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PROFESSOR: OK.

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As you're settling into your
seats, why don't we take 10

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00:00:28,800 --> 00:00:41,990
more seconds on the clicker
question here.

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00:00:41,990 --> 00:00:45,390
All right, so this is a question
that you saw on your

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problem-set, so this is how many
electrons would we expect

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00:00:48,680 --> 00:00:51,530
to see in a single atom
in the 2 p state.

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00:00:51,530 --> 00:00:53,490
So, let's see what
you said here.

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00:00:53,490 --> 00:00:54,210
Six.

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00:00:54,210 --> 00:00:57,420
And the correct answer
is, in fact, six.

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00:00:57,420 --> 00:00:59,790
And most of you got
that, about 75% of

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00:00:59,790 --> 00:01:01,000
you got that right.

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00:01:01,000 --> 00:01:06,970
So, let's consider some people
got it wrong, however, and

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let's see where that wrong
answer might have come from,

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or actually, more importantly,
let's see how we can all get

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00:01:11,400 --> 00:01:12,570
to the correct answer.

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00:01:12,570 --> 00:01:16,590
So if we say that we have a 2
p orbital here, that means

24
00:01:16,590 --> 00:01:19,780
that we can have how many
different complete orbitals

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00:01:19,780 --> 00:01:26,160
have a 2 for an n, and a p
as its l value? three.

26
00:01:26,160 --> 00:01:32,600
So, we can have the 2 p x, 2
p y, and 2 p z orbitals.

27
00:01:32,600 --> 00:01:36,150
Each of these orbitals can have
two electrons in them, so

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00:01:36,150 --> 00:01:38,250
we get two electrons here,
here, and here.

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00:01:38,250 --> 00:01:43,320
So, we end up with a total
of six electrons that are

30
00:01:43,320 --> 00:01:46,670
possible that have that
2 p orbital value.

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00:01:46,670 --> 00:01:49,910
So this is a question that,
hopefully, if we see another

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00:01:49,910 --> 00:01:52,870
one like this we'll get a 100%
on, because you've already

33
00:01:52,870 --> 00:01:56,100
seen this in your problem-set as
much as you're going to see

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00:01:56,100 --> 00:01:57,780
it, and you're seen it in
class as much as you're

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00:01:57,780 --> 00:01:58,300
going to see it.

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00:01:58,300 --> 00:02:00,050
So if you're still having
trouble with this, this is

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00:02:00,050 --> 00:02:02,690
something you want to bring
up in your recitation.

38
00:02:02,690 --> 00:02:05,250
And the idea behind this, of
course, is that we know that

39
00:02:05,250 --> 00:02:08,320
every electron has to have its
own distinct set of four

40
00:02:08,320 --> 00:02:09,530
quantum numbers.

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00:02:09,530 --> 00:02:12,790
So that means that if we have
three orbitals, we can only

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00:02:12,790 --> 00:02:15,440
have six electrons in those
complete three orbitals.

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00:02:15,440 --> 00:02:19,210
All right, so today we're
going to fully have our

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00:02:19,210 --> 00:02:21,760
discussion focused on
multi-electron atoms. We

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00:02:21,760 --> 00:02:24,880
started talking about these on
Wednesday, and what we're

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00:02:24,880 --> 00:02:28,130
going to start with is
considering specifically the

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00:02:28,130 --> 00:02:36,540
wave functions for
multi-electron atoms. So, the

48
00:02:36,540 --> 00:02:39,040
wave functions for
multi-electron atoms. Then

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00:02:39,040 --> 00:02:41,830
we'll move on to talking about
the binding energies, and

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we'll specifically talk about
how that differs from the

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00:02:44,590 --> 00:02:47,530
binding energies we saw of
hydrogen atoms. We talked

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00:02:47,530 --> 00:02:50,580
about that quite in depth, but
there are some differences now

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00:02:50,580 --> 00:02:53,440
that we have more than one
electron in the atom.

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00:02:53,440 --> 00:02:55,770
Then something that you
probably have a lot of

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00:02:55,770 --> 00:02:59,010
experience with is talking about
electron configuration

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and writing out the electron
configuration.

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00:03:01,260 --> 00:03:03,890
But we'll go over that,
particularly some exceptions,

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when we're filling in electron
configurations, and how we

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00:03:06,870 --> 00:03:10,310
would go about doing that for
positive ions, which follow a

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little bit of a different
procedure.

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And if we have time today,
we'll start in on the

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photo-electron spectroscopy,
if not, that's where we'll

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start when we come back
on Wednesday.

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So, what we saw just on
Wednesday, in particular, but

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00:03:25,580 --> 00:03:27,335
also as we have been discussing
the Schrodinger

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equation for the hydrogen atom,
is that this equation

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can be used to correctly predict
the atomic structure

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00:03:32,860 --> 00:03:36,150
of hydrogen, and also all of
the energy levels of the

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00:03:36,150 --> 00:03:38,770
different orbitals in hydrogen,
which matched up

70
00:03:38,770 --> 00:03:41,080
with what we observed, for
example, when we looked at the

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00:03:41,080 --> 00:03:43,030
hydrogen atom emission
spectra.

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00:03:43,030 --> 00:03:45,190
And what we can do is we can
also use the Schrodinger

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00:03:45,190 --> 00:03:47,900
equation to make these accurate
predictions for any

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other atom that we want
to talk about in

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00:03:49,590 --> 00:03:51,450
the periodic table.

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00:03:51,450 --> 00:03:55,610
The one problem that we run into
is as we go to more and

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00:03:55,610 --> 00:04:01,440
more atoms on the table, as
we add on electrons, the

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00:04:01,440 --> 00:04:03,690
Schrodinger equation is going
to get more complicated.

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00:04:03,690 --> 00:04:06,640
So here I've written for the
hydrogen atom that deceptively

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00:04:06,640 --> 00:04:08,850
simple form of the Schrodinger
equation, where we don't

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00:04:08,850 --> 00:04:11,260
actually write out the
Hamiltonian operator, but you

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00:04:11,260 --> 00:04:13,800
remember that's a series of
second derivatives, so we have

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00:04:13,800 --> 00:04:16,960
a differential equation that
were actually dealing with.

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00:04:16,960 --> 00:04:18,920
If you think about what happens
when we go from

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00:04:18,920 --> 00:04:23,700
hydrogen to helium, now instead
of one electron, so

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00:04:23,700 --> 00:04:26,000
three position variables,
we have to describe two

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00:04:26,000 --> 00:04:29,800
electrons, so now we have six
position variables that we

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00:04:29,800 --> 00:04:32,810
need to plug into our
Schrodinger equation.

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00:04:32,810 --> 00:04:36,000
So similarly, as we now move up
only one more atom in the

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00:04:36,000 --> 00:04:40,810
table, so to an atomic number of
three or lithium, now we're

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00:04:40,810 --> 00:04:45,500
going from six variables all
the way to nine variables.

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00:04:45,500 --> 00:04:48,290
So you can see that we're
starting to have a very

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00:04:48,290 --> 00:04:51,330
complicated equation, and
it turns out that it's

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00:04:51,330 --> 00:04:53,800
mathematically impossible
to even solve the exact

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00:04:53,800 --> 00:04:56,050
Schrodinger equation
as we move up to

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higher numbers of electrons.

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So, what we say here is we need
to take a step back here

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00:05:02,370 --> 00:05:04,000
and come up with an
approximation that's going to

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00:05:04,000 --> 00:05:07,050
allow us to think about using
the Schrodinger equation when

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00:05:07,050 --> 00:05:09,580
we're not just talking about
hydrogen or one electron, but

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00:05:09,580 --> 00:05:13,340
when we have these
multi-electron atoms.

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00:05:13,340 --> 00:05:15,860
The most straightforward way to
do this is to make what's

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00:05:15,860 --> 00:05:19,390
called a one electron orbital
approximation, and when you do

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00:05:19,390 --> 00:05:22,610
you get out what are called
Hartree orbitals, and what

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00:05:22,610 --> 00:05:25,690
this means is that instead of
considering the wave function

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as a function, for example, for
helium as six different

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variables, what we do is we
break it up and treat each

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00:05:32,380 --> 00:05:35,670
electron has a separate wave
function and say that our

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00:05:35,670 --> 00:05:38,900
assumption is that the total
wave function is equal to the

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00:05:38,900 --> 00:05:41,630
product of the two individual
wave functions.

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So, for example, for helium, we
can break it up into wave

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00:05:44,520 --> 00:05:48,280
function for it the r, theta,
and phi value for electron

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00:05:48,280 --> 00:05:52,480
one, and multiply that by the
wave function for the r,

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00:05:52,480 --> 00:05:55,570
theta, and phi value for
electron number two.

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00:05:55,570 --> 00:05:58,250
So essentially what we're
saying is we have a wave

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00:05:58,250 --> 00:06:00,770
function for electron one,
and a wave function

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00:06:00,770 --> 00:06:02,890
for electron two.

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00:06:02,890 --> 00:06:05,660
We know how to write that in
terms of the state numbers, so

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00:06:05,660 --> 00:06:07,610
it would be 1, 0, 0, because
we're talking

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00:06:07,610 --> 00:06:09,000
about the ground state.

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We're always talking about the
ground state unless we specify

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00:06:12,270 --> 00:06:14,680
that we're talking about
an excited state.

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00:06:14,680 --> 00:06:18,720
And we have the spin quantum
number as plus 1/2 for

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00:06:18,720 --> 00:06:21,580
electron one, and minus 1/2
for the electron two.

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It's arbitrary which one I
assigned to which, but we know

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that we have to have each of
those two magnetic spin

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00:06:28,770 --> 00:06:36,110
quantum numbers in order to have
the distinct four letter

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description of an electron.

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00:06:37,700 --> 00:06:39,770
We know that it's not enough
just to describe the orbital

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00:06:39,770 --> 00:06:42,530
by three quantum numbers, we
need that fourth number to

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00:06:42,530 --> 00:06:44,110
fully describe an electron.

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And when we describe this in
terms of talking about

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00:06:46,470 --> 00:06:49,540
chemistry terminology, we would
call the first one the 1

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00:06:49,540 --> 00:06:51,900
s, and 1 is in parentheses
because we're talking about

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00:06:51,900 --> 00:06:54,780
the first electron there, and
we would multiply it by the

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00:06:54,780 --> 00:06:57,800
wave function for the second
one, which is also 1 s, but

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00:06:57,800 --> 00:07:01,290
now we are talking about
that second electron.

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00:07:01,290 --> 00:07:04,250
We can do the exact same thing
when we talk about lithium,

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00:07:04,250 --> 00:07:07,000
but now instead of breaking it
up into two wave functions,

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00:07:07,000 --> 00:07:09,250
we're breaking it up into three
wave functions because

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00:07:09,250 --> 00:07:10,440
we have three electrons.

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00:07:10,440 --> 00:07:15,730
So, the first again is
the 1 s 1 electron.

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00:07:15,730 --> 00:07:19,050
We then have the 1 s 2 electron,
and what is our

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00:07:19,050 --> 00:07:21,830
third electron going to be?

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00:07:21,830 --> 00:07:22,190
Yeah.

