radiation
that is going to be twice as

379
00:28:44,000 --> 00:28:47,000
intense because they are
coherent.

380
00:28:47,000 --> 00:28:51,000
They are in phase.
And then, what happens is that

381
00:28:51,000 --> 00:28:55,000
these two photons,
they each then interact with

382
00:28:55,000 --> 00:29:01,000
another neon atom in this same
excited state.

383
00:29:01,000 --> 00:29:06,000
And each of those photons
stimulates another atom to emit

384
00:29:06,000 --> 00:29:09,000
photons.
And the result is now that you

385
00:29:09,000 --> 00:29:14,000
have four photons being emitted,
the same frequency,

386
00:29:14,000 --> 00:29:17,000
same direction,
and same phase.

387
00:29:17,000 --> 00:29:22,000
And it is in this way that we
amplify the light in any kind of

388
00:29:22,000 --> 00:29:25,000
laser.
This is what is going on,

389
00:29:25,000 --> 00:29:30,000
this process of simulated
emission.

390
00:29:30,000 --> 00:29:34,000
Where you have a photon that
now is exactly the frequency of

391
00:29:34,000 --> 00:29:40,000
the energy difference of the
transition that you are going to

392
00:29:40,000 --> 00:29:44,000
make in this excited atom.
This stimulates that atom to

393
00:29:44,000 --> 00:29:48,000
emit a photon.
The two photons then come off

394
00:29:48,000 --> 00:29:51,000
coherently.
And then, these two interact

395
00:29:51,000 --> 00:29:55,000
with two other atoms.
Now you have four photons that

396
00:29:55,000 --> 00:29:58,000
are coming off.
That is the process of

397
00:29:58,000 --> 00:30:03,000
amplification in any type of
laser.

398
00:30:08,000 --> 00:30:13,000
Of course, in order to make
this work, you have to have a

399
00:30:13,000 --> 00:30:19,000
lot of these excited neon atoms
around because you have to be

400
00:30:19,000 --> 00:30:25,000
able to have a photon interact
with them before they just emit

401
00:30:25,000 --> 00:30:30,000
spontaneously.
This is stimulated emission.

402
00:30:30,000 --> 00:30:34,000
The other kind of emission that
we were talking about is

403
00:30:34,000 --> 00:30:36,000
spontaneous emission.
In other words,

404
00:30:36,000 --> 00:30:40,000
you have to have a high
concentration of these excited

405
00:30:40,000 --> 00:30:44,000
neon atoms so that the photons
that are originally emitted

406
00:30:44,000 --> 00:30:48,000
here, by just spontaneous
emission, can interact with

407
00:30:48,000 --> 00:30:52,000
those excited state neon atoms
and stimulate the emission and

408
00:30:52,000 --> 00:30:57,000
get this whole process rolling.
In order to produce a whole lot

409
00:30:57,000 --> 00:31:01,000
of those excited neon atoms,
what happens is we add in a

410
00:31:01,000 --> 00:31:06,000
little bit of helium.
It turns out that in helium

411
00:31:06,000 --> 00:31:10,000
there are some excited states
that are just,

412
00:31:10,000 --> 00:31:13,000
by accident,
at the same energy as this

413
00:31:13,000 --> 00:31:17,000
excited state of neon.
And the helium actually

414
00:31:17,000 --> 00:31:21,000
transfers its energy to the
neon, into this state,

415
00:31:21,000 --> 00:31:25,000
and maintains,
then, that very high population

416
00:31:25,000 --> 00:31:30,000
of neon atoms here in this
excited state.

417
00:31:30,000 --> 00:31:32,000
That is the function of the
helium.

418
00:31:32,000 --> 00:31:37,000
It is just the energy transfer
from the helium excited state to

419
00:31:37,000 --> 00:31:42,000
the neon excited state.
It keeps the population of the

420
00:31:42,000 --> 00:31:46,000
neon atoms really high.
The helium, you don't see that

421
00:31:46,000 --> 00:31:49,000
emission.
That is just a helper in this

422
00:31:49,000 --> 00:31:53,000
device.
It is the neon transition that

423
00:31:53,000 --> 00:31:59,000
you are looking at here.
That was just a short story

424
00:31:59,000 --> 00:32:06,000
about the usefulness of knowing
about the energy levels in atoms

425
00:32:06,000 --> 00:32:14,000
and how ultimately you can make
a practical device because you

426
00:32:14,000 --> 00:32:20,000
know something about the energy
levels of your atoms.

