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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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00:00:32 --> 00:00:37
energy increase.
They increase because the

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00:00:37 --> 00:00:44
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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00:00:54 --> 00:01:00


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00:01:00 --> 00:01:04
Z increases as you go across
the periodic table here.

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00:01:04 --> 00:01:07
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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00:01:15 --> 00:01:18
meaning the electrons are more
strongly bound,

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00:01:18 --> 00:01:23
meaning ionization energy and
electron affinity increases as

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you go across.
And this also means,

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00:01:25 --> 00:01:30
as you go across,
r, the radius decreases.

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00:01:30 --> 00:01:34
The radius decreases again
because Z increases.

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00:01:34 --> 00:01:38
The nucleus is pulling the
electrons in closer.

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00:01:38 --> 00:01:44
Since they are all in the same
shell, r is remaining the same.

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

25
00:01:49 --> 00:01:53
decreases.
As you go down the Periodic

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00:01:53 --> 00:02:00
Table, the ionization energy and
the electron affinity decrease.

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

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

29
00:02:07 --> 00:02:10
increasing, but not as fast as
r.

30
00:02:10 --> 00:02:16
As you go down the Periodic
Table, you are going to shells

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00:02:16 --> 00:02:20
that, on the average,
are further out from the

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00:02:20 --> 00:02:24
nucleus.
And that dependence takes over,

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00:02:24 --> 00:02:30
causing EA and IE to decrease.
And then the radius,

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

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00:02:34 --> 00:02:41
you are putting the electrons
into shells which are on the

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00:02:41 --> 00:02:44
average farther away from the
nucleus.

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

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

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00:02:53 --> 00:02:59
term, and that is the
electronegativity.

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

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00:03:01 --> 00:03:05
The electronegativity is an
empirical quantity.

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

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00:03:09 --> 00:03:13
electronegativity.
There is a Pauling definition.

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00:03:13 --> 00:03:17
Mulliken is a little bit more
straightforward.

45
00:03:17 --> 00:03:21
And that electronegativity is
defined as one-half times the

46
00:03:21 --> 00:03:26
quantity ionization energy plus
the electron affinity.

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00:03:26 --> 00:03:31
The electronegativity is

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00:03:31 --> 00:03:37
proportional to the average of
the ionization energy and the

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00:03:37 --> 00:03:42
electron affinity.
The electronegativity is a

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00:03:42 --> 00:03:48
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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00:03:57 --> 00:04:02
the Periodic Table.
Well, they have high

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00:04:02 --> 00:04:07
electronegativities.
They are good electron

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acceptors.
They have high

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00:04:09 --> 00:04:15
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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00:04:54 --> 00:05:00
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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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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00:05:44 --> 00:05:46
These are good electron
acceptors.

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00:05:46 --> 00:05:51
And one thing you already know
probably is that some of the

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00:05:51 --> 00:05:56
strongest ionic bonds are made
between elements in these two

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00:05:56 --> 00:06:01
corners of the periodic table.
An ionic bond,

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00:06:01 --> 00:06:06
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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00:06:45 --> 00:06:48
1s 2 2s 2 2p 6.

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00:06:48 --> 00:06:51
For example,
this nitrogen,

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N minus 3,
it has added three electrons to

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00:06:55 --> 00:07:01
be nitrogen minus three.
It has added three electrons to

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00:07:01 --> 00:07:07
get this electron configuration,
this rare gas configuration,

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00:07:07 --> 00:07:13
this octet configuration which
is a very stable configuration.

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00:07:13 --> 00:07:18
Aluminum has three electrons
removed to obtain this

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particular electron
configuration.

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00:07:21 --> 00:07:25
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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00:07:37 --> 00:07:42
you will often see compounds
with nitrogen minus three.

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00:07:42 --> 00:07:44
You won't very often see a

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00:07:44 --> 00:07:49
compound with nitrogen minus two
or nitrogen minus one

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00:07:49 --> 00:07:54
because those are not
as stable as nitrogen minus

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three,
given this rare gas or the

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00:07:57 --> 00:08:00
octet configuration.
All right.

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00:08:00 --> 00:08:04
That is just a little odd and
end.

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00:08:04 --> 00:08:09
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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00:08:25 --> 00:08:31
This is going to be on the side
boards here.

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00:08:31 --> 00:08:36
I wanted to just show you in
kind of simple terms how a wave

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00:08:36 --> 00:08:42
function actually determines the
intensity of some transition.

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00:08:42 --> 00:08:47
Many of you have asked me about
the intensities of transitions,

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00:08:47 --> 00:08:53
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 --> 00:09:03
First of all,
I have to explain this diagram

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00:09:03 --> 00:09:06
to you.
This is going to be a diagram

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00:09:06 --> 00:09:10
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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00:09:37 --> 00:09:45
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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00:09:50 --> 00:09:55
plot right here,
n equals 1, n equals 2,

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00:09:55 --> 00:10:00
n equals 3.
But then, what is also

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

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00:10:07 --> 00:10:11
interaction is plotted as a
function of r.

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

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

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00:10:22 --> 00:10:27
energy of interaction.
The potential energy of

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00:10:27 --> 00:10:33
interaction kind of looks like
that.

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

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

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

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00:10:48 --> 00:10:51
this plot.
Then what we do is we actually

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00:10:51 --> 00:10:56
plot the form of the wave
function, kind of on top of the

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00:10:56 --> 00:11:01
energy levels.
What we do is to say,

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

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00:11:04 --> 00:11:10
function, which starts at r
equals 0 at some finite value

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00:11:10 --> 00:11:14
and it is just an exponential
decay.