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00:07:22,190 --> 00:07:25,250
So it's going to be the
2 s 1 electron.

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00:07:25,250 --> 00:07:28,300
So we can do this essentially
for any atom we want, we just

148
00:07:28,300 --> 00:07:30,490
have more and more wave
functions that we're breaking

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00:07:30,490 --> 00:07:35,940
it up to as we get to more
and more electrons.

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00:07:35,940 --> 00:07:38,940
And we can also write this in an
even simpler form, which is

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00:07:38,940 --> 00:07:41,330
what's called electron
configuration, and this is

152
00:07:41,330 --> 00:07:45,130
just a shorthand notation for
these electron wave functions.

153
00:07:45,130 --> 00:07:49,280
So, for example, again we see
hydrogen is 1 s 1, helium we

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00:07:49,280 --> 00:07:53,340
say is 1 s 2, or 1 s squared, so
instead of writing out the

155
00:07:53,340 --> 00:07:57,300
1 s 1 and the 1 s 2, we just
combine it as 1 s squared,

156
00:07:57,300 --> 00:08:00,020
lithium is 1 s 2, 2 s 1.

157
00:08:00,020 --> 00:08:02,590
So writing out electron
configurations I realize is

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00:08:02,590 --> 00:08:04,820
something that a lot of you had
experience with in high

159
00:08:04,820 --> 00:08:06,570
school, you're probably --
many of you are very

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00:08:06,570 --> 00:08:08,860
comfortable doing it, especially
for the more

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00:08:08,860 --> 00:08:11,790
straightforward atoms. But
what's neat to kind of think

162
00:08:11,790 --> 00:08:14,350
about is if you think about
what a question might have

163
00:08:14,350 --> 00:08:16,640
been in high school, which is
please write the electron

164
00:08:16,640 --> 00:08:20,050
configuration for lithium, now
we can also answer what sounds

165
00:08:20,050 --> 00:08:22,530
like a much more impressive,
and a much more complicated

166
00:08:22,530 --> 00:08:26,610
question, which would be write
the shorthand notation for the

167
00:08:26,610 --> 00:08:29,220
one electron orbital
approximation to solve the

168
00:08:29,220 --> 00:08:30,550
Schrodinger equation
for lithium.

169
00:08:30,550 --> 00:08:34,300
So essentially, that is
the exact same thing.

170
00:08:34,300 --> 00:08:37,900
The electronic configuration,
all it is is the shorthand

171
00:08:37,900 --> 00:08:41,260
notation for that one electron
approximation for the

172
00:08:41,260 --> 00:08:42,980
Schrodinger equation
for lithium.

173
00:08:42,980 --> 00:08:46,090
So, if you're at hanging your
exam from high school on the

174
00:08:46,090 --> 00:08:47,800
fridge and you want to make it
look more impressive, you

175
00:08:47,800 --> 00:08:49,480
could just rewrite the
question as that, and

176
00:08:49,480 --> 00:08:51,340
essentially you're answering
the same thing.

177
00:08:51,340 --> 00:08:53,460
But now, hopefully, we
understand where that comes

178
00:08:53,460 --> 00:08:56,350
from, why it is that we use
the shorthand notation.

179
00:08:56,350 --> 00:08:59,040
So, let's write this one
electron orbital approximation

180
00:08:59,040 --> 00:09:02,050
for berylium, that sounds like a
pretty complicated question,

181
00:09:02,050 --> 00:09:05,620
but hopefully we know that it's
not at all, it's just 1 s

182
00:09:05,620 --> 00:09:08,410
2, and then 2 s 2.

183
00:09:08,410 --> 00:09:10,760
And we can go on and
on down the table.

184
00:09:10,760 --> 00:09:15,040
So, for example, for boron, now
we're dealing with 1 s 2,

185
00:09:15,040 --> 00:09:18,780
then 2 s 2, and now we have to
move into the p orbital so we

186
00:09:18,780 --> 00:09:19,990
go to 2 p 1.

187
00:09:19,990 --> 00:09:23,380
So that's a little bit of an
introduction into electron

188
00:09:23,380 --> 00:09:24,050
configuration.

189
00:09:24,050 --> 00:09:26,120
We'll get into some spots
where it gets a little

190
00:09:26,120 --> 00:09:30,110
trickier, a little bit more
complicated later in class.

191
00:09:30,110 --> 00:09:33,000
But that's an idea of what it
actually means to talk about

192
00:09:33,000 --> 00:09:35,320
electron configuration.

193
00:09:35,320 --> 00:09:38,690
So now that we can do this, we
can compare and think about,

194
00:09:38,690 --> 00:09:41,770
we know how to consider wave
functions for individual

195
00:09:41,770 --> 00:09:45,600
electrons in multi-electron
atoms using those Hartree

196
00:09:45,600 --> 00:09:49,040
orbitals or the one electron
wave approximations.

197
00:09:49,040 --> 00:09:51,190
So let's compare what some
of the similarities and

198
00:09:51,190 --> 00:09:53,910
differences are between hydrogen
atom orbitals, which

199
00:09:53,910 --> 00:09:56,750
we spent a lot of time studying,
and now these one

200
00:09:56,750 --> 00:09:59,040
electron orbital approximations
for these

201
00:09:59,040 --> 00:10:00,600
multi-electron atoms.

202
00:10:00,600 --> 00:10:03,460
So, as an example, let's take
argon, I've written up the

203
00:10:03,460 --> 00:10:06,480
electron configuration here,
and let's think about what

204
00:10:06,480 --> 00:10:09,700
some of the similarities might
be between wave functions in

205
00:10:09,700 --> 00:10:13,550
argon and wave functions
for hydrogen.

206
00:10:13,550 --> 00:10:16,430
So the first is that the
orbitals are similar in shape.

207
00:10:16,430 --> 00:10:19,910
So for example, if you know how
to draw an s orbital for a

208
00:10:19,910 --> 00:10:22,400
hydrogen atom, then you already
know how to draw the

209
00:10:22,400 --> 00:10:27,670
shape of an s orbital or
a p orbital for argon.

210
00:10:27,670 --> 00:10:30,090
Similarly, if we were to look
at the radial probability

211
00:10:30,090 --> 00:10:32,130
distributions, what we would
find is that there's an

212
00:10:32,130 --> 00:10:34,230
identical nodal structure.

213
00:10:34,230 --> 00:10:39,090
So, for example, if we look at
the 2 s orbital of argon, it's

214
00:10:39,090 --> 00:10:41,870
going to have the same amount of
nodes and the same type of

215
00:10:41,870 --> 00:10:45,310
nodes that the 2 s orbital
for hydrogen has.

216
00:10:45,310 --> 00:10:50,010
So how many nodes does the 2 s
orbital for hydrogen have?

217
00:10:50,010 --> 00:10:52,280
It has one node, right, because
if we're talking about

218
00:10:52,280 --> 00:10:56,840
nodes it's just n minus 1 is
total nodes, so you would just

219
00:10:56,840 --> 00:11:03,450
say 2 minus 1 equals 1 node
for the 2 s orbital.

220
00:11:03,450 --> 00:11:07,710
And how many of those nodes
are angular nodes? zero.

221
00:11:07,710 --> 00:11:11,670
L equals 0, so we have zero
angular nodes, that means that

222
00:11:11,670 --> 00:11:12,860
they're all radial nodes.

223
00:11:12,860 --> 00:11:15,590
So what we end up with is one
radial node for the 2 s

224
00:11:15,590 --> 00:11:18,860
orbital of hydrogen, and we can
apply that for argon or

225
00:11:18,860 --> 00:11:23,640
any other multi-electron atom
here, we also have one radial

226
00:11:23,640 --> 00:11:27,390
node for the 2 s orbital
of argon.

227
00:11:27,390 --> 00:11:29,350
But there's also some
differences that we need to

228
00:11:29,350 --> 00:11:31,460
keep in mind, and that will be
the focus of a lot of the

229
00:11:31,460 --> 00:11:32,500
lecture today.

230
00:11:32,500 --> 00:11:34,820
One of the main difference is
is that when you're talking

231
00:11:34,820 --> 00:11:38,700
about multi-electron orbitals,
they're actually smaller than

232
00:11:38,700 --> 00:11:41,840
the corresponding orbital
for the hydrogen atom.

233
00:11:41,840 --> 00:11:43,730
We can think about why
that would be.

234
00:11:43,730 --> 00:11:47,540
Let's consider again an s
orbital for argon, so let's

235
00:11:47,540 --> 00:11:50,170
say we're looking at the
1 s orbital for argon.

236
00:11:50,170 --> 00:11:53,050
What is the pull from the
nucleus from argon

237
00:11:53,050 --> 00:11:53,760
going to be equal to?

238
00:11:53,760 --> 00:11:57,790
What is the charge
of the nucleus?

239
00:11:57,790 --> 00:12:01,280
Does anyone know, it's a quick
addition problem here.

240
00:12:01,280 --> 00:12:02,510
Yeah, so it's 18.

241
00:12:02,510 --> 00:12:06,960
So z equals 18, so the nucleus
is going to be pulling at the

242
00:12:06,960 --> 00:12:09,970
electron with a Coulombic
attraction that has a charge

243
00:12:09,970 --> 00:12:14,980
of plus 18, if we're talking
about the 1 s electron or the

244
00:12:14,980 --> 00:12:16,810
1 s orbital in argon.

245
00:12:16,810 --> 00:12:19,220
It turns out, and we're going to
get the idea of shielding,

246
00:12:19,220 --> 00:12:22,320
so it's not going to actually
feel that full plus 18, but

247
00:12:22,320 --> 00:12:24,450
it'll feel a whole lot more
than it will just feel in

248
00:12:24,450 --> 00:12:26,560
terms of a hydrogen atom
where we only have a

249
00:12:26,560 --> 00:12:28,120
nuclear charge of one.

250
00:12:28,120 --> 00:12:31,440
So because we're feeling a
stronger attractive force from

251
00:12:31,440 --> 00:12:34,180
the nucleus, we're actually
pulling that electron in

252
00:12:34,180 --> 00:12:37,530
closer, which means that the
probability squared of where

253
00:12:37,530 --> 00:12:40,570
the electron is going to be is
actually a smaller radius.

254
00:12:40,570 --> 00:12:44,150
So when we talk about the size
of multi-electron orbitals,

255
00:12:44,150 --> 00:12:46,140
they're actually going to be
smaller because they're being

256
00:12:46,140 --> 00:12:48,340
pulled in closer to the nucleus
because of that

257
00:12:48,340 --> 00:12:51,350
stronger attraction because of
the higher charge of the

258
00:12:51,350 --> 00:12:53,380
nucleus in a multi-electron
atom compared

259
00:12:53,380 --> 00:12:56,540
to a hydrogen atom.

260
00:12:56,540 --> 00:12:58,440
The other main difference that
we're really going to get to

261
00:12:58,440 --> 00:13:00,830
today is that in multi-electron
atoms, orbital

262
00:13:00,830 --> 00:13:03,290
energies depend not just on the
shell, which is what we

263
00:13:03,290 --> 00:13:06,260
saw before, not just on the
value of n, but also on the

264
00:13:06,260 --> 00:13:07,770
angular momentum
quantum number.