427
00:32:20,000 --> 00:32:25,000
Well, that is going to finish
up, right now,

428
00:32:25,000 --> 00:32:32,000
our discussion of atoms.
And now, it is time to move

429
00:32:32,000 --> 00:32:36,000
onto one of the very important
parts of chemistry,

430
00:32:36,000 --> 00:32:42,000
and that is chemical bonds and
the combination of atoms to form

431
00:32:42,000 --> 00:32:46,000
a chemical bond.
That is what we are going to

432
00:32:46,000 --> 00:32:48,000
start talking about,
now.

433
00:32:48,000 --> 00:32:53,000
Today, what we are going to do
is just talk about the

434
00:32:53,000 --> 00:32:58,000
fundamental interactions that
are present in every chemical

435
00:32:58,000 --> 00:33:02,000
bond.
Let's start with that.

436
00:33:02,000 --> 00:33:07,000
Let me come over here while the
lights are warming up so you can

437
00:33:07,000 --> 00:33:12,000
see that board.
Suppose we have a hydrogen atom

438
00:33:12,000 --> 00:33:14,000
here, nucleus a,
plus charge.

439
00:33:14,000 --> 00:33:19,000
And it, of course,
has electron a attached to it.

440
00:33:19,000 --> 00:33:23,000
And way out here,
we have nucleus b and electron

441
00:33:23,000 --> 00:33:30,000
b that is attached to it.
And they are very far apart.

442
00:33:30,000 --> 00:33:34,000
And so, in this case,
where they are very far apart,

443
00:33:34,000 --> 00:33:39,000
the energy of interaction is
just the energy of interaction

444
00:33:39,000 --> 00:33:44,000
between the electron and the
nucleus, the electron-nuclear

445
00:33:44,000 --> 00:33:46,000
attraction.
Here it is, the

446
00:33:46,000 --> 00:33:52,000
electron-nuclear attraction.
However, as we bring these two

447
00:33:52,000 --> 00:33:56,000
hydrogen atoms together,
at some point this electron

448
00:33:56,000 --> 00:34:01,000
that was only attracted to
nucleus a is now begins to

449
00:34:01,000 --> 00:34:06,000
experience an attraction with
nucleus b.

450
00:34:06,000 --> 00:34:10,000
And this electron that was
attracted only to nucleus b

451
00:34:10,000 --> 00:34:14,000
experiences an interaction
whereby it is now attracted to

452
00:34:14,000 --> 00:34:17,000
nucleus a.
And that kind of mutual

453
00:34:17,000 --> 00:34:22,000
attractive interaction then
brings those two nuclei closer

454
00:34:22,000 --> 00:34:25,000
together.
However, at the same time,

455
00:34:25,000 --> 00:34:29,000
when you bring those two nuclei
closer together,

456
00:34:29,000 --> 00:34:34,000
you are bringing the electrons
closer together.

457
00:34:34,000 --> 00:34:38,000
And so there is an
electron-electron repulsion that

458
00:34:38,000 --> 00:34:40,000
is present.
In addition,

459
00:34:40,000 --> 00:34:45,000
as you bring these two nuclei
together, what is happening here

460
00:34:45,000 --> 00:34:49,000
is you are having a
nuclear-nuclear repulsion.

461
00:34:49,000 --> 00:34:54,000
A chemical bond is really the
sum of these three interactions

462
00:34:54,000 --> 00:35:00,000
and the interplay between these
three interactions.

463
00:35:00,000 --> 00:35:05,000
That is what we want to try to
look at and try to understand.

464
00:35:05,000 --> 00:35:10,000
How are we going to do that?
Well, the first thing I am

465
00:35:10,000 --> 00:35:15,000
going to do is I am going to
draw an energy of interaction as

466
00:35:15,000 --> 00:35:21,000
a function of the distance
between the two hydrogen atoms.

467
00:35:21,000 --> 00:35:26,000
I am going to take two hydrogen
atoms and I am going to call the

468
00:35:26,000 --> 00:35:32,000
distance between them r.
Now, I have changed my

469
00:35:32,000 --> 00:35:36,000
definition of r.
r is the distance between the

470
00:35:36,000 --> 00:35:39,000
two nuclei.
It is no longer the distance

471
00:35:39,000 --> 00:35:43,000
between the nucleus and the
electron.