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

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00:11:19 --> 00:11:23
energy here as the value of Psi
equals 0.

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

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

152
00:11:34 --> 00.


153
0. --> 00:11:36
This is the value of Psi,

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

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

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00:11:41 --> 00:11:46
We plot the wave function on
top of that energy level.

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00:11:46 --> 00:11:49
In other words,
this is a complex diagram here.

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00:11:49 --> 00:11:53
You are going to see,
if you take any course beyond

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00:11:53 --> 00:11:58
this, this diagram a lot,
with energy levels and wave

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00:11:58 --> 00:12:02
functions plotted on top of
them.

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

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00:12:07 --> 00:12:11
the n equals 2 energy level.
Again, at r equals 0,

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00:12:11 --> 00:12:14
it is some finite value and
then it drops.

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00:12:14 --> 00:12:19
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 --> 00:12:25
equals 0.
Right here, you have a radial

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00:12:25 --> 00:12:27
node.
Then it goes up and then it

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00:12:27 --> 00:12:32
comes back.
It goes down to a negative

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00:12:32 --> 00:12:37
value and then comes back up.
That is n equals 2.

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

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00:12:42 --> 00:12:47
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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00:12:51.286 --> 235.


174
235. --> 00:12:54
Here is the wave function.

175
00:12:54 --> 00:12:59
Is this is a hydrogen atom and
you have n equals 235,

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00:12:59 --> 00:13:04
how many radial nodes do you
have?

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00:13:04 --> 234.


178
234. --> 00:13:06
This wave function is passing

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

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

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

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00:13:20 --> 00:13:23
looks like.
Now, how do these relate to the

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00:13:23 --> 00:13:28
intensity of some transition?
Well, the intensity of a

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00:13:28 --> 00:13:32
transition is related to the
overlap between the wave

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00:13:32 --> 00:13:37
function of the initial state
and the wave function of the

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00:13:37 --> 00:13:42
final state.
What do I mean by overlap?

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

188
00:13:46 --> 00:13:49
function, here,
of the initial state,

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

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

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

192
00:14:03 --> 00:14:06
state.
What I am going to do,

193
00:14:06 --> 00:14:09
to get the overlap,
is I'm going to take the

194
00:14:09 --> 00:14:14
product of the wave function of
the initial state times that of

195
00:14:14 --> 00:14:17
the final state,
and essentially I am going to

196
00:14:17 --> 00:14:19
integrate that resulting
function.

197
00:14:19 --> 00:14:23
I am going to multiply these
two wave functions together,

198
00:14:23 --> 00:14:27
and I am going to integrate
over all r the resulting

199
00:14:27 --> 00:14:31
function.
That is what I mean by overlap.

200
00:14:31 --> 00:14:33
But there is another term here.
There is an r,

201
00:14:33 --> 00:14:35
too.
That r is important.

202
00:14:35 --> 00:14:38
It has to do with the
transition moment dipole.

203
00:14:38 --> 00:14:41
And we won't go into that,
but it is there.

204
00:14:41 --> 00:14:44
But it won't affect the
argument I am going to make for

205
00:14:44 --> 00:14:47
you right now.
We take the wave function of

206
00:14:47 --> 00:14:50
the initial state,
multiply it by the final state

207
00:14:50 --> 00:14:54
times r, and then we integrate
this whole thing from r equals 0

208
00:14:54 --> 00:15:00
to infinity and then square it.
That quantity is proportional

209
00:15:00 --> 00:15:03
to the intensity of some
transition.

210
00:15:03 --> 00:15:07
Let's do that.
Here is Psi n equals 235,

211
00:15:07 --> 00:15:11
we are multiplying it by Psi of

212
00:15:11 --> 00:15:16
n equals 0 and
actually multiplying it by r.

213
00:15:16 --> 00:15:22
And what we are going to see,
if we just look at this product

214
00:15:22 --> 00:15:28
here, if we just looked at Psi n
equals 235 and

215
00:15:28 --> 00:15:33
Psi n equals 1,
if we just looked at that

216
00:15:33 --> 00:15:39
product, we are going to
multiply this times that.

217
00:15:39 --> 00:15:42
In a graphical form,
it is going to look like this.

218
00:15:42 --> 00:15:44
It is going to go up,
down, up, down,

219
00:15:44 --> 00:15:47
up, down.
It is going to oscillate and

220
00:15:47 --> 00:15:51
then tail off in an exponential
way because we are multiply this

221
00:15:51 --> 00:15:53
up, down, up,
down, up down times this

222
00:15:53 --> 00:15:56
exponential decay.
It is going to look something

223
00:15:56 --> 00:16:00
like that.
But now, we are going to

224
00:16:00 --> 00:16:04
integrate this resulting curve.
What you can see is that the

225
00:16:04 --> 00:16:09
area above this curve is equal
to the area below this curve,

226
00:16:09 --> 00:16:12
approximately.
And, when we integrate

227
00:16:12 --> 00:16:17
something, we are calculating
the area underneath the curve.

228
00:16:17 --> 00:16:23
These positive areas are going
to cancel these negative areas.

229
00:16:23 --> 00:16:27
The result is that this
integral is going to be very

230
00:16:27 --> 00:16:31
small.
And the result is that the

231
00:16:31 --> 00:16:34
intensity of that line is very
low.