265
00:13:07,770 --> 00:13:10,360
So they also depend on
the sub-shell or l.

266
00:13:10,360 --> 00:13:12,870
And we'll really get to see a
picture of that, and I'll be

267
00:13:12,870 --> 00:13:15,170
repeating that again and again
today, because this is

268
00:13:15,170 --> 00:13:17,870
something I really want everyone
to get firmly into

269
00:13:17,870 --> 00:13:18,450
their heads.

270
00:13:18,450 --> 00:13:21,570
So, let's now take a look
at the energies.

271
00:13:21,570 --> 00:13:23,870
We looked at the wave functions,
we know the other

272
00:13:23,870 --> 00:13:25,760
part of solving the Schrodinger
equation is to

273
00:13:25,760 --> 00:13:28,860
solve for the binding energy of
electrons to the nucleus,

274
00:13:28,860 --> 00:13:31,360
so let's take a look at those.

275
00:13:31,360 --> 00:13:33,650
And there again is another
difference between

276
00:13:33,650 --> 00:13:36,280
multi-electron atom and the
hydrogen atoms. So when we

277
00:13:36,280 --> 00:13:39,160
talk about orbitals in
multi-electron atoms, they're

278
00:13:39,160 --> 00:13:41,160
actually lower in
energy than the

279
00:13:41,160 --> 00:13:43,120
corresponding h atom orbitals.

280
00:13:43,120 --> 00:13:45,930
And when we say lower in energy,
of course, what we

281
00:13:45,930 --> 00:13:48,070
mean is more negative.

282
00:13:48,070 --> 00:13:51,010
Right, because when we think
of an energy diagram, that

283
00:13:51,010 --> 00:13:54,040
lowest spot there is going to
have the lowest value of the

284
00:13:54,040 --> 00:14:00,390
binding energy or the most
negative value of binding.

285
00:14:00,390 --> 00:14:03,690
So, let's take a look here at
an example of an energy

286
00:14:03,690 --> 00:14:06,930
diagram for the hydrogen atom,
and we can also look at a

287
00:14:06,930 --> 00:14:09,930
energy diagram for a
multi-electron atom, and this

288
00:14:09,930 --> 00:14:12,430
is just a generic one here, so
I haven't actually listed

289
00:14:12,430 --> 00:14:15,460
energy numbers, but I want
you to see the trend.

290
00:14:15,460 --> 00:14:19,490
So for example, if you look at
the 1 s orbital here, you can

291
00:14:19,490 --> 00:14:23,210
see that actually it is lower
in the case of the

292
00:14:23,210 --> 00:14:26,480
multi-electron atom than it
is for the hydrogen atom.

293
00:14:26,480 --> 00:14:28,665
You see the same thing
regardless of which orbital

294
00:14:28,665 --> 00:14:30,090
you're looking at.

295
00:14:30,090 --> 00:14:33,090
For example, for the 2 s, again
what you see is that the

296
00:14:33,090 --> 00:14:37,180
multi-electron atom, its 2 s
orbital is lower in energy

297
00:14:37,180 --> 00:14:39,480
than it is for the hydrogen.

298
00:14:39,480 --> 00:14:41,720
The same thing we
see for the 2 p.

299
00:14:41,720 --> 00:14:45,890
Again the 2 p orbitals for the
multi-electron atom, lower in

300
00:14:45,890 --> 00:14:48,300
energy than for the
hydrogen atom.

301
00:14:48,300 --> 00:14:50,940
But there's something you'll
note here also when I point

302
00:14:50,940 --> 00:14:54,340
out the case of the 2 s versus
the 2 p, which is what I

303
00:14:54,340 --> 00:14:56,920
mentioned that I would be saying
again and again, which

304
00:14:56,920 --> 00:14:59,600
is when we look at the hydrogen
atom, the energy of

305
00:14:59,600 --> 00:15:03,640
all of the n equals 2 orbitals
are exactly the same.

306
00:15:03,640 --> 00:15:05,460
That's what we call degenerate
orbitals,

307
00:15:05,460 --> 00:15:07,070
they're the same energy.

308
00:15:07,070 --> 00:15:09,910
But when we get to the
multi-electron atoms, we see

309
00:15:09,910 --> 00:15:13,150
that actually the p orbitals are
higher in energy than the

310
00:15:13,150 --> 00:15:14,450
s orbitals.

311
00:15:14,450 --> 00:15:17,570
So we'll see specifically why it
is that the s orbitals are

312
00:15:17,570 --> 00:15:18,490
lower in energy.

313
00:15:18,490 --> 00:15:21,210
We'll get to discussing that,
but what I want to point out

314
00:15:21,210 --> 00:15:24,320
here again is the fact that
instead of just being

315
00:15:24,320 --> 00:15:27,030
dependent on n, the energy
level is dependent

316
00:15:27,030 --> 00:15:29,780
on both n and l.

317
00:15:29,780 --> 00:15:34,400
And is no longer that sole
determining factor for energy,

318
00:15:34,400 --> 00:15:38,080
energy also depends both
on n and on l.

319
00:15:38,080 --> 00:15:41,930
And we can look at precisely why
that is by looking at the

320
00:15:41,930 --> 00:15:45,150
equations for the energy levels
for a hydrogen atom

321
00:15:45,150 --> 00:15:47,030
versus the multi-electron
atom.

322
00:15:47,030 --> 00:15:50,320
So, for a hydrogen atom, and
actually for any one electron

323
00:15:50,320 --> 00:15:54,070
atom at all, this is our energy
or our binding energy.

324
00:15:54,070 --> 00:15:55,990
This is what came out of
solving the Schrodinger

325
00:15:55,990 --> 00:15:59,260
equation, we've seen this
several times before that the

326
00:15:59,260 --> 00:16:03,150
energy is equal to negative z
squared times the Rydberg

327
00:16:03,150 --> 00:16:05,400
constant over n squared.

328
00:16:05,400 --> 00:16:08,500
Remember the z squared, that's
just the atomic number or the

329
00:16:08,500 --> 00:16:13,050
charge on the nucleus, and we
can figure that out for any

330
00:16:13,050 --> 00:16:14,740
one electron atom at all.

331
00:16:14,740 --> 00:16:17,180
And an important thing to note
is in terms of what that

332
00:16:17,180 --> 00:16:19,930
physically means, so physically
the binding energy

333
00:16:19,930 --> 00:16:22,760
is just the negative of
the ionization energy.

334
00:16:22,760 --> 00:16:25,090
So if we can figure out the
binding energy, we can also

335
00:16:25,090 --> 00:16:28,170
figure out how much energy we
have to put into our atom in

336
00:16:28,170 --> 00:16:31,950
order to a eject or ionize
an electron.

337
00:16:31,950 --> 00:16:35,770
We can also look at the energy
equation now for a

338
00:16:35,770 --> 00:16:37,820
multi-electron atom.

339
00:16:37,820 --> 00:16:40,800
And the big difference is
right here in this term.

340
00:16:40,800 --> 00:16:43,960
So instead of being equal to
negative z squared, now we're

341
00:16:43,960 --> 00:16:47,650
equal to negative z effective
squared times r

342
00:16:47,650 --> 00:16:49,970
h all over n squared.

343
00:16:49,970 --> 00:16:53,230
So when we say z effective, what
we're talking about is

344
00:16:53,230 --> 00:16:56,290
instead of z, the charge on
the nucleus, we're talking

345
00:16:56,290 --> 00:16:58,980
about the effective charge
on a nucleus.

346
00:16:58,980 --> 00:17:02,550
So for an example, even if a
nucleus has a charge of 7, but

347
00:17:02,550 --> 00:17:05,850
the electron we're interested in
only feels the charge as if

348
00:17:05,850 --> 00:17:09,350
it were a 5, then what we
would say is that the z

349
00:17:09,350 --> 00:17:12,260
effective for the nucleus
is 5 for that electron.

350
00:17:12,260 --> 00:17:14,790
And we'll talk about this
more, so if this is not

351
00:17:14,790 --> 00:17:17,710
completely intuitive, we'll
see why in a second.

352
00:17:17,710 --> 00:17:20,590
So the main idea here is z
effective is not z, so don't

353
00:17:20,590 --> 00:17:23,590
try to plug one in for the
other, they're absolutely

354
00:17:23,590 --> 00:17:26,310
different quantities in any case
when we're not talking

355
00:17:26,310 --> 00:17:29,200
about a 1 electron atom.

356
00:17:29,200 --> 00:17:32,190
And the point that I also want
to make is the way that they

357
00:17:32,190 --> 00:17:36,400
differ, z effective actually
differs from the total charge

358
00:17:36,400 --> 00:17:39,960
in the nucleus due to an
idea called shielding.

359
00:17:39,960 --> 00:17:43,455
So, shielding happens when you
have more than one electron in

360
00:17:43,455 --> 00:17:46,980
an atom, and the reason that
it's happening is because

361
00:17:46,980 --> 00:17:50,120
you're actually canceling out
some of that positive charge

362
00:17:50,120 --> 00:17:53,510
from the nucleus or that
attractive force with a

363
00:17:53,510 --> 00:17:56,230
repulsive force between
two electrons.

364
00:17:56,230 --> 00:17:59,370
So if you have some charge in
the nucleus, but you also have

365
00:17:59,370 --> 00:18:02,550
repulsion with another electron,
the net attractive

366
00:18:02,550 --> 00:18:05,990
charge that a given electron
going to feel is actually less

367
00:18:05,990 --> 00:18:08,120
than that total charge
in the nucleus.

368
00:18:08,120 --> 00:18:10,960
And shielding is a little bit of
a misnomer because it's not

369
00:18:10,960 --> 00:18:13,930
actually that's the electron's
blocking the charge from

370
00:18:13,930 --> 00:18:17,150
another electron, it's more like
you're canceling out a

371
00:18:17,150 --> 00:18:20,530
positive attractive force with
a negative repulsive force.

372
00:18:20,530 --> 00:18:23,520
But shielding is a good way to
think about it, and actually,

373
00:18:23,520 --> 00:18:26,070
that's what we'll use in this
class to sort of visualize

374
00:18:26,070 --> 00:18:29,400
what's happening when we have
many electrons in an atom and

375
00:18:29,400 --> 00:18:30,470
they're shielding each other.

376
00:18:30,470 --> 00:18:33,240
Shielding is the term that's
used, it brings up a certain

377
00:18:33,240 --> 00:18:35,520
image in our mind, and even
though that's not precisely

378
00:18:35,520 --> 00:18:38,630
what's going on, it's a very
good way to visualize what

379
00:18:38,630 --> 00:18:39,880
we're trying to think
about here.

380
00:18:39,880 --> 00:18:43,250
So let's take two cases of
shielding if we're talking

381
00:18:43,250 --> 00:18:47,300
about, for example, the helium,
a helium nucleus or a

382
00:18:47,300 --> 00:18:48,270
helium atom.

383
00:18:48,270 --> 00:18:52,130
So what is the charge
on a helium nucleus?

384
00:18:52,130 --> 00:18:54,850
What is z?

385
00:18:54,850 --> 00:18:56,790
Yup, so it's plus 2.