472
00:35:43,000 --> 00:35:46,000
I have just changed my
definition of r.

473
00:35:46,000 --> 00:35:51,000
And I am going to plot the
energy of interaction as a

474
00:35:51,000 --> 00:35:55,000
function of that distance
between the two nuclei.

475
00:35:55,000 --> 00:36:00,000
Here is my energy of
interaction.

476
00:36:00,000 --> 00:36:04,000
There is going to be a zero of
energy, here.

477
00:36:04,000 --> 00:36:08,000
I am going to plot this as a
function of r,

478
00:36:08,000 --> 00:36:12,000
and the plot is going to look
like this.

479
00:36:12,000 --> 00:36:15,000
Way out here,
where r is large,

480
00:36:15,000 --> 00:36:19,000
I have two separated hydrogen
atoms.

481
00:36:19,000 --> 00:36:24,000
The energy, here,
is minus 2,624 kilojoules per

482
00:36:24,000 --> 00:36:27,000
mole.
That is what this energy of

483
00:36:27,000 --> 00:36:31,000
interaction is,
here.

484
00:36:31,000 --> 00:36:35,000
Now, as I bring these two
hydrogen atoms together,

485
00:36:35,000 --> 00:36:40,000
what happens is that this
energy is going to decrease.

486
00:36:40,000 --> 00:36:44,000
And it is going to keep
decreasing until we get to some

487
00:36:44,000 --> 00:36:47,000
point.
And then, as r gets even

488
00:36:47,000 --> 00:36:51,000
smaller, that energy of
interaction is going to

489
00:36:51,000 --> 00:36:56,000
skyrocket and go to infinity.
Starting about here somewhere,

490
00:36:56,000 --> 00:37:02,000
where the energy of interaction
is less, is more negative than

491
00:37:02,000 --> 00:37:08,000
the separated hydrogen atoms.
Well, what that means is that

492
00:37:08,000 --> 00:37:12,000
we are forming a chemical bond.
The two hydrogen atoms are more

493
00:37:12,000 --> 00:37:15,000
stable then when they are
separated.

494
00:37:15,000 --> 00:37:19,000
The two hydrogen atoms are
bound as soon as this energy of

495
00:37:19,000 --> 00:37:24,000
interaction gets more negative
than the separated atom limit.

496
00:37:24,000 --> 00:37:26,000
And it keeps getting more
negative.

497
00:37:26,000 --> 00:37:29,000
And, of course,
the value of r at which that

498
00:37:29,000 --> 00:37:33,000
energy of interaction is a
maximum negative number,

499
00:37:33,000 --> 00:37:38,000
well, that is the equilibrium
bond length.

500
00:37:38,000 --> 00:37:45,000
This is the most stable value
of r at which the energy is the

501
00:37:45,000 --> 00:37:49,000
lowest.
It is the most stable

502
00:37:49,000 --> 00:37:54,000
configuration.
In the case of hydrogen,

503
00:37:54,000 --> 00:38:00,000
that value of r is 0.74
angstroms.

504
00:38:00,000 --> 00:38:05,000
In this potential energy curve,
as it is often called,

505
00:38:05,000 --> 00:38:11,000
everywhere where this energy of
interaction is lower than the

506
00:38:11,000 --> 00:38:15,000
separated hydrogen atom limit,
everywhere here,

507
00:38:15,000 --> 00:38:21,000
this is called the attractive
region of the interaction

508
00:38:21,000 --> 00:38:24,000
potential.
It is attractive because the

509
00:38:24,000 --> 00:38:32,000
hydrogen atoms bound are more
stable than they are separated.

510
00:38:32,000 --> 00:38:34,000
Or, the hydrogen atoms are
bound.

511
00:38:34,000 --> 00:38:40,000
They are more stable than the
two hydrogen atoms separated.

512
00:38:40,000 --> 00:38:45,000
We call this the attractive
region of the potential energy

513
00:38:45,000 --> 00:38:47,000
curve.
We also call this region,

514
00:38:47,000 --> 00:38:51,000
this attractive region,
we call that the well.

515
00:38:51,000 --> 00:38:56,000
And the well depth,
here, from the bottom to the

516
00:38:56,000 --> 00:39:01,000
separated hydrogen atom limit,
if you measure the energy from

517
00:39:01,000 --> 00:39:04,000
the bottom up,
that energy is the bond

518
00:39:04,000 --> 00:39:10,000
association energy.
We are going to call it delta E

519
00:39:10,000 --> 00:39:14,000
sub d,
from the bottom here to the

520
00:39:14,000 --> 00:39:18,000
separated hydrogen atom limit.
That is the bond energy.