232
00:16:34 --> 00:16:38
The intensities are
proportional to this overlap,

233
00:16:38 --> 00:16:42
the overlap of the initial
state wave function and the

234
00:16:42 --> 00:16:46
final state wave function.
And you can see,

235
00:16:46 --> 00:16:49
here, graphically,
how if you integrate that

236
00:16:49 --> 00:16:53
product in this case,
the positive areas cancel the

237
00:16:53 --> 00:16:57
negative areas,
and you don't have a very

238
00:16:57 --> 00:17:02
intense transition.
However, suppose we look at the

239
00:17:02 --> 00:17:06
transition from n equals 3 to n
equals 2.

240
00:17:06 --> 00:17:10
Well, here is the n equals 3
wave function,

241
00:17:10 --> 00:17:13
here is the n equals 2 wave
function.

242
00:17:13 --> 00:17:19
And our intensity expression
says that we have to multiply

243
00:17:19 --> 00:17:21
these two.
Let's do that.

244
00:17:21 --> 00:17:25
Let's multiply n equals 3 times
n equals 2, here.

245
00:17:25 --> 00:17:30
Well, the result,
if you excuse my not so great

246
00:17:30 --> 00:17:37
drawing, is we start out with a
very positive function here.

247
00:17:37 --> 00:17:42
But then we have two negatives
here, which make it a little bit

248
00:17:42 --> 00:17:45
less negative.
But then, we have a positive,

249
00:17:45 --> 00:17:50
here, times a negative,
and what that makes is a large

250
00:17:50 --> 00:17:54
area that is negative.
And, if we go and integrate

251
00:17:54 --> 00:17:59
that, now we don't have the same
cancellation of positive and

252
00:17:59 --> 00:18:03
negative areas.
We integrate that,

253
00:18:03 --> 00:18:06
and that transition energy is
large.

254
00:18:06 --> 00:18:10
Or, that area is large,
therefore the intensity of that

255
00:18:10 --> 00:18:12
transition is large.
Bottom line,

256
00:18:12 --> 00:18:17
that is one of the elements
that dictates the intensity of a

257
00:18:17 --> 00:18:20
transition.
It is also one of the elements

258
00:18:20 --> 00:18:24
that dictates the intensity of
your photoelectron spectra.

259
00:18:24 --> 00:18:29
Somebody asked me about it the
other day.

260
00:18:29 --> 00:18:32
I had drawn lines in the
photoelectronic spectra that

261
00:18:32 --> 00:18:36
were of the same intensity,
1s, 2s, 2p 6.

262
00:18:36 --> 00:18:40
Somebody said,
well, you have more electrons

263
00:18:40 --> 00:18:43
in the 2p state.
Why don't you have a larger

264
00:18:43 --> 00:18:46
number of electrons coming off?
The answer is,

265
00:18:46 --> 00:18:51
that is part of what goes into
determining the intensity of the

266
00:18:51 --> 00:18:54
transition, but there is more to
it.

267
00:18:54 --> 00:18:57
It is not just the number of
electrons.

268
00:18:57 --> 00:19:01
Here is one of the elements
that goes into determining the

269
00:19:01 --> 00:19:07
intensity of some transition.
It is the wave functions and

270
00:19:07 --> 00:19:13
the overlap between the final
and the initial state.

271
00:19:13 --> 00:19:17
And then, I just wanted to also
show you, here,

272
00:19:17 --> 00:19:23
for this atom in the n equals
235 state, I plotted just for

273
00:19:23 --> 00:19:29
fun, kind of schematically,
what the radial probability

274
00:19:29 --> 00:19:35
distribution would look like.
That is just r squared times

275
00:19:35 --> 00:19:38
the radial part squared.
And, of course,

276
00:19:38 --> 00:19:41
since the wave function goes
like this, oscillates,

277
00:19:41 --> 00:19:45
that is what the radial
probability distribution is

278
00:19:45 --> 00:19:48
going to do.
And you are going to see

279
00:19:48 --> 00:19:52
nodes here, 234 values of r,
that is going to make the wave

280
00:19:52 --> 00:19:56
function be equal to zero.
And then way out here,

281
00:19:56 --> 00:20:00
you are going to have a
feature.

282
00:20:00 --> 00:20:04
That last feature,
here, is going to have the

283
00:20:04 --> 00:20:09
maximum probability,
and that is your value of r

284
00:20:09 --> 00:20:15
that is most probable.
It turns out for n equals

285
00:20:15 --> 00:20:21
that the most probable value of
r is 43,800 angstroms.

286
00:20:21 --> 00:20:24
That is about 4.38x10^-6
meters.

287
00:20:24 --> 00:20:31
This is a really large hydrogen
atom, n equals 235.

288
00:20:31 --> 00:20:33
Do they exist?
The answer is yes,

289
00:20:33 --> 00:20:37
they do exist.
They exist, particularly in

290
00:20:37 --> 00:20:41
outer space, where there is lots
of UV radiation to get these

291
00:20:41 --> 00:20:45
hydrogen atoms up into these
very excited states.

292
00:20:45 --> 00:20:50
And they exist in deep outer
space, where the temperatures

293
00:20:50 --> 00:20:53
are pretty cold.
And you need those cold

294
00:20:53 --> 00:20:58
temperatures because this
hydrogen atom is not very stable

295
00:20:58 --> 00:21:06
in n equals 235.
And, if you went and calculated

296
00:21:06 --> 00:21:12
here, I am going to draw a line,
here.