386
00:18:56,790 --> 00:19:00,480
So the charge is actually just
equal to z, we can write plus

387
00:19:00,480 --> 00:19:03,720
2, or you can write plus 2 e,
e just means the absolute

388
00:19:03,720 --> 00:19:05,520
value of the charge
on an electron.

389
00:19:05,520 --> 00:19:09,020
When we plug it into equations
we just use the number, the e

390
00:19:09,020 --> 00:19:11,140
is assumed there.

391
00:19:11,140 --> 00:19:13,940
So, let's think of what we
could have if we have two

392
00:19:13,940 --> 00:19:17,160
electrons in a helium atom
that are shielded in two

393
00:19:17,160 --> 00:19:17,960
extreme ways.

394
00:19:17,960 --> 00:19:21,510
So, in the first extreme way,
let's consider that our first

395
00:19:21,510 --> 00:19:25,000
electron is at some distance
very far away from the

396
00:19:25,000 --> 00:19:28,400
nucleus, we'll call this
electron one, and our second

397
00:19:28,400 --> 00:19:31,570
electron is, in fact, much, much
closer to the nucleus,

398
00:19:31,570 --> 00:19:34,250
and let's think of the idea of
shielding in more of the

399
00:19:34,250 --> 00:19:37,780
classical sense where we're
actually blocking some of that

400
00:19:37,780 --> 00:19:39,080
positive charge.

401
00:19:39,080 --> 00:19:42,090
So if we have total and complete
shielding where that

402
00:19:42,090 --> 00:19:45,400
can actually negate a full
positive charge, because

403
00:19:45,400 --> 00:19:47,980
remember our nucleus is plus
2, one of the electrons is

404
00:19:47,980 --> 00:19:50,950
minus 1, so if it totally blocks
it, all we would have

405
00:19:50,950 --> 00:19:54,590
left from the nucleus is an
effective charge of plus 1.

406
00:19:54,590 --> 00:19:57,410
So in our first case, our first
extreme case, would be

407
00:19:57,410 --> 00:20:01,090
that the z effective that is
felt by electron number 1, is

408
00:20:01,090 --> 00:20:04,100
going to be plus 1.

409
00:20:04,100 --> 00:20:06,730
So, what we can do is figure out
what we would expect the

410
00:20:06,730 --> 00:20:09,330
binding energy of that electron
to be in the case of

411
00:20:09,330 --> 00:20:10,960
this total shielding.

412
00:20:10,960 --> 00:20:14,440
And remember again, the binding
energy physically is

413
00:20:14,440 --> 00:20:17,070
the negative of the ionization
energy, and that's actually

414
00:20:17,070 --> 00:20:19,400
how you can experimentally
check to see if this is

415
00:20:19,400 --> 00:20:20,790
actually correct.

416
00:20:20,790 --> 00:20:23,290
And that's going to be equal
to negative z effective

417
00:20:23,290 --> 00:20:25,890
squared times r h
over n squared.

418
00:20:25,890 --> 00:20:28,880
So, let's plug in these values
and see what we would expect

419
00:20:28,880 --> 00:20:30,600
to see for the energy.

420
00:20:30,600 --> 00:20:34,890
So it would be negative 1
squared times r h all over 1

421
00:20:34,890 --> 00:20:38,520
squared, since our z effective
we're saying is 1, and n is

422
00:20:38,520 --> 00:20:41,440
also equal to 1, because we're
in the ground state here so

423
00:20:41,440 --> 00:20:46,980
we're talking about
a 1 s orbital.

424
00:20:46,980 --> 00:20:49,370
So if we have a look at what
the answer would be, this

425
00:20:49,370 --> 00:20:50,430
looks very familiar.

426
00:20:50,430 --> 00:20:53,530
We would expect our binding
energy to be a negative 2 .

427
00:20:53,530 --> 00:20:56,730
1 8 times 10 to the negative
18 joules.

428
00:20:56,730 --> 00:20:59,410
This is actually what the
binding energy is for hydrogen

429
00:20:59,410 --> 00:21:02,710
atom, and in fact, that makes
sense because in our extreme

430
00:21:02,710 --> 00:21:04,920
case where we have total
shielding by the second

431
00:21:04,920 --> 00:21:07,910
electron of the electron of
interest, it's essentially

432
00:21:07,910 --> 00:21:11,610
seeing the same nuclear force
that an electron in a hydrogen

433
00:21:11,610 --> 00:21:12,190
atom would see.

434
00:21:12,190 --> 00:21:13,680
All right.

435
00:21:13,680 --> 00:21:17,080
Let's consider now the second
extreme case, or extreme case

436
00:21:17,080 --> 00:21:18,870
b, for our helium atom.

437
00:21:18,870 --> 00:21:22,080
Again we have the charge of
the nucleus on plus 2, but

438
00:21:22,080 --> 00:21:24,340
let's say this time the electron
now is going to be

439
00:21:24,340 --> 00:21:26,310
very, very close
to the nucleus.

440
00:21:26,310 --> 00:21:29,390
And let's say our second
electron now is really far

441
00:21:29,390 --> 00:21:32,640
away, such that it's actually
not going to shield any of the

442
00:21:32,640 --> 00:21:36,490
nuclear charge at all from
that first electron.

443
00:21:36,490 --> 00:21:39,640
So what we end up saying is that
the z effective or the

444
00:21:39,640 --> 00:21:42,730
effective charge that that first
electron feels is now

445
00:21:42,730 --> 00:21:45,920
going to be plus 2.

446
00:21:45,920 --> 00:21:49,240
Again, we can just plug this
into our equation, so if we

447
00:21:49,240 --> 00:21:52,390
write in our numbers now saying
that z effective is

448
00:21:52,390 --> 00:21:57,340
equal to 2, we find that we get
negative 2 squared r h,

449
00:21:57,340 --> 00:22:00,520
all divided again by 1 squared
-- we're still talking about a

450
00:22:00,520 --> 00:22:03,890
1 s orbital here.

451
00:22:03,890 --> 00:22:06,870
And if we do that calculation,
what we find out is that the

452
00:22:06,870 --> 00:22:10,840
binding energy, in this case
where we have no shielding, is

453
00:22:10,840 --> 00:22:12,260
negative 8 .

454
00:22:12,260 --> 00:22:17,410
7 2 times 10 to the negative
18 joules.

455
00:22:17,410 --> 00:22:20,450
So, let's compare what we've
just seen as our two extremes.

456
00:22:20,450 --> 00:22:24,540
So in extreme case a, we saw
that z effective was 1.

457
00:22:24,540 --> 00:22:26,910
This is what we call
total shielding.

458
00:22:26,910 --> 00:22:29,380
The electron completely canceled
out it's equivalent

459
00:22:29,380 --> 00:22:32,790
of charge from the nucleus, such
that we only saw in a z

460
00:22:32,790 --> 00:22:33,900
effective of 1.

461
00:22:33,900 --> 00:22:38,240
In an extreme case b, we had
a z effective of 2, so

462
00:22:38,240 --> 00:22:41,170
essentially what we had was
no shielding at all.

463
00:22:41,170 --> 00:22:44,070
We said that that second
electron was so far out of the

464
00:22:44,070 --> 00:22:46,310
picture, that it had absolutely
no affect on what

465
00:22:46,310 --> 00:22:49,870
the charge was felt by
that first electron.

466
00:22:49,870 --> 00:22:52,440
So, we can actually think about
now, we know the extreme

467
00:22:52,440 --> 00:22:55,840
cases, but what is the reality,
and the reality is if

468
00:22:55,840 --> 00:22:58,260
we think about the ionization
energy, and we measure it

469
00:22:58,260 --> 00:23:00,480
experimentally, we find
that it's 3 .

470
00:23:00,480 --> 00:23:03,980
9 4 times 10 to the negative
18 joules, and what you can

471
00:23:03,980 --> 00:23:07,040
see is that falls right in the
middle between the two

472
00:23:07,040 --> 00:23:08,960
ionization energies that
we would expect

473
00:23:08,960 --> 00:23:10,460
for the extreme cases.

474
00:23:10,460 --> 00:23:13,730
And this is absolutely
confirming that what is

475
00:23:13,730 --> 00:23:16,240
happening is what we would
expect to happen, because we

476
00:23:16,240 --> 00:23:19,350
would expect the case of reality
is that, in fact, some

477
00:23:19,350 --> 00:23:21,900
shielding is going on, but it's
not going to be total

478
00:23:21,900 --> 00:23:24,340
shielding, but at the same time
it's not going to be no

479
00:23:24,340 --> 00:23:26,290
shielding at all.

480
00:23:26,290 --> 00:23:30,290
And if we experimentally know
what the ionization energy is,

481
00:23:30,290 --> 00:23:33,460
we actually have a way to find
out what the z effective will

482
00:23:33,460 --> 00:23:34,990
be equal to.

483
00:23:34,990 --> 00:23:37,950
And we can use this equation
here, this is just the

484
00:23:37,950 --> 00:23:40,630
equation for the ionization
energy, which is the same

485
00:23:40,630 --> 00:23:44,060
thing as saying the negative of
the binding energy that's

486
00:23:44,060 --> 00:23:48,490
equal to z effective squared
r h over n squared.

487
00:23:48,490 --> 00:23:51,830
So, what we can do instead of
talking about the ionization

488
00:23:51,830 --> 00:23:55,015
energy, because that's one of
our known quantities, is we

489
00:23:55,015 --> 00:23:58,810
can instead solve so that
we can find z effective.

490
00:23:58,810 --> 00:24:03,680
So, if we just rearrange this
equation, what we find is that

491
00:24:03,680 --> 00:24:10,060
z effective is equal to n
squared times the ionization

492
00:24:10,060 --> 00:24:16,370
energy, all over the Rydberg
constant and the

493
00:24:16,370 --> 00:24:17,320
square root of this.

494
00:24:17,320 --> 00:24:22,500
So the square root of n
squared r e over r h.

495
00:24:22,500 --> 00:24:27,710
So what's our value
for n here? one.

496
00:24:27,710 --> 00:24:29,770
Yup, that's right.

497
00:24:29,770 --> 00:24:35,410
And then what's our value
for ionization energy?

498
00:24:35,410 --> 00:24:35,670
Yup.

499
00:24:35,670 --> 00:24:37,590
So it's just that ionization
energy that we have

500
00:24:37,590 --> 00:24:40,210
experimentally measured, 3 .

501
00:24:40,210 --> 00:24:44,360
9 4 times 10 to the negative
18 joules.

502
00:24:44,360 --> 00:24:48,490
We put all of this over the
Rydberg constant, which is 2 .

503
00:24:48,490 --> 00:24:53,390
1 8 times 10 to the negative
18 joules, and we want to

504
00:24:53,390 --> 00:24:59,230
raise this all to the 1/2.

505
00:24:59,230 --> 00:25:03,080
So what we end up seeing is that
the z effective is equal

506
00:25:03,080 --> 00:25:05,280
to positive 1 .

507
00:25:05,280 --> 00:25:07,430
3 4.

508
00:25:07,430 --> 00:25:11,090
So, this is what we find the
actual z effective is for an

509
00:25:11,090 --> 00:25:13,800
electron in the helium atom.

510
00:25:13,800 --> 00:25:17,490
Does this seem like a
reasonable number?

