WEBVTT

00:00:00.030 --> 00:00:02.400
The following content is
provided under a Creative

00:00:02.400 --> 00:00:03.300
Commons license.

00:00:03.300 --> 00:00:05.650
Your supports will
help MIT OpenCourseWare

00:00:05.650 --> 00:00:09.760
continue to offer high quality
educational resources for free.

00:00:09.760 --> 00:00:12.355
To make a donation or to
view addional materials

00:00:12.355 --> 00:00:16.125
from hundreds of MIT courses
visit MIT OpenCourseWare

00:00:16.125 --> 00:00:16.920
at ocw.mit.edu.

00:00:20.040 --> 00:00:22.600
CATHERINE DRENNAN: We gotta move
up to the next lowest energy

00:00:22.600 --> 00:00:26.958
orbital, which we'll
also talk about today.

00:00:26.958 --> 00:00:28.530
All right.

00:00:28.530 --> 00:00:33.950
So that kind of completes
our one electron systems,

00:00:33.950 --> 00:00:36.912
and now we're gonna talk
about multi-electrons.

00:00:36.912 --> 00:00:39.900
But we're not going to move
far away from the topics

00:00:39.900 --> 00:00:43.170
that we've discussed because
with multi-electrons there

00:00:43.170 --> 00:00:46.592
are several things that are
the same and some things that

00:00:46.592 --> 00:00:47.175
are different.

00:00:47.175 --> 00:00:48.550
But a lot of things
are the same,

00:00:48.550 --> 00:00:51.230
so we're going to come
back to radial probability

00:00:51.230 --> 00:00:55.260
distributions and energy
levels and things like that.

00:00:55.260 --> 00:00:56.760
So we'll move on
to today's handout.

00:01:00.030 --> 00:01:03.420
So similarities and differences.

00:01:03.420 --> 00:01:04.617
Similarities.

00:01:04.617 --> 00:01:07.280
We have the same
shapes of orbitals,

00:01:07.280 --> 00:01:10.450
whether we're talking about a
one electron system or more.

00:01:10.450 --> 00:01:14.240
So again, we're gonna
have our s orbital.

00:01:14.240 --> 00:01:17.250
So this is my version
of an s orbital

00:01:17.250 --> 00:01:20.800
that you can hold in your hand,
where you have it spherically

00:01:20.800 --> 00:01:24.210
symmetric and you
have probability out

00:01:24.210 --> 00:01:28.710
in very direction of r that
you might find an electron,

00:01:28.710 --> 00:01:30.720
except at our radial nodes.

00:01:30.720 --> 00:01:33.770
And then we have our
p orbitals, which

00:01:33.770 --> 00:01:37.100
can be in three different
directions, where

00:01:37.100 --> 00:01:38.280
you have nodal planes.

00:01:38.280 --> 00:01:41.620
So it doesn't matter what you're
talking about-- one electron

00:01:41.620 --> 00:01:43.130
system or more--
you still are going

00:01:43.130 --> 00:01:47.211
to have those same shapes
of the wave functions.

00:01:47.211 --> 00:01:51.350
Other similarities again
include the nodal structure,

00:01:51.350 --> 00:01:52.490
which I just mentioned.

00:01:52.490 --> 00:01:55.380
Whether s is always going to
be spherically symmetrical.

00:01:55.380 --> 00:01:58.675
p is gonna have
those nodal planes.

00:01:58.675 --> 00:02:00.500
The angular nodal planes.

00:02:00.500 --> 00:02:02.910
So that's the same.

00:02:02.910 --> 00:02:07.100
Differences, though, have to
do with the energy levels.

00:02:07.100 --> 00:02:09.959
So orbitals in a
multi-electron atoms

00:02:09.959 --> 00:02:12.400
are lower-- more
negative-- in energy

00:02:12.400 --> 00:02:17.670
than their corresponding
orbitals in the H atom.

00:02:17.670 --> 00:02:22.472
So let's take a look at this and
think about why this is true.

00:02:22.472 --> 00:02:25.590
So here we have our
friend the hydrogen atom.

00:02:25.590 --> 00:02:27.900
It has a small Z. Z equals 1.