297
00:21:12 --> 00:21:21
This is going to be n equals
235, and this is the zero of

298
00:21:21 --> 00:21:27
energy.
This energy difference here is

299
00:21:27 --> 00:21:34
about 4x10^-23 joules.
Whereas, at room temperature,

300
00:21:34 --> 00:21:38
we will just talk about the
thermal energy,

301
00:21:38 --> 00:21:41
thermal energy is about
4x10^-21 joules.

302
00:21:41 --> 00:21:46
You can see that any little
fluctuation at room temperature,

303
00:21:46 --> 00:21:52
since this is two orders of
magnitude larger than what this

304
00:21:52 --> 00:21:57
bound by, any little fluctuation
would kick this very weakly

305
00:21:57 --> 00:22:02
bound electron up and ionize it.
And it would.

306
00:22:02 --> 00:22:07
You really only see these in
environments that are very cold,

307
00:22:07 --> 00:22:12
where you don't perturb what
are called Rydberg atoms

308
00:22:12 --> 00:22:16
sometimes.
I think in the laboratory the

309
00:22:16 --> 00:22:22
largest Rydberg atom that has
been made is n equals 180 or n

310
00:22:22 --> 00:22:26
equals 200 or so.
Anyway, that was really just

311
00:22:26 --> 00:22:32
for fun that I wanted to tell
you about that.

312
00:22:32 --> 00:22:38
Now, there is another little
tidbit that I want to talk to

313
00:22:38 --> 00:22:44
you about that has to do with
how knowing something about the

314
00:22:44 --> 00:22:51
energy levels in an atom leads
to a nice practical device,

315
00:22:51 --> 00:22:57
like a helium neon laser.
We have to take a look at the

316
00:22:57 --> 00:23:02
neon energy levels.
And so we have another

317
00:23:02 --> 00:23:07
discharge lamp here,
and we have some more of these

318
00:23:07 --> 00:23:12
glasses, here,
so that you can resolve the

319
00:23:12 --> 00:23:16
neon lines here.
The TAs will get them out.

320
00:23:16 --> 00:23:21
Here is our neon discharge
lamp.

321
00:23:21 --> 00:23:27


322
00:23:27 --> 00:23:30
You can resolve,
here, the neon spectrum.

323
00:23:30 --> 00:23:34
The spectrum that you should
see should be what is shown on

324
00:23:34 --> 00:23:38
the side walls here.
Let me turn off the lights so

325
00:23:38 --> 00:23:43
that you can see it a little bit
better, hopefully.

326
00:23:43 --> 00:23:52


327
00:23:52 --> 00:23:57
You can see lots of lines in
the case of neon because we have

328
00:23:57 --> 00:24:00
lots of different occupied
states.

329
00:24:00 --> 00:24:05
The glasses that I have
actually are doing a phenomenal

330
00:24:05 --> 00:24:10
job in resolving those very
closely spaced lines.

331
00:24:10 --> 00:24:15
I must have a better quality
glass today.

332
00:24:15 --> 00:24:35


333
00:24:35 --> 00:24:40
And, if you look at the side
walls, you can see that I drew

334
00:24:40 --> 00:24:44
one of those lines.
One of those emission lines is

335
00:24:44 --> 00:24:48
at 632 nanometers,
which is the emission line of a

336
00:24:48 --> 00:24:52
helium neon laser.
But it is really a neon

337
00:24:52 --> 00:24:56
transition that we will talk
about in a moment.

338
00:24:56 --> 00:25:01
I drew it as very thick on the
board.

339
00:25:01 --> 00:25:05
Because when I looked at the
discharge lamp and drew that

340
00:25:05 --> 00:25:10
picture, my glasses did not
resolve those lines so very

341
00:25:10 --> 00:25:13
well.
And so that one looked really

342
00:25:13 --> 00:25:16
thick to me.
At least my glasses,

343
00:25:16 --> 00:25:20
I can really see lots and lots
of discrete lines.

344
00:25:20 --> 00:25:23
But it is this transition,
632 nanometers,

345
00:25:23 --> 00:25:27
that is the output of the
helium neon laser,

346
00:25:27 --> 00:25:32
which is the red laser that I
use sometimes in the lecture,

347
00:25:32 --> 00:25:37
here, to point.
It is the basis of the laser

348
00:25:37 --> 00:25:43
that is used in the grocery
stores to scan the prices on

349
00:25:43 --> 00:25:46
your items.
And it turns out that what is

350
00:25:46 --> 00:25:50
going on, here,
is the following.

351
00:25:50 --> 00:25:55
If you look on the side walls,
we have neon in the ground

352
00:25:55 --> 00:26:00
state before we turn the
discharge on.

353
00:26:00 --> 00:26:04
And then, when we turn the
discharge on,

354
00:26:04 --> 00:26:11
that pumps energy into the neon
atoms such that one of those

355
00:26:11 --> 00:26:17
electrons, the 2p electron,
gets promoted into the 5s

356
00:26:17 --> 00:26:20
state.
And then, of course,

357
00:26:20 --> 00:26:26
that atom wants to relax.
And so here it comes again.