511
00:25:17,490 --> 00:25:17,830
Yeah?

512
00:25:17,830 --> 00:25:20,520
Who says yes, raise your hand
if this seems reasonable.

513
00:25:20,520 --> 00:25:23,270
Does anyone think this
seems not reasonable?

514
00:25:23,270 --> 00:25:23,650
OK.

515
00:25:23,650 --> 00:25:26,170
How can we check, for example,
if it does or if it doesn't

516
00:25:26,170 --> 00:25:27,040
seem reasonable.

517
00:25:27,040 --> 00:25:29,590
Well, the reason, the way that
we can check it is just to see

518
00:25:29,590 --> 00:25:32,090
if it's in between our
two extreme cases.

519
00:25:32,090 --> 00:25:34,880
We know that it has to be more
than 1, because even if we had

520
00:25:34,880 --> 00:25:36,870
total shielding, we would
at least feel is the

521
00:25:36,870 --> 00:25:38,100
effective of 1.

522
00:25:38,100 --> 00:25:41,490
We know that it has to be equal
to less than 2, because

523
00:25:41,490 --> 00:25:45,070
even if we had absolutely no
shielding at all, the highest

524
00:25:45,070 --> 00:25:47,560
z effective we could have is 2,
so it makes perfect sense

525
00:25:47,560 --> 00:25:50,240
that we have a z effective that
falls somewhere in the

526
00:25:50,240 --> 00:25:51,570
middle of those two.

527
00:25:51,570 --> 00:25:55,220
So, let's look at another
example of thinking about

528
00:25:55,220 --> 00:25:57,140
whether we get an answer
out that's reasonable.

529
00:25:57,140 --> 00:26:00,085
So we should be able to
calculate a z effective for

530
00:26:00,085 --> 00:26:02,490
any atom that we want to talk
about, as long as we know what

531
00:26:02,490 --> 00:26:04,550
that ionization energy is.

532
00:26:04,550 --> 00:26:06,980
And I'm not expecting you to
do that calculation here,

533
00:26:06,980 --> 00:26:09,610
because it involves the
calculator, among maybe a

534
00:26:09,610 --> 00:26:10,890
piece of paper as well.

535
00:26:10,890 --> 00:26:13,660
But what you should be able to
do is take a look at a list of

536
00:26:13,660 --> 00:26:17,460
answers for what we're saying
z effective might be, and

537
00:26:17,460 --> 00:26:20,570
determining which ones are
possible versus which ones are

538
00:26:20,570 --> 00:26:21,340
not possible.

539
00:26:21,340 --> 00:26:23,700
So, why don't you take a look at
this and tell me which are

540
00:26:23,700 --> 00:26:28,230
possible for a 2 s electron in
a lithium atom where z is

541
00:26:28,230 --> 00:26:48,010
going to be equal to three?

542
00:26:48,010 --> 00:27:04,490
Let's do 10 more seconds
on that.

543
00:27:04,490 --> 00:27:05,080
OK, great.

544
00:27:05,080 --> 00:27:06,860
So, the majority of
you got it right.

545
00:27:06,860 --> 00:27:09,520
There are some people that are a
little bit confused still on

546
00:27:09,520 --> 00:27:11,650
where this make sense, so, let's
just think about this a

547
00:27:11,650 --> 00:27:12,700
little bit more.

548
00:27:12,700 --> 00:27:16,830
So now we're saying that z
is equal to 3, so if, for

549
00:27:16,830 --> 00:27:20,080
example, we had total shielding
by the other two

550
00:27:20,080 --> 00:27:23,970
electrons, if they totally
canceled out one unit of

551
00:27:23,970 --> 00:27:27,050
positive charge each in the
nucleus, what we would end up

552
00:27:27,050 --> 00:27:31,140
with is we started with 3 and
then we would subtract a

553
00:27:31,140 --> 00:27:34,960
charge of 2, so we would end up
with a plus 1 z effective

554
00:27:34,960 --> 00:27:36,570
from the nucleus.

555
00:27:36,570 --> 00:27:39,920
So our minimum that we're
going to see is that the

556
00:27:39,920 --> 00:27:42,505
smallest we can have for
a z effective is going

557
00:27:42,505 --> 00:27:43,630
to be equal to 1.

558
00:27:43,630 --> 00:27:46,730
So any of the answers that
said a z effective of .

559
00:27:46,730 --> 00:27:47,680
3 9 or .

560
00:27:47,680 --> 00:27:50,210
8 7 are possible, they actually
aren't possible

561
00:27:50,210 --> 00:27:53,180
because even if we saw a total
shielding, the minimum z

562
00:27:53,180 --> 00:27:54,880
effective we would see is 1.

563
00:27:54,880 --> 00:27:58,250
And then I think it looks like
most people understood that

564
00:27:58,250 --> 00:27:59,680
four was not a possibility.

565
00:27:59,680 --> 00:28:02,680
Of course, if we saw no
shielding at all what we would

566
00:28:02,680 --> 00:28:05,020
end up with is a z
effective of 3.

567
00:28:05,020 --> 00:28:07,460
So again, when we check these,
what we want to see is that

568
00:28:07,460 --> 00:28:10,690
our z effective falls in between
the two extreme cases

569
00:28:10,690 --> 00:28:13,120
that we could envision
for shielding.

570
00:28:13,120 --> 00:28:15,630
And again, just go back and look
at this and think about

571
00:28:15,630 --> 00:28:17,650
this, this should make sense if
you kind of look at those

572
00:28:17,650 --> 00:28:20,600
two extreme examples, so even
if it doesn't make entire

573
00:28:20,600 --> 00:28:22,810
sense in the 10 seconds you
have to answer a clicker

574
00:28:22,810 --> 00:28:25,640
question right now, make sure
this weekend you can go over

575
00:28:25,640 --> 00:28:29,100
it and be able to predict if you
saw a list of answers or

576
00:28:29,100 --> 00:28:31,990
if you calculate your own answer
on the p-set, whether

577
00:28:31,990 --> 00:28:33,990
or not it's right or it's wrong,
you should be able to

578
00:28:33,990 --> 00:28:37,550
qualitatively confirm whether
you have a reasonable or a not

579
00:28:37,550 --> 00:28:42,100
reasonable answer after you
do the calculation part.

580
00:28:42,100 --> 00:28:42,370
All right.

581
00:28:42,370 --> 00:28:44,710
So now that we have a general
idea of what we're talking

582
00:28:44,710 --> 00:28:47,820
about with shielding, we can
now go back and think about

583
00:28:47,820 --> 00:28:50,500
why it is that the orbitals
are ordered in the

584
00:28:50,500 --> 00:28:51,770
order that they are.

585
00:28:51,770 --> 00:28:54,790
We know that the orbitals for
multi-electron atoms depend

586
00:28:54,790 --> 00:28:56,970
both on n and on l.

587
00:28:56,970 --> 00:29:00,440
But we haven't yet addressed
why, for example, a 2 s

588
00:29:00,440 --> 00:29:04,480
orbital is lower in energy than
the 2 p orbital, or why,

589
00:29:04,480 --> 00:29:08,450
for example, a 3 s orbital is
lower in energy than a 3 p,

590
00:29:08,450 --> 00:29:11,160
which in turn is lower
than a 3 d orbital.

591
00:29:11,160 --> 00:29:15,082
So let's think about shielding
in trying to answer why, in

592
00:29:15,082 --> 00:29:20,500
fact, it's those s orbitals that
are the lowest in energy.

593
00:29:20,500 --> 00:29:22,860
And when we make these
comparisons, one thing I want

594
00:29:22,860 --> 00:29:26,790
to point out is that we need to
keep the constant principle

595
00:29:26,790 --> 00:29:29,260
quantum number constant, so
we're talking about a certain

596
00:29:29,260 --> 00:29:31,910
state, so we could talk about
the n equals 2 state, or the n

597
00:29:31,910 --> 00:29:33,410
equals 3 state.

598
00:29:33,410 --> 00:29:36,240
And when we're talking about
orbitals in the same state,

599
00:29:36,240 --> 00:29:39,800
what we find is that orbitals
that have lower values of l

600
00:29:39,800 --> 00:29:42,720
can actually penetrate closer
to the nucleus.

601
00:29:42,720 --> 00:29:45,520
This is an idea we introduced
on Wednesday when we were

602
00:29:45,520 --> 00:29:48,310
looking at the radial
probability distributions of p

603
00:29:48,310 --> 00:29:51,550
orbitals versus s orbitals
versus d orbitals.

604
00:29:51,550 --> 00:29:53,810
But now it's going to make more
sense because in that

605
00:29:53,810 --> 00:29:57,290
case we were just talking about
single electron atoms,

606
00:29:57,290 --> 00:29:59,060
and now we're talking about
a case where we

607
00:29:59,060 --> 00:30:00,890
actually can see shielding.

608
00:30:00,890 --> 00:30:03,940
So what is actually going to
matter is how closely that

609
00:30:03,940 --> 00:30:06,840
electron can penetrate to the
nucleus, and what I mean by

610
00:30:06,840 --> 00:30:10,890
penetrate to the nucleus is is
there probability density a

611
00:30:10,890 --> 00:30:13,730
decent amount that's very
close to the nucleus.

612
00:30:13,730 --> 00:30:16,910
So, if we superimpose, for
example, the 2 s radial

613
00:30:16,910 --> 00:30:20,870
probability distribution over
the 2 p, what we see is

614
00:30:20,870 --> 00:30:23,290
there's this little bit of
probability density in the 2

615
00:30:23,290 --> 00:30:27,370
s, but it is significant, and
that's closer to the nucleus

616
00:30:27,370 --> 00:30:29,040
than it is for the 2 p.

617
00:30:29,040 --> 00:30:33,480
And remember, this is in
complete opposition to what we

618
00:30:33,480 --> 00:30:37,010
call the size of the orbitals,
because we know that the 2 p

619
00:30:37,010 --> 00:30:39,450
is actually a smaller orbital.

620
00:30:39,450 --> 00:30:41,370
For example, when we're
talking about radial

621
00:30:41,370 --> 00:30:44,930
probability distributions, the
most probable radius is closer

622
00:30:44,930 --> 00:30:47,630
into the nucleus than it
is for the s orbital.

623
00:30:47,630 --> 00:30:50,510
But what's important is not
where that most probable

624
00:30:50,510 --> 00:30:52,810
radius is when we're talking
about the z effective it

625
00:30:52,810 --> 00:30:55,770
feels, what's more important
is how close the electron

626
00:30:55,770 --> 00:30:57,690
actually can get the nucleus.

627
00:30:57,690 --> 00:31:01,140
And for the s electron, since it
can get closer, what we're

628
00:31:01,140 --> 00:31:04,520
going to see is that s electrons
are actually less

629
00:31:04,520 --> 00:31:07,980
shielded than the corresponding
p electrons.

630
00:31:07,980 --> 00:31:10,630
They're less shielded because
they're closer to the nucleus,

631
00:31:10,630 --> 00:31:15,280
they feel a greater
z effective.

632
00:31:15,280 --> 00:31:18,420
We can see the same thing when
we compare p electrons to d

633
00:31:18,420 --> 00:31:20,220
electrons, or p and
d orbitals.