521
00:39:18,000 --> 00:39:23,000
432 kilojoules per mole is the
energy that you have to put into

522
00:39:23,000 --> 00:39:28,000
the H two molecule to
separate it.

523
00:39:28,000 --> 00:39:32,000
You have to get it from the
bottom of this well to the

524
00:39:32,000 --> 00:39:35,000
separated hydrogen atom limit
here.

525
00:39:35,000 --> 00:39:39,000
Now, you can also see,
here, as you push those two

526
00:39:39,000 --> 00:39:43,000
hydrogen atoms even closer
together than the equilibrium

527
00:39:43,000 --> 00:39:48,000
bond length, you can see that
the energy is going back up.

528
00:39:48,000 --> 00:39:52,000
And at some point,
if you push the two hydrogen

529
00:39:52,000 --> 00:39:57,000
atoms close enough together such
that the energy is equal to that

530
00:39:57,000 --> 00:40:02,000
of the separated hydrogen atom,
it then becomes greater than

531
00:40:02,000 --> 00:40:07,000
that of the separated hydrogen
atom.

532
00:40:07,000 --> 00:40:10,000
From this value of r on,
the hydrogen atoms are no

533
00:40:10,000 --> 00:40:14,000
longer bound because their
energy is greater than the

534
00:40:14,000 --> 00:40:18,000
separated hydrogen atom limit.
We call this part of the

535
00:40:18,000 --> 00:40:22,000
potential energy of interaction
the repulsive part.

536
00:40:22,000 --> 00:40:26,000
In other words,
as you push the two hydrogen

537
00:40:26,000 --> 00:40:30,000
atoms closer together,
they form a bond.

538
00:40:30,000 --> 00:40:36,000
But if you push them too close,
they are going to fly apart.

539
00:40:36,000 --> 00:40:42,000
They are no longer bound.
This is the general potential

540
00:40:42,000 --> 00:40:46,000
energy of interaction for every
chemical bond.

541
00:40:46,000 --> 00:40:51,000
Every single bond has this
general shape.

542
00:40:51,000 --> 00:40:55,000
That is important.
But that shape is really a

543
00:40:55,000 --> 00:41:01,000
consequence of these three
interactions that I talked about

544
00:41:01,000 --> 00:41:07,000
when we started this problem,
here.

545
00:41:07,000 --> 00:41:11,000
And so, what I want to try to
do is now try to dissect that

546
00:41:11,000 --> 00:41:17,000
curve into the three components
that give rise to that potential

547
00:41:17,000 --> 00:41:21,000
energy of interaction,
that dependence as a function

548
00:41:21,000 --> 00:41:25,000
of r.
I want to pull that apart.

549
00:41:30,000 --> 00:41:36,000
This energy of interaction is
the sum of the nuclear

550
00:41:36,000 --> 00:41:41,000
repulsion.
Pushing the nuclei too close

551
00:41:41,000 --> 00:41:47,000
together, there is a repulsive
interaction.

552
00:41:47,000 --> 00:41:51,000
That is one of the
interactions.

553
00:41:51,000 --> 00:41:58,000
Plus, the electron-nuclear
attraction is the attraction

554
00:41:58,000 --> 00:42:07,000
between the electron and the
nucleus on which it came in.

555
00:42:07,000 --> 00:42:11,000
And also between the electron
and the other nucleus.

556
00:42:11,000 --> 00:42:14,000
That is the electron-nuclear
attraction.

557
00:42:14,000 --> 00:42:17,000
Plus the electron-electron
repulsive.

558
00:42:17,000 --> 00:42:21,000
Well, when you bring two
hydrogen atoms together those

559
00:42:21,000 --> 00:42:25,000
electrons are going to repel.
That is the energy of

560
00:42:25,000 --> 00:42:28,000
interaction.
It is the sum of those three

561
00:42:28,000 --> 00:42:34,000
fundamental interactions.
But what I want to do is figure

562
00:42:34,000 --> 00:42:39,000
out an r dependence for each one
of these interactions.

563
00:42:39,000 --> 00:42:44,000
And the sum of that r
dependence should give me a

564
00:42:44,000 --> 00:42:48,000
shape that looks like this.
I want to see which

565
00:42:48,000 --> 00:42:53,000
interactions are important at
what values of r.