358
00:26:26 --> 00:26:33
That 5s state relaxes.
That electron relaxes to the 3p

359
00:26:33 --> 00:26:35
state.
And it is actually that

360
00:26:35 --> 00:26:41
transition that occurs at 632.8
nanometers, the basis of the

361
00:26:41 --> 00:26:45
helium neon laser.
It is that transition,

362
00:26:45 --> 00:26:50
from the 5s to the 3p.
It is not all the way down,

363
00:26:50 --> 00:26:54
but ultimately,
of course, that state relaxes.

364
00:26:54 --> 00:27:00
But what is going on in the
helium neon laser?

365
00:27:00 --> 00:27:05
Well, in the helium neon laser,
we have a discharge ignited

366
00:27:05 --> 00:27:10
where we have a lot of neon
atoms here in this excited

367
00:27:10 --> 00:27:16
state, with the one electron in
the 5s state right as I show

368
00:27:16 --> 00:27:18
you.
And that is emitting,

369
00:27:18 --> 00:27:24
a photon comes out.
But what is happening here is

370
00:27:24 --> 00:27:30
that the photon that is emitted
is able to, because of the

371
00:27:30 --> 00:27:36
construction of this laser,
contact or to interact with

372
00:27:36 --> 00:27:41
another neon atom in this same
excited state,

373
00:27:41 --> 00:27:48
that 2p 5 5s state.
That photon interacts with this

374
00:27:48 --> 00:27:53
excited atom.
When it interacts with that

375
00:27:53 --> 00:27:58
excited atom,
what happens is that the photon

376
00:27:58 --> 00:28:04
stimulates that excited atom to
actually emit a photon of the

377
00:28:04 --> 00:28:10
same energy.
This photon stimulates this

378
00:28:10 --> 00:28:14
excited atom to release its
energy right at that time.

379
00:28:14 --> 00:28:18
The result is that you have two
photons coming out.

380
00:28:18 --> 00:28:23
They are going to come out in
the same direction and they are

381
00:28:23 --> 00:28:26
going to be what is called
coherent.

382
00:28:26 --> 00:28:31
That is, their phases are going
to match.

383
00:28:31 --> 00:28:36
If you think now of the photon
as a wave, they are going to be

384
00:28:36 --> 00:28:39
coherent.
And the result is that you are

385
00:28:39 --> 00:28:44
going to have some radiation
that is going to be twice as

386
00:28:44 --> 00:28:47
intense because they are
coherent.

387
00:28:47 --> 00:28:51
They are in phase.
And then, what happens is that

388
00:28:51 --> 00:28:55
these two photons,
they each then interact with

389
00:28:55 --> 00:29:01
another neon atom in this same
excited state.

390
00:29:01 --> 00:29:06
And each of those photons
stimulates another atom to emit

391
00:29:06 --> 00:29:09
photons.
And the result is now that you

392
00:29:09 --> 00:29:14
have four photons being emitted,
the same frequency,

393
00:29:14 --> 00:29:17
same direction,
and same phase.

394
00:29:17 --> 00:29:22
And it is in this way that we
amplify the light in any kind of

395
00:29:22 --> 00:29:25
laser.
This is what is going on,

396
00:29:25 --> 00:29:30
this process of simulated
emission.

397
00:29:30 --> 00:29:34
Where you have a photon that
now is exactly the frequency of

398
00:29:34 --> 00:29:40
the energy difference of the
transition that you are going to

399
00:29:40 --> 00:29:44
make in this excited atom.
This stimulates that atom to

400
00:29:44 --> 00:29:48
emit a photon.
The two photons then come off

401
00:29:48 --> 00:29:51
coherently.
And then, these two interact

402
00:29:51 --> 00:29:55
with two other atoms.
Now you have four photons that

403
00:29:55 --> 00:29:58
are coming off.
That is the process of

404
00:29:58 --> 00:30:03
amplification in any type of
laser.

405
00:30:03 --> 00:30:08


406
00:30:08 --> 00:30:13
Of course, in order to make
this work, you have to have a

407
00:30:13 --> 00:30:19
lot of these excited neon atoms
around because you have to be

408
00:30:19 --> 00:30:25
able to have a photon interact
with them before they just emit

409
00:30:25 --> 00:30:30
spontaneously.
This is stimulated emission.

410
00:30:30 --> 00:30:34
The other kind of emission that
we were talking about is

411
00:30:34 --> 00:30:36
spontaneous emission.
In other words,

412
00:30:36 --> 00:30:40
you have to have a high
concentration of these excited

413
00:30:40 --> 00:30:44
neon atoms so that the photons
that are originally emitted

414
00:30:44 --> 00:30:48
here, by just spontaneous
emission, can interact with

415
00:30:48 --> 00:30:52
those excited state neon atoms
and stimulate the emission and

416
00:30:52 --> 00:30:57
get this whole process rolling.
In order to produce a whole lot

417
00:30:57 --> 00:31:01
of those excited neon atoms,
what happens is we add in a

418
00:31:01 --> 00:31:06
little bit of helium.
It turns out that in helium

419
00:31:06 --> 00:31:10
there are some excited states
that are just,

420
00:31:10 --> 00:31:13
by accident,
at the same energy as this

421
00:31:13 --> 00:31:17
excited state of neon.
And the helium actually

422
00:31:17 --> 00:31:21
transfers its energy to the
neon, into this state,

423
00:31:21 --> 00:31:25
and maintains,
then, that very high population

424
00:31:25 --> 00:31:30
of neon atoms here in this
excited state.

425
00:31:30 --> 00:31:32
That is the function of the
helium.