634
00:31:20,220 --> 00:31:24,450
I've drawn the 3 p and the 3 d
orbital here, and again, what

635
00:31:24,450 --> 00:31:27,260
you can see is that the p
electron are going to be able

636
00:31:27,260 --> 00:31:30,770
to penetrate closer to the
nucleus because of the fact

637
00:31:30,770 --> 00:31:33,810
that there's this bit of
probability density that's in

638
00:31:33,810 --> 00:31:35,960
significantly closer to
the nucleus than it

639
00:31:35,960 --> 00:31:38,810
is for the 3 d orbital.

640
00:31:38,810 --> 00:31:42,470
And if we go ahead and
superimpose the 3 s on top of

641
00:31:42,470 --> 00:31:46,060
the 3 p, you can see that the
3 s actually has some bit of

642
00:31:46,060 --> 00:31:49,400
probability density that gets
even closer to the nucleus

643
00:31:49,400 --> 00:31:51,010
than the 3 p did.

644
00:31:51,010 --> 00:31:53,840
So that's where that trend comes
from where the s orbital

645
00:31:53,840 --> 00:31:55,410
is lower than the d
orbital, which is

646
00:31:55,410 --> 00:31:59,800
lower than the d orbital.

647
00:31:59,800 --> 00:32:03,130
So now that we have this idea
of shielding and we can talk

648
00:32:03,130 --> 00:32:05,700
about the differences in
the radial probability

649
00:32:05,700 --> 00:32:09,130
distributions, we can consider
more completely why, for

650
00:32:09,130 --> 00:32:11,870
example, if we're talking about
lithium, we write the

651
00:32:11,870 --> 00:32:16,950
electron configuration as 1 s 2,
2 s 1, and we don't instead

652
00:32:16,950 --> 00:32:20,260
jump from the 1 s 2 all the
way to a p orbital.

653
00:32:20,260 --> 00:32:23,420
So the most basic answer that
doesn't explain why is just to

654
00:32:23,420 --> 00:32:26,340
say well, the s orbital is lower
in energy than the p

655
00:32:26,340 --> 00:32:29,180
orbital, but we now have a more
complete answer, so we

656
00:32:29,180 --> 00:32:32,850
can actually describe
why that is.

657
00:32:32,850 --> 00:32:35,100
And what we're actually
talking about

658
00:32:35,100 --> 00:32:37,020
again is the z effective.

659
00:32:37,020 --> 00:32:41,210
So that z effective felt by the
2 p is going to be less

660
00:32:41,210 --> 00:32:44,940
than the z effective
felt by the 2 s.

661
00:32:44,940 --> 00:32:48,210
And another way to say this, I
think it's easiest to look at

662
00:32:48,210 --> 00:32:50,760
just the fact that there's some
probability density very

663
00:32:50,760 --> 00:32:54,120
close the nucleus, but what we
can actually do is average the

664
00:32:54,120 --> 00:32:56,930
z effective over this entire
radial probability

665
00:32:56,930 --> 00:33:00,020
distribution, and when we find
that, we find that it does

666
00:33:00,020 --> 00:33:03,890
turn out that the average of the
z effective over the 2 p

667
00:33:03,890 --> 00:33:07,590
is going to be less than
that of the 2 s.

668
00:33:07,590 --> 00:33:10,590
So we know that we can relate
to z effective to the actual

669
00:33:10,590 --> 00:33:14,510
energy level of each of those
orbitals, and we can do that

670
00:33:14,510 --> 00:33:17,550
using this equation here where
it's negative z effective

671
00:33:17,550 --> 00:33:19,280
squared r h over n squared,
we're going to see

672
00:33:19,280 --> 00:33:20,720
that again and again.

673
00:33:20,720 --> 00:33:24,770
And it turns out that if we have
a, for example, for s, a

674
00:33:24,770 --> 00:33:28,670
very large z effective or larger
z effective than for 2

675
00:33:28,670 --> 00:33:32,880
p, and we plug in a large value
here in the numerator,

676
00:33:32,880 --> 00:33:34,760
that means we're going
to end up with a very

677
00:33:34,760 --> 00:33:36,530
large negative number.

678
00:33:36,530 --> 00:33:39,370
So in other words a very low
energy is what we're going to

679
00:33:39,370 --> 00:33:42,230
have when we talk about the
orbitals -- the energy of the

680
00:33:42,230 --> 00:33:44,720
2 s orbital is going
to be less than the

681
00:33:44,720 --> 00:33:46,920
energy of the 2 p orbital.

682
00:33:46,920 --> 00:33:49,460
Another way to say that it's
going to be less, so you don't

683
00:33:49,460 --> 00:33:51,980
get confused with that the fact
this is in the numerator

684
00:33:51,980 --> 00:33:54,900
here, there is that negative
sign so it's less energy but

685
00:33:54,900 --> 00:33:57,540
it's a bigger negative
number that gives us

686
00:33:57,540 --> 00:34:01,630
that less energy there.

687
00:34:01,630 --> 00:34:04,620
All right, so let's go back to
electrons configurations now

688
00:34:04,620 --> 00:34:09,160
that we have an idea of why the
orbitals are listed in the

689
00:34:09,160 --> 00:34:12,730
energy that they are listed
under, why, for example, the 2

690
00:34:12,730 --> 00:34:14,580
s is lower than the 2 p.

691
00:34:14,580 --> 00:34:18,270
So now we can go back and think
about filling in these

692
00:34:18,270 --> 00:34:20,890
electron configurations
for any atom.

693
00:34:20,890 --> 00:34:23,565
I think most and you are
familiar with the Aufbau or

694
00:34:23,565 --> 00:34:27,350
the building up principle, you
probably have seen it quite a

695
00:34:27,350 --> 00:34:29,730
bit in high school, and this is
the idea that we're filling

696
00:34:29,730 --> 00:34:33,440
up our energy states, again,
which depend on both n and l,

697
00:34:33,440 --> 00:34:36,440
one electron at a time starting
with that lowest

698
00:34:36,440 --> 00:34:38,890
energy and then working
our way up into

699
00:34:38,890 --> 00:34:41,750
higher and higher orbitals.

700
00:34:41,750 --> 00:34:44,630
And when we follow the Aufbau
principle, we have to follow

701
00:34:44,630 --> 00:34:45,560
two other rules.

702
00:34:45,560 --> 00:34:48,220
One is the Pauli exclusion
principal, we discussed this

703
00:34:48,220 --> 00:34:49,390
on Wednesday.

704
00:34:49,390 --> 00:34:52,780
So this is just the idea that
the most electrons that you

705
00:34:52,780 --> 00:34:54,520
can have in a single orbital
is two electrons.

706
00:34:54,520 --> 00:34:58,670
That makes sense because we
know that every single

707
00:34:58,670 --> 00:35:02,190
electron has to have its own
distinct set of four quantum

708
00:35:02,190 --> 00:35:05,340
numbers, the only way that we
can do that is to have a

709
00:35:05,340 --> 00:35:08,520
maximum of two spins in any
single orbital or two

710
00:35:08,520 --> 00:35:10,750
electrons per orbital.

711
00:35:10,750 --> 00:35:13,610
We also need to follow Hund's
rule, this is that a single

712
00:35:13,610 --> 00:35:16,100
electron enters each
state before it

713
00:35:16,100 --> 00:35:18,000
enters a second state.

714
00:35:18,000 --> 00:35:20,570
And by state we just mean
orbital, so if we're looking

715
00:35:20,570 --> 00:35:24,370
at the p orbitals here, that
means that a single electron

716
00:35:24,370 --> 00:35:27,930
goes in x, and then it will go
in the z orbital before a

717
00:35:27,930 --> 00:35:30,120
second one goes in
the x orbital.

718
00:35:30,120 --> 00:35:32,910
This intuitively should make a
lot of sense, because we know

719
00:35:32,910 --> 00:35:36,240
we're trying to minimize
electron repulsions to keep

720
00:35:36,240 --> 00:35:39,520
things in as low an energy state
as possible, so it makes

721
00:35:39,520 --> 00:35:43,240
sense that we would put one
electron in each orbital first

722
00:35:43,240 --> 00:35:46,390
before we double up
in any orbital.

723
00:35:46,390 --> 00:35:49,450
And the third fact that we need
to keep in mind is that

724
00:35:49,450 --> 00:35:53,210
spins remain parallel prior to
adding a second electron in

725
00:35:53,210 --> 00:35:54,780
any of the orbitals.

726
00:35:54,780 --> 00:35:57,450
So by parallel we mean they're
either both spin up or they're

727
00:35:57,450 --> 00:36:00,080
both spin down -- remember
that's our spin quantum

728
00:36:00,080 --> 00:36:02,020
number, that fourth
quantum number.

729
00:36:02,020 --> 00:36:04,120
And the reason for this comes
out of solving the

730
00:36:04,120 --> 00:36:06,610
relativistic version of the
Schrodinger equation, so

731
00:36:06,610 --> 00:36:09,260
unfortunately it's not as
intuitive as knowing that we

732
00:36:09,260 --> 00:36:12,630
want to fill separate before
we double up a degenerate

733
00:36:12,630 --> 00:36:16,450
orbital, but you just need to
keep this in mind and you need

734
00:36:16,450 --> 00:36:20,200
to just memorize the fact that
you need to be parallel before

735
00:36:20,200 --> 00:36:22,280
you double up in the orbital.

736
00:36:22,280 --> 00:36:24,510
So, we'll see how this
works in a second.

737
00:36:24,510 --> 00:36:29,020
So let's do this considering,
for example, what it would

738
00:36:29,020 --> 00:36:31,730
look like if we were to write
out the electron configuration

739
00:36:31,730 --> 00:36:34,980
for oxygen where z is going
to be equal to 8.

740
00:36:34,980 --> 00:36:37,510
So what we're doing is filling
in those eight electrons

741
00:36:37,510 --> 00:36:40,760
following the Aufbau principle,
so our first

742
00:36:40,760 --> 00:36:44,640
electron is going to go in the 1
s, and then we have no other

743
00:36:44,640 --> 00:36:47,540
options for other orbitals that
are at that same energy,

744
00:36:47,540 --> 00:36:50,690
so we put the second electron
in the 1 s as well.

745
00:36:50,690 --> 00:36:54,050
Then we go up to the 2 s, and we
have two electrons that we

746
00:36:54,050 --> 00:36:55,880
can fill in the 2 s.

747
00:36:55,880 --> 00:36:59,370
And now we get the p orbitals,
remember we want to fill up 1

748
00:36:59,370 --> 00:37:02,740
orbital at a time before we
double up, so we'll put one in

749
00:37:02,740 --> 00:37:08,000
the 2 p x, then one in the 2 p
z, and then one in the 2 p y.

750
00:37:08,000 --> 00:37:10,730
At this point, we have no other
choice but to double up

751
00:37:10,730 --> 00:37:13,860
before going to the next energy
level, so we'll put a

752
00:37:13,860 --> 00:37:15,650
second one in the 2 p x.