566
00:42:53,000 --> 00:42:56,000
Let me start.
Let's start with the

567
00:42:56,000 --> 00:43:01,000
nuclear-nuclear repulsion here.
If I wanted an r dependence for

568
00:43:01,000 --> 00:43:04,000
what that nuclear-nuclear
repulsion looked like,

569
00:43:04,000 --> 00:43:06,000
what would that be?

570
00:43:11,000 --> 00:43:14,000
Coulomb force.
It is the repulsive Coulomb

571
00:43:14,000 --> 00:43:18,000
interaction.
It is e squared over 4 pi

572
00:43:18,000 --> 00:43:22,000
epsilon nought r.

573
00:43:22,000 --> 00:43:27,000
This is just two like charges
that are repelling.

574
00:43:27,000 --> 00:43:32,000
And so now let me draw that
repulsive interaction as a

575
00:43:32,000 --> 00:43:37,000
function of r on an energy level
diagram.

576
00:43:37,000 --> 00:43:40,000
Here is my energy of
interaction.

577
00:43:40,000 --> 00:43:44,000
It is a function of r.
There is going to be a zero

578
00:43:44,000 --> 00:43:48,000
here.
And this repulsive interaction

579
00:43:48,000 --> 00:43:51,000
is going to be positive
everywhere.

580
00:43:51,000 --> 00:43:56,000
It is going to be infinite here
and a one over r

581
00:43:56,000 --> 00:44:01,000
dependence coming down.
This is the Coulomb

582
00:44:01,000 --> 00:44:05,000
interaction.
This is the nuclear-nuclear

583
00:44:05,000 --> 00:44:09,000
repulsion.
That is what it looks like as a

584
00:44:09,000 --> 00:44:12,000
function of r.
That is one component.

585
00:44:12,000 --> 00:44:16,000
Now, what about the other
components here?

586
00:44:16,000 --> 00:44:21,000
Well, it turns out I have no
simple way of estimating what

587
00:44:21,000 --> 00:44:28,000
the r dependence is for the
electron-nuclear attraction.

588
00:44:28,000 --> 00:44:32,000
I have no simple way of
estimating what the r dependence

589
00:44:32,000 --> 00:44:35,000
is for the electron-electron
repulsion.

590
00:44:35,000 --> 00:44:39,000
And I have no simple way of
doing that for the sum of those

591
00:44:39,000 --> 00:44:42,000
two terms.
Actually, the sum of these two

592
00:44:42,000 --> 00:44:46,000
terms, I am going to call the
electron interactions.

593
00:44:46,000 --> 00:44:50,000
Each one of these terms
involves the electrons.

594
00:44:50,000 --> 00:44:54,000
The is the electron-electron
repulsion, electron-nuclear

595
00:44:54,000 --> 00:44:57,000
attraction.
This term does not have any

596
00:44:57,000 --> 00:45:03,000
electrons in it.
I have no simple way of telling

597
00:45:03,000 --> 00:45:09,000
you or estimating what the r
dependence is of the sum of

598
00:45:09,000 --> 00:45:13,000
these two terms.
However, what I can do is

599
00:45:13,000 --> 00:45:18,000
figure out what the energy is
for the sum of those two

600
00:45:18,000 --> 00:45:25,000
interactions at two extremes.
I can tell you what the energy

601
00:45:25,000 --> 00:45:30,000
is at r equal infinity,
and then I can tell you what it

602
00:45:30,000 --> 00:45:35,000
is at r equal zero.
And, therefore,

603
00:45:35,000 --> 00:45:38,000
on this plot,
I am going to come in with a

604
00:45:38,000 --> 00:45:43,000
value for r equal infinity and a
value for r equal zero.

605
00:45:43,000 --> 00:45:48,000
I am going to draw a straight
line as an estimate for the r

606
00:45:48,000 --> 00:45:51,000
dependence.
Then I am going to add them up

607
00:45:51,000 --> 00:45:56,000
and see if the result looks,
in fact, like this energy of

608
00:45:56,000 --> 00:46:02,000
interaction that I drew for you.
And so that is what I am going

609
00:46:02,000 --> 00:46:06,000
to have to do on Friday.
I will see you on Wednesday,

610
00:46:06,000 --> 00:46:09,000
if not sooner.