426
00:31:32 --> 00:31:37
It is just the energy transfer
from the helium excited state to

427
00:31:37 --> 00:31:42
the neon excited state.
It keeps the population of the

428
00:31:42 --> 00:31:46
neon atoms really high.
The helium, you don't see that

429
00:31:46 --> 00:31:49
emission.
That is just a helper in this

430
00:31:49 --> 00:31:53
device.
It is the neon transition that

431
00:31:53 --> 00:31:59
you are looking at here.
That was just a short story

432
00:31:59 --> 00:32:06
about the usefulness of knowing
about the energy levels in atoms

433
00:32:06 --> 00:32:14
and how ultimately you can make
a practical device because you

434
00:32:14 --> 00:32:20
know something about the energy
levels of your atoms.

435
00:32:20 --> 00:32:25
Well, that is going to finish
up, right now,

436
00:32:25 --> 00:32:32
our discussion of atoms.
And now, it is time to move

437
00:32:32 --> 00:32:36
onto one of the very important
parts of chemistry,

438
00:32:36 --> 00:32:42
and that is chemical bonds and
the combination of atoms to form

439
00:32:42 --> 00:32:46
a chemical bond.
That is what we are going to

440
00:32:46 --> 00:32:48
start talking about,
now.

441
00:32:48 --> 00:32:53
Today, what we are going to do
is just talk about the

442
00:32:53 --> 00:32:58
fundamental interactions that
are present in every chemical

443
00:32:58 --> 00:33:02
bond.
Let's start with that.

444
00:33:02 --> 00:33:07
Let me come over here while the
lights are warming up so you can

445
00:33:07 --> 00:33:12
see that board.
Suppose we have a hydrogen atom

446
00:33:12 --> 00:33:14
here, nucleus a,
plus charge.

447
00:33:14 --> 00:33:19
And it, of course,
has electron a attached to it.

448
00:33:19 --> 00:33:23
And way out here,
we have nucleus b and electron

449
00:33:23 --> 00:33:30
b that is attached to it.
And they are very far apart.

450
00:33:30 --> 00:33:34
And so, in this case,
where they are very far apart,

451
00:33:34 --> 00:33:39
the energy of interaction is
just the energy of interaction

452
00:33:39 --> 00:33:44
between the electron and the
nucleus, the electron-nuclear

453
00:33:44 --> 00:33:46
attraction.
Here it is, the

454
00:33:46 --> 00:33:52
electron-nuclear attraction.
However, as we bring these two

455
00:33:52 --> 00:33:56
hydrogen atoms together,
at some point this electron

456
00:33:56 --> 00:34:01
that was only attracted to
nucleus a is now begins to

457
00:34:01 --> 00:34:06
experience an attraction with
nucleus b.

458
00:34:06 --> 00:34:10
And this electron that was
attracted only to nucleus b

459
00:34:10 --> 00:34:14
experiences an interaction
whereby it is now attracted to

460
00:34:14 --> 00:34:17
nucleus a.
And that kind of mutual

461
00:34:17 --> 00:34:22
attractive interaction then
brings those two nuclei closer

462
00:34:22 --> 00:34:25
together.
However, at the same time,

463
00:34:25 --> 00:34:29
when you bring those two nuclei
closer together,

464
00:34:29 --> 00:34:34
you are bringing the electrons
closer together.

465
00:34:34 --> 00:34:38
And so there is an
electron-electron repulsion that

466
00:34:38 --> 00:34:40
is present.
In addition,

467
00:34:40 --> 00:34:45
as you bring these two nuclei
together, what is happening here

468
00:34:45 --> 00:34:49
is you are having a
nuclear-nuclear repulsion.

469
00:34:49 --> 00:34:54
A chemical bond is really the
sum of these three interactions

470
00:34:54 --> 00:35:00
and the interplay between these
three interactions.

471
00:35:00 --> 00:35:05
That is what we want to try to
look at and try to understand.

472
00:35:05 --> 00:35:10
How are we going to do that?
Well, the first thing I am

473
00:35:10 --> 00:35:15
going to do is I am going to
draw an energy of interaction as

474
00:35:15 --> 00:35:21
a function of the distance
between the two hydrogen atoms.

475
00:35:21 --> 00:35:26
I am going to take two hydrogen
atoms and I am going to call the

476
00:35:26 --> 00:35:32
distance between them r.
Now, I have changed my

477
00:35:32 --> 00:35:36
definition of r.
r is the distance between the

478
00:35:36 --> 00:35:39
two nuclei.
It is no longer the distance

479
00:35:39 --> 00:35:43
between the nucleus and the
electron.

480
00:35:43 --> 00:35:46
I have just changed my
definition of r.

481
00:35:46 --> 00:35:51
And I am going to plot the
energy of interaction as a

482
00:35:51 --> 00:35:55
function of that distance
between the two nuclei.

483
00:35:55 --> 00:36:00
Here is my energy of
interaction.

484
00:36:00 --> 00:36:04
There is going to be a zero of
energy, here.

485
00:36:04 --> 00:36:08
I am going to plot this as a
function of r,

486
00:36:08 --> 00:36:12
and the plot is going to look
like this.

487
00:36:12 --> 00:36:15
Way out here,
where r is large,

488
00:36:15 --> 00:36:19
I have two separated hydrogen
atoms.

489
00:36:19 --> 00:36:24
The energy, here,
is minus 2,624 kilojoules per

490
00:36:24 --> 00:36:27
mole.
That is what this energy of

491
00:36:27 --> 00:36:31
interaction is,
here.