753
00:37:15,650 --> 00:37:18,760
And I arbitrarily chose to put
it in the 2 p x, we also could

754
00:37:18,760 --> 00:37:21,940
have put it in the 2 p y or the
2 p z, it doesn't matter

755
00:37:21,940 --> 00:37:24,750
where you double up, they're
all the same energy.

756
00:37:24,750 --> 00:37:27,940
So if we think about what we
would do to actually write out

757
00:37:27,940 --> 00:37:30,900
this configuration, we just
write the energy levels that

758
00:37:30,900 --> 00:37:34,940
we see here or the orbital
approximations.

759
00:37:34,940 --> 00:37:38,630
So if we're talking about
oxygen, we would say that it's

760
00:37:38,630 --> 00:37:45,240
1 s 2, then we have 2 s 2, and
then we have 2 p, and our

761
00:37:45,240 --> 00:37:49,320
total number of electrons in
the p orbitals are four.

762
00:37:49,320 --> 00:37:51,730
So it's OK to not specify.

763
00:37:51,730 --> 00:37:54,690
I want to point out, whether
you're in the p x, the p y, or

764
00:37:54,690 --> 00:37:58,550
the p z, unless a question
specifically asks you to

765
00:37:58,550 --> 00:38:02,310
specify the m sub l, which
occasionally will happen, but

766
00:38:02,310 --> 00:38:04,570
if it doesn't happen you just
write it like this.

767
00:38:04,570 --> 00:38:09,380
But if, in fact, you are asked
to specify the m sub l's, then

768
00:38:09,380 --> 00:38:11,730
we would have to write it out
more completely, which would

769
00:38:11,730 --> 00:38:19,950
be the 1 s 2, the 2 s 2, and
then we would say 2 p x 2, 2 p

770
00:38:19,950 --> 00:38:22,660
z 1, and 2 p y 1.

771
00:38:22,660 --> 00:38:29,380
So again, in general, just go
ahead and write it out like

772
00:38:29,380 --> 00:38:32,720
this, but if we do ask you to
specify you should be able to

773
00:38:32,720 --> 00:38:35,970
know that the p orbital
separates into these three --

774
00:38:35,970 --> 00:38:42,250
the p sub-shell separates into
these three orbitals.

775
00:38:42,250 --> 00:38:46,480
So let's do a clicker question
on assigning electron

776
00:38:46,480 --> 00:38:49,700
configurations using the
Aufbau principle.

777
00:38:49,700 --> 00:38:52,430
So why don't you go ahead and
identify the correct electron

778
00:38:52,430 --> 00:38:55,570
configuration for carbon,
and I'll tell you that z

779
00:38:55,570 --> 00:38:57,760
is equal to 6 here.

780
00:38:57,760 --> 00:39:01,230
And in terms of doing this for
your homework, I actually want

781
00:39:01,230 --> 00:39:04,160
to mention that in the back page
of your notes I attached

782
00:39:04,160 --> 00:39:06,530
a periodic table that does
not have electron

783
00:39:06,530 --> 00:39:08,040
configurations on them.

784
00:39:08,040 --> 00:39:10,570
It's better to practice doing
electron configurations when

785
00:39:10,570 --> 00:39:13,140
you cannot actually see the
electron configurations.

786
00:39:13,140 --> 00:39:15,490
And this is the same periodic
table that you're going to get

787
00:39:15,490 --> 00:39:17,650
in your exams, so it's good
to practice doing your

788
00:39:17,650 --> 00:39:20,330
problem-sets with that periodic
table so you're not

789
00:39:20,330 --> 00:39:22,860
relying on having the double
check right there of seeing

790
00:39:22,860 --> 00:39:24,920
what the electron configuration
is.

791
00:39:24,920 --> 00:39:39,700
So, let's do 10 seconds
on this problem here.

792
00:39:39,700 --> 00:39:40,370
OK, great.

793
00:39:40,370 --> 00:39:43,370
So this might be our best
clicker question yet.

794
00:39:43,370 --> 00:39:47,760
Most people were able to
identify the correct electron

795
00:39:47,760 --> 00:39:50,000
configuration here.

796
00:39:50,000 --> 00:39:52,990
Some people, the next most
popular answer with 5%, which

797
00:39:52,990 --> 00:39:56,790
is a nice low number, wanted to
put two in the 2 p x before

798
00:39:56,790 --> 00:39:57,820
they moved on.

799
00:39:57,820 --> 00:40:01,200
Remember we have to put one in
each degenerate orbital before

800
00:40:01,200 --> 00:40:04,490
we double up on any orbital, so
just keep that rule in mind

801
00:40:04,490 --> 00:40:07,320
that we would fill one in each
p orbital before we a to the

802
00:40:07,320 --> 00:40:07,820
second one.

803
00:40:07,820 --> 00:40:10,950
But it looks like you guys are
all experts here on doing

804
00:40:10,950 --> 00:40:12,820
these electron configurations.

805
00:40:12,820 --> 00:40:15,990
So, let's move on to some more
complicated electron

806
00:40:15,990 --> 00:40:17,290
configurations.

807
00:40:17,290 --> 00:40:19,990
So, for example, we can move
to the next periods in the

808
00:40:19,990 --> 00:40:21,190
periodic table.

809
00:40:21,190 --> 00:40:24,140
When we talk about a period,
we're just talking about that

810
00:40:24,140 --> 00:40:27,870
principle quantum number, so
period 2 means that we're

811
00:40:27,870 --> 00:40:31,420
talking about starting with
the 2 s orbitals, period 3

812
00:40:31,420 --> 00:40:34,000
starts with, what we're
now filling into the

813
00:40:34,000 --> 00:40:35,210
3 s orbitals here.

814
00:40:35,210 --> 00:40:38,310
So if we're talking about the
third period, that starts with

815
00:40:38,310 --> 00:40:41,080
sodium and it goes all
the way up to argon.

816
00:40:41,080 --> 00:40:43,550
So if we write the electron
configuration for sodium,

817
00:40:43,550 --> 00:40:46,140
which you can try later --
hopefully you would all get it

818
00:40:46,140 --> 00:40:49,250
correctly -- you see that this
is the electron configuration

819
00:40:49,250 --> 00:40:54,060
here, 1 s 2, 2 s 2, 2 p 6, and
now we're going into that

820
00:40:54,060 --> 00:40:57,750
third shell, 3 s 1.

821
00:40:57,750 --> 00:41:00,150
And I want to point out the
difference between core

822
00:41:00,150 --> 00:41:02,440
electrons and valence
electrons here.

823
00:41:02,440 --> 00:41:05,450
If we look at this
configuration, what we say is

824
00:41:05,450 --> 00:41:09,080
all of the electrons in these
inner shells are what we call

825
00:41:09,080 --> 00:41:10,750
core electrons.

826
00:41:10,750 --> 00:41:14,020
The core electrons tend not to
be involved in much chemistry

827
00:41:14,020 --> 00:41:15,980
in bonding or in reactions.

828
00:41:15,980 --> 00:41:19,190
They're very deep and held very
tightly to the nucleus,

829
00:41:19,190 --> 00:41:22,240
so we can often lump them
together, and instead of

830
00:41:22,240 --> 00:41:25,110
writing them all out separately,
we can just write

831
00:41:25,110 --> 00:41:28,440
the equivalent noble gas that
has that configuration.

832
00:41:28,440 --> 00:41:31,740
So, for example, for sodium, we
can instead write neon and

833
00:41:31,740 --> 00:41:33,690
then 3 s 1.

834
00:41:33,690 --> 00:41:36,980
So the 3 s 1, or any of the
other electrons that are in

835
00:41:36,980 --> 00:41:39,890
the outer-most shell, those are
what we call our valence

836
00:41:39,890 --> 00:41:43,300
electrons, and those are where
all the excitement happens.

837
00:41:43,300 --> 00:41:45,220
That's what we see are
involved in bonding.

838
00:41:45,220 --> 00:41:47,270
It makes sense, right, because
they're the furthest away from

839
00:41:47,270 --> 00:41:50,520
the nucleus, they're the ones
that are most willing to be

840
00:41:50,520 --> 00:41:54,160
involved in some chemistry or in
some bonding, or those are

841
00:41:54,160 --> 00:41:56,500
the orbitals that are most
likely to accept an electron

842
00:41:56,500 --> 00:41:59,130
from another atom,
for example.

843
00:41:59,130 --> 00:42:01,660
So the valence electrons, those
are the exciting ones.

844
00:42:01,660 --> 00:42:04,020
We want to make sure we
have a full picture of

845
00:42:04,020 --> 00:42:05,390
what's going on there.

846
00:42:05,390 --> 00:42:08,830
So, no matter whether or not
you write out the full form

847
00:42:08,830 --> 00:42:11,630
here, or the noble gas
configuration where you write

848
00:42:11,630 --> 00:42:14,950
ne first or whatever the
corresponding noble gas is to

849
00:42:14,950 --> 00:42:17,660
the core electrons, we always
write out the valence

850
00:42:17,660 --> 00:42:18,860
electrons here.

851
00:42:18,860 --> 00:42:23,310
So for sodium, again, we can
write n e and then 3 s 1.

852
00:42:23,310 --> 00:42:26,710
We can go all the way down,
magnesium, aluminum, all the

853
00:42:26,710 --> 00:42:30,980
way to this noble gas, argon,
which would be n e and then 3

854
00:42:30,980 --> 00:42:35,060
s 2, 3 p 6.

855
00:42:35,060 --> 00:42:37,990
Now we can think about the
fourth period, and the fourth

856
00:42:37,990 --> 00:42:41,130
period is where we start to run
into some exceptions, so

857
00:42:41,130 --> 00:42:43,390
this is where things get a teeny
bit more complicated,

858
00:42:43,390 --> 00:42:46,010
but you just need to remember
the exceptions and then you

859
00:42:46,010 --> 00:42:49,240
should be OK, no matter what
you're asked to write.

860
00:42:49,240 --> 00:42:52,910
So for the fourth period, now
we're into the 4 s 1 for

861
00:42:52,910 --> 00:42:54,070
potassium here.

862
00:42:54,070 --> 00:42:58,370
And what we notice when we get
to the third element in and

863
00:42:58,370 --> 00:43:02,450
the fourth period is that we go
4 s 2 and then we're back

864
00:43:02,450 --> 00:43:03,700
to the 3 d's.

865
00:43:03,700 --> 00:43:07,160
So if you look at the energy
diagram, what we see is that

866
00:43:07,160 --> 00:43:10,890
the 4 s orbitals are actually
just a teeny bit lower in

867
00:43:10,890 --> 00:43:14,330
energy -- they're just ever so
slightly lower in energy than

868
00:43:14,330 --> 00:43:15,830
the 3 d orbitals.

869
00:43:15,830 --> 00:43:18,760
You can see that as you fill up
your periodic table, it's

870
00:43:18,760 --> 00:43:19,800
very clear.

871
00:43:19,800 --> 00:43:22,910
But also we'll tell you a
pneumonic device to keep that

872
00:43:22,910 --> 00:43:24,870
in mind, so you always remember
and get the orbital

873
00:43:24,870 --> 00:43:26,100
energy straight.

874
00:43:26,100 --> 00:43:28,960
But it just turns out that the
4 s is so low in energy that

875
00:43:28,960 --> 00:43:32,060
it actually surpasses the 3 d,
because we know the 3 d is

876
00:43:32,060 --> 00:43:35,200
going to be pretty high in terms
of the three shell, and

877
00:43:35,200 --> 00:43:37,510
the 4 s is going to be the
lowest in terms of the 4

878
00:43:37,510 --> 00:43:40,590
shell, and it turns out that
we need to fill up the 4 s

879
00:43:40,590 --> 00:43:42,780
before we fill in the 3 d.

880
00:43:42,780 --> 00:43:46,690
And we can do that just going
along, 3 d 1, 2 3, and the

881
00:43:46,690 --> 00:43:49,700
problem comes when we get to
chromium here, which is

882
00:43:49,700 --> 00:43:53,030
instead of what we would expect,
we might expect to see

883
00:43:53,030 --> 00:43:55,980
4 s 2, 3 d 4.

884
00:43:55,980 --> 00:44:01,750
What we see is that instead
it's 4 s 1, and 3 d 5.

885
00:44:01,750 --> 00:44:03,610
So this is the first exception
that you need

886
00:44:03,610 --> 00:44:05,720
to the Aufbau principle.

887
00:44:05,720 --> 00:44:08,670
The reason this an exception is
because it turns out that

888
00:44:08,670 --> 00:44:11,680
half filled d orbitals
are more stable than

889
00:44:11,680 --> 00:44:13,550
we could even predict.

890
00:44:13,550 --> 00:44:16,250
You wouldn't be expected to be
able to guess that this would

891
00:44:16,250 --> 00:44:19,810
happen, because using any kind
of simple theory, we would, in

892
00:44:19,810 --> 00:44:22,680
fact, predict that this would
not be the case, but what we

893
00:44:22,680 --> 00:44:25,920
find experimentally is that it's
more stable to have half

894
00:44:25,920 --> 00:44:32,170
filled d orbital than to have
a 4 s 2, and a 3 d 4.

895
00:44:32,170 --> 00:44:34,250
So you're going to need to
remember, so this is an

896
00:44:34,250 --> 00:44:36,070
exception, you have
to memorize.

897
00:44:36,070 --> 00:44:39,030
Another exception in the fourth
period is in copper

898
00:44:39,030 --> 00:44:43,550
here, we see that again, we have
4 s 1 instead of 4 s 2.

899
00:44:43,550 --> 00:44:49,340
This is 4 s 1, 3 d 10, we might
expect 4 s 2, 3 d 9, but

900
00:44:49,340 --> 00:44:52,280
again, this exception comes
out of experimental

901
00:44:52,280 --> 00:44:56,290
observation, which is the fact
that full d orbitals also are

902
00:44:56,290 --> 00:45:00,160
lower in energy then we could
theoretically predict using

903
00:45:00,160 --> 00:45:01,830
simple calculations.

904
00:45:01,830 --> 00:45:04,930
So again, you need to memorize
these two exceptions, and the

905
00:45:04,930 --> 00:45:09,180
exception in general is that
filled d 10, or half-filled d

906
00:45:09,180 --> 00:45:13,690
5 orbitals are lower in energy
than would be expected, so we

907
00:45:13,690 --> 00:45:16,940
got this flip-flip where if we
can get to that half filled

908
00:45:16,940 --> 00:45:20,280
orbital by only removing one s
electron, then we're going to

909
00:45:20,280 --> 00:45:22,200
do it, and the same with
the filled d orbital.

910
00:45:22,200 --> 00:45:27,280
And actually, when we get to
the fifth period of the

911
00:45:27,280 --> 00:45:30,500
periodic table, that again takes
place, so when you get

912
00:45:30,500 --> 00:45:34,250
to a half filled, or a filled
d orbital, again you want to

913
00:45:34,250 --> 00:45:36,920
do it, so those exceptions would
be with molybdenum and

914
00:45:36,920 --> 00:45:40,220
silver would be the
corresponding elements in the

915
00:45:40,220 --> 00:45:42,780
fifth period where you're going
to see the same case

916
00:45:42,780 --> 00:45:46,310
here where it's lower in energy
to have the half filled

917
00:45:46,310 --> 00:45:49,490
or the filled d orbitals.

918
00:45:49,490 --> 00:45:52,190
So here's the pneumonic I
mentioned for writing the

919
00:45:52,190 --> 00:45:54,450
electron configuration and
getting those orbital energies

920
00:45:54,450 --> 00:45:55,540
in the right order.

921
00:45:55,540 --> 00:45:58,540
All you do is just write out
all the orbitals, the 1 s,

922
00:45:58,540 --> 00:46:02,120
then the 2 s 2 p 3, 3 s 3 p d,
just write them in a straight

923
00:46:02,120 --> 00:46:05,760
line like this, and then if you
draw diagonals down them,

924
00:46:05,760 --> 00:46:07,770
what you'll get is the
correct order in

925
00:46:07,770 --> 00:46:09,770
terms of orbital energies.

926
00:46:09,770 --> 00:46:12,810
So if we go down the diagonal,
we start with 1 s, then we get

927
00:46:12,810 --> 00:46:17,570
2 s, then 2 p and 3 s, then 3
p, and 4 s, and then that's

928
00:46:17,570 --> 00:46:20,300
how we see here that 4 s is
actually lower in energy than

929
00:46:20,300 --> 00:46:23,920
3 d, then 4 p, 5 s and so on.

930
00:46:23,920 --> 00:46:26,570
So if you want to on an exam,
you can just write this down

931
00:46:26,570 --> 00:46:29,520
quickly at the beginning and
refer to it as you're filling

932
00:46:29,520 --> 00:46:31,970
up your electron configurations,
but also if

933
00:46:31,970 --> 00:46:34,550
you look at the periodic table
it's very clear as you try to

934
00:46:34,550 --> 00:46:38,280
fill it up that way that the
same order comes out of that.

935
00:46:38,280 --> 00:46:40,710
So, whichever works best for
you can do in terms of

936
00:46:40,710 --> 00:46:44,300
figuring out electron
configurations.

937
00:46:44,300 --> 00:46:47,130
So the last thing I want to
mention today is how we can

938
00:46:47,130 --> 00:46:50,030
think about electron
configurations for ions.

939
00:46:50,030 --> 00:46:52,170
It turns out that it's going to
be a little bit different

940
00:46:52,170 --> 00:46:54,150
when we're talking about
positive ions here.

941
00:46:54,150 --> 00:46:57,320
We need to change our
rules just slightly.

942
00:46:57,320 --> 00:47:01,210
So what we know is that these
3 d orbitals are higher in

943
00:47:01,210 --> 00:47:03,970
energy than 4 s orbitals, so
I've written the energy of the

944
00:47:03,970 --> 00:47:07,960
orbital here for potassium
and for calcium.

945
00:47:07,960 --> 00:47:12,730
But what happens is that once a
d orbital is filled, I said

946
00:47:12,730 --> 00:47:15,480
the two are very close in
energy, and once a d orbital

947
00:47:15,480 --> 00:47:18,620
is filled, it actually drops to
become lower in energy than

948
00:47:18,620 --> 00:47:20,170
the 4 s orbital.

949
00:47:20,170 --> 00:47:24,360
So once we move past, we fill
the 4 s first, but once we

950
00:47:24,360 --> 00:47:26,720
fill in the d orbital,
now that's going

951
00:47:26,720 --> 00:47:28,440
to be lower in energy.

952
00:47:28,440 --> 00:47:30,620
So that doesn't make a
difference for us when we're

953
00:47:30,620 --> 00:47:34,650
talking about neutral atoms,
because we would fill up the 4

954
00:47:34,650 --> 00:47:37,860
s first, because that's lower
in energy until we fill it,

955
00:47:37,860 --> 00:47:39,520
and then we just keep going
with the d orbitals.

956
00:47:39,520 --> 00:47:42,740
So, for example, if we needed
to figure out the electron

957
00:47:42,740 --> 00:47:46,810
configuration for titanium, it
would just be argon then 4 s

958
00:47:46,810 --> 00:47:52,280
2, and then we would
fill in the 3 d 2.

959
00:47:52,280 --> 00:47:55,110
So, actually we don't have to
worry about this fact any time

960
00:47:55,110 --> 00:47:56,950
we're dealing with neutrals.

961
00:47:56,950 --> 00:47:59,820
The problem comes when instead
we're dealing with ions.

962
00:47:59,820 --> 00:48:02,770
So what I want to point out is
what we said now is that the 3

963
00:48:02,770 --> 00:48:05,240
d 2 is actually lower in energy,
so if we were to

964
00:48:05,240 --> 00:48:08,770
rewrite this in terms of what
the actual energy order is, we

965
00:48:08,770 --> 00:48:11,940
should instead write
it 3 d 2, 4 s 2.

966
00:48:11,940 --> 00:48:14,170
So you might ask in terms of
when you're writing electron

967
00:48:14,170 --> 00:48:16,400
configurations, which way
should you write it.

968
00:48:16,400 --> 00:48:18,380
And we'll absolutely
accept both answers

969
00:48:18,380 --> 00:48:19,580
for a neutral atom.

970
00:48:19,580 --> 00:48:20,480
They're both correct.

971
00:48:20,480 --> 00:48:24,080
In one case you decided to order
in terms of energy and

972
00:48:24,080 --> 00:48:27,080
in one case you decided
to order in terms of

973
00:48:27,080 --> 00:48:28,280
how it fills up.

974
00:48:28,280 --> 00:48:32,480
I don't care how you do it on
exams or on problem sets, but

975
00:48:32,480 --> 00:48:36,680
you do need to be aware that the
3 d once filled is lower

976
00:48:36,680 --> 00:48:40,580
in energy than the 4 s, and
the reason you need to be

977
00:48:40,580 --> 00:48:43,580
aware of that is if you're
asked for the electron

978
00:48:43,580 --> 00:48:45,380
configuration now of
the titanium ion.

979
00:48:45,380 --> 00:48:48,380
So, let's say we're asked
for the plus two ion.

980
00:48:48,380 --> 00:48:51,680
So a plus two ion means that
we're removing two electrons

981
00:48:51,680 --> 00:48:54,680
from the atom and the electrons
that we're going to

982
00:48:54,680 --> 00:48:57,680
remove are always going to be
the highest energy electrons.

983
00:48:57,680 --> 00:49:00,980
So it's good to write it like
this because this illustrates

984
00:49:00,980 --> 00:49:04,880
the fact that in fact the 4 s
electrons are the ones that

985
00:49:04,880 --> 00:49:06,080
are higher in energy.

986
00:49:06,080 --> 00:49:09,380
So the correct answer for
titanium plus two is going to

987
00:49:09,380 --> 00:49:13,280
be argon 3 d 2, whereas if we
did not rearrange our order

988
00:49:13,280 --> 00:49:17,180
here we might have been tempted
to write as 4 s 2 so

989
00:49:17,180 --> 00:49:20,480
keep that in mind when you're
doing the positive ions of

990
00:49:20,480 --> 00:49:22,880
corresponding atoms. Alright,
so we'll pick up with

991
00:49:22,880 --> 00:49:24,080
photoelectron spectroscopy
on Wednesday.

992
00:49:24,080 --> 00:49:26,230
Have a great weekend.