492
00:36:31 --> 00:36:35
Now, as I bring these two
hydrogen atoms together,

493
00:36:35 --> 00:36:40
what happens is that this
energy is going to decrease.

494
00:36:40 --> 00:36:44
And it is going to keep
decreasing until we get to some

495
00:36:44 --> 00:36:47
point.
And then, as r gets even

496
00:36:47 --> 00:36:51
smaller, that energy of
interaction is going to

497
00:36:51 --> 00:36:56
skyrocket and go to infinity.
Starting about here somewhere,

498
00:36:56 --> 00:37:02
where the energy of interaction
is less, is more negative than

499
00:37:02 --> 00:37:08
the separated hydrogen atoms.
Well, what that means is that

500
00:37:08 --> 00:37:12
we are forming a chemical bond.
The two hydrogen atoms are more

501
00:37:12 --> 00:37:15
stable then when they are
separated.

502
00:37:15 --> 00:37:19
The two hydrogen atoms are
bound as soon as this energy of

503
00:37:19 --> 00:37:24
interaction gets more negative
than the separated atom limit.

504
00:37:24 --> 00:37:26
And it keeps getting more
negative.

505
00:37:26 --> 00:37:29
And, of course,
the value of r at which that

506
00:37:29 --> 00:37:33
energy of interaction is a
maximum negative number,

507
00:37:33 --> 00:37:38
well, that is the equilibrium
bond length.

508
00:37:38 --> 00:37:45
This is the most stable value
of r at which the energy is the

509
00:37:45 --> 00:37:49
lowest.
It is the most stable

510
00:37:49 --> 00:37:54
configuration.
In the case of hydrogen,

511
00:37:54 --> 00:38:00
that value of r is 0.74
angstroms.

512
00:38:00 --> 00:38:05
In this potential energy curve,
as it is often called,

513
00:38:05 --> 00:38:11
everywhere where this energy of
interaction is lower than the

514
00:38:11 --> 00:38:15
separated hydrogen atom limit,
everywhere here,

515
00:38:15 --> 00:38:21
this is called the attractive
region of the interaction

516
00:38:21 --> 00:38:24
potential.
It is attractive because the

517
00:38:24 --> 00:38:32
hydrogen atoms bound are more
stable than they are separated.

518
00:38:32 --> 00:38:34
Or, the hydrogen atoms are
bound.

519
00:38:34 --> 00:38:40
They are more stable than the
two hydrogen atoms separated.

520
00:38:40 --> 00:38:45
We call this the attractive
region of the potential energy

521
00:38:45 --> 00:38:47
curve.
We also call this region,

522
00:38:47 --> 00:38:51
this attractive region,
we call that the well.

523
00:38:51 --> 00:38:56
And the well depth,
here, from the bottom to the

524
00:38:56 --> 00:39:01
separated hydrogen atom limit,
if you measure the energy from

525
00:39:01 --> 00:39:04
the bottom up,
that energy is the bond

526
00:39:04 --> 00:39:10
association energy.
We are going to call it delta E

527
00:39:10 --> 00:39:14
sub d,
from the bottom here to the

528
00:39:14 --> 00:39:18
separated hydrogen atom limit.
That is the bond energy.

529
00:39:18 --> 00:39:23
432 kilojoules per mole is the
energy that you have to put into

530
00:39:23 --> 00:39:28
the H two molecule to
separate it.

531
00:39:28 --> 00:39:32
You have to get it from the
bottom of this well to the

532
00:39:32 --> 00:39:35
separated hydrogen atom limit
here.

533
00:39:35 --> 00:39:39
Now, you can also see,
here, as you push those two

534
00:39:39 --> 00:39:43
hydrogen atoms even closer
together than the equilibrium

535
00:39:43 --> 00:39:48
bond length, you can see that
the energy is going back up.

536
00:39:48 --> 00:39:52
And at some point,
if you push the two hydrogen

537
00:39:52 --> 00:39:57
atoms close enough together such
that the energy is equal to that

538
00:39:57 --> 00:40:02
of the separated hydrogen atom,
it then becomes greater than

539
00:40:02 --> 00:40:07
that of the separated hydrogen
atom.

540
00:40:07 --> 00:40:10
From this value of r on,
the hydrogen atoms are no

541
00:40:10 --> 00:40:14
longer bound because their
energy is greater than the

542
00:40:14 --> 00:40:18
separated hydrogen atom limit.
We call this part of the

543
00:40:18 --> 00:40:22
potential energy of interaction
the repulsive part.

544
00:40:22 --> 00:40:26
In other words,
as you push the two hydrogen

545
00:40:26 --> 00:40:30
atoms closer together,
they form a bond.

546
00:40:30 --> 00:40:36
But if you push them too close,
they are going to fly apart.

547
00:40:36 --> 00:40:42
They are no longer bound.
This is the general potential

548
00:40:42 --> 00:40:46
energy of interaction for every
chemical bond.

549
00:40:46 --> 00:40:51
Every single bond has this
general shape.

550
00:40:51 --> 00:40:55
That is important.
But that shape is really a

551
00:40:55 --> 00:41:01
consequence of these three
interactions that I talked about

552
00:41:01 --> 00:41:07
when we started this problem,
here.

553
00:41:07 --> 00:41:11
And so, what I want to try to
do is now try to dissect that

554
00:41:11 --> 00:41:17
curve into the three components
that give rise to that potential

555
00:41:17 --> 00:41:21
energy of interaction,
that dependence as a function

556
00:41:21 --> 00:41:25
of r.
I want to pull that apart.

557
00:41:25 --> 00:41:30


558
00:41:30 --> 00:41:36
This energy of interaction is
the sum of the nuclear

559
00:41:36 --> 00:41:41
repulsion.
Pushing the nuclei too close

560
00:41:41 --> 00:41:47
together, there is a repulsive
interaction.

561
00:41:47 --> 00:41:51
That is one of the
interactions.

562
00:41:51 --> 00:41:58
Plus, the electron-nuclear
attraction is the attraction

563
00:41:58 --> 00:42:07
between the electron and the
nucleus on which it came in.

564
00:42:07 --> 00:42:11
And also between the electron
and the other nucleus.

565
00:42:11 --> 00:42:14
That is the electron-nuclear
attraction.

566
00:42:14 --> 00:42:17
Plus the electron-electron
repulsive.

567
00:42:17 --> 00:42:21
Well, when you bring two
hydrogen atoms together those

568
00:42:21 --> 00:42:25
electrons are going to repel.
That is the energy of

569
00:42:25 --> 00:42:28
interaction.
It is the sum of those three

570
00:42:28 --> 00:42:34
fundamental interactions.
But what I want to do is figure

571
00:42:34 --> 00:42:39
out an r dependence for each one
of these interactions.

572
00:42:39 --> 00:42:44
And the sum of that r
dependence should give me a

573
00:42:44 --> 00:42:48
shape that looks like this.
I want to see which

574
00:42:48 --> 00:42:53
interactions are important at
what values of r.

575
00:42:53 --> 00:42:56
Let me start.
Let's start with the

576
00:42:56 --> 00:43:01
nuclear-nuclear repulsion here.
If I wanted an r dependence for

577
00:43:01 --> 00:43:04
what that nuclear-nuclear
repulsion looked like,

578
00:43:04 --> 00:43:06
what would that be?

579
00:43:06 --> 00:43:11


580
00:43:11 --> 00:43:14
Coulomb force.
It is the repulsive Coulomb

581
00:43:14 --> 00:43:18
interaction.
It is e squared over 4 pi

582
00:43:18 --> 00:43:22
epsilon nought r.

583
00:43:22 --> 00:43:27
This is just two like charges
that are repelling.

584
00:43:27 --> 00:43:32
And so now let me draw that
repulsive interaction as a

585
00:43:32 --> 00:43:37
function of r on an energy level
diagram.

586
00:43:37 --> 00:43:40
Here is my energy of
interaction.

587
00:43:40 --> 00:43:44
It is a function of r.
There is going to be a zero

588
00:43:44 --> 00:43:48
here.
And this repulsive interaction

589
00:43:48 --> 00:43:51
is going to be positive
everywhere.

590
00:43:51 --> 00:43:56
It is going to be infinite here
and a one over r

591
00:43:56 --> 00:44:01
dependence coming down.
This is the Coulomb

592
00:44:01 --> 00:44:05
interaction.
This is the nuclear-nuclear

593
00:44:05 --> 00:44:09
repulsion.
That is what it looks like as a

594
00:44:09 --> 00:44:12
function of r.
That is one component.

595
00:44:12 --> 00:44:16
Now, what about the other
components here?

596
00:44:16 --> 00:44:21
Well, it turns out I have no
simple way of estimating what

597
00:44:21 --> 00:44:28
the r dependence is for the
electron-nuclear attraction.

598
00:44:28 --> 00:44:32
I have no simple way of
estimating what the r dependence

599
00:44:32 --> 00:44:35
is for the electron-electron
repulsion.

600
00:44:35 --> 00:44:39
And I have no simple way of
doing that for the sum of those

601
00:44:39 --> 00:44:42
two terms.
Actually, the sum of these two

602
00:44:42 --> 00:44:46
terms, I am going to call the
electron interactions.

603
00:44:46 --> 00:44:50
Each one of these terms
involves the electrons.

604
00:44:50 --> 00:44:54
The is the electron-electron
repulsion, electron-nuclear

605
00:44:54 --> 00:44:57
attraction.
This term does not have any

606
00:44:57 --> 00:45:03
electrons in it.
I have no simple way of telling

607
00:45:03 --> 00:45:09
you or estimating what the r
dependence is of the sum of

608
00:45:09 --> 00:45:13
these two terms.
However, what I can do is

609
00:45:13 --> 00:45:18
figure out what the energy is
for the sum of those two

610
00:45:18 --> 00:45:25
interactions at two extremes.
I can tell you what the energy

611
00:45:25 --> 00:45:30
is at r equal infinity,
and then I can tell you what it

612
00:45:30 --> 00:45:35
is at r equal zero.
And, therefore,

613
00:45:35 --> 00:45:38
on this plot,
I am going to come in with a

614
00:45:38 --> 00:45:43
value for r equal infinity and a
value for r equal zero.

615
00:45:43 --> 00:45:48
I am going to draw a straight
line as an estimate for the r

616
00:45:48 --> 00:45:51
dependence.
Then I am going to add them up

617
00:45:51 --> 00:45:56
and see if the result looks,
in fact, like this energy of

618
00:45:56 --> 00:46:02
interaction that I drew for you.
And so that is what I am going

619
00:46:02 --> 00:46:06
to have to do on Friday.
I will see you on Wednesday,

620
00:46:06 --> 46:09
if not sooner.