00:02:27.900 --> 00:02:29.285
Doesn't get smaller than that.

00:02:29.285 --> 00:02:31.040
We have our 1s.

00:02:31.040 --> 00:02:33.350
Then we have our n equals 2.

00:02:33.350 --> 00:02:36.545
And we talked about the
fact that in a 1 electron

00:02:36.545 --> 00:02:39.480
system like hydrogen--
these are all

00:02:39.480 --> 00:02:42.350
degenerate in energy with
respect to each other,

00:02:42.350 --> 00:02:44.370
so they're all equal in energy.

00:02:44.370 --> 00:02:46.200
And then we have our n equals 3.

00:02:46.200 --> 00:02:50.810
Again, degenerate energy
levels and n equals 4 up here.

00:02:50.810 --> 00:02:53.760
But when you go to a
multi-electron system,

00:02:53.760 --> 00:02:56.395
the first thing
that I'll point out

00:02:56.395 --> 00:02:58.820
is that the energy
level is lower.

00:02:58.820 --> 00:03:00.570
So we have 1s over here.

00:03:00.570 --> 00:03:04.325
Now 1s is a more
negative lower number.

00:03:04.325 --> 00:03:07.960
And we can think about this in
multi-electron systems-- you

00:03:07.960 --> 00:03:11.995
have a bigger Z. So you
have more positive charge

00:03:11.995 --> 00:03:16.820
and it's kind of hauling all
of those energy levels closer.

00:03:16.820 --> 00:03:20.760
So it's a lower energy
for all of those.

00:03:20.760 --> 00:03:25.310
So 1s, again, lower,
and we have 2s.

00:03:25.310 --> 00:03:28.310
Again, that's lower in energy.

00:03:28.310 --> 00:03:32.620
And now importantly,
2s and 2p are no longer

00:03:32.620 --> 00:03:35.610
degenerate with respect
to each other in energy.

00:03:35.610 --> 00:03:40.300
So now the 2p system is
higher in energy than the 1s

00:03:40.300 --> 00:03:41.310
and so on.

00:03:41.310 --> 00:03:46.416
So we have 3s down
here and then the 3p's.

00:03:46.416 --> 00:03:52.660
So compared to hydrogen
in a multi-electron atom,

00:03:52.660 --> 00:03:57.690
n is not the sole determinate
of what the energy levels are.

00:03:57.690 --> 00:04:02.090
Now, instead of just
n we have n and l.

00:04:05.145 --> 00:04:06.565
So let's review.

00:04:06.565 --> 00:04:07.810
This is good.

00:04:07.810 --> 00:04:09.650
This is all getting
ready for the test.

00:04:09.650 --> 00:04:12.505
Some equations that
you've seen before.

00:04:12.505 --> 00:04:16.490
And again, equations will
be on the equations sheet.

00:04:16.490 --> 00:04:18.379
You don't have to memorize them.

00:04:18.379 --> 00:04:20.649
And the equation
sheet for the exam

00:04:20.649 --> 00:04:23.880
is handed out today, so
you can take a look a it

00:04:23.880 --> 00:04:25.050
and see where things are.

00:04:25.050 --> 00:04:27.635
If I forgot anything
you can ask me questions

00:04:27.635 --> 00:04:30.660
and maybe we'll add some
more if I forgot any ones.

00:04:30.660 --> 00:04:34.700
So for a one electron
system, binding energy

00:04:34.700 --> 00:04:40.250
equals minus the ionization
energy equals minus Z squared

00:04:40.250 --> 00:04:43.912
RH, the Rydberg
constant, over N squared.

00:04:43.912 --> 00:04:48.550
And so for hydrogens Z is 1,
but there are other 1 electron

00:04:48.550 --> 00:04:53.950
at least ions and then
you have to worry about Z.

00:04:53.950 --> 00:04:57.400
What about a
multi-electron system?

00:04:57.400 --> 00:05:01.500
Looks pretty much the same, but
now instead of just having n we

00:05:01.500 --> 00:05:06.250
have n and l because l matters
with a multi-electron system.

00:05:06.250 --> 00:05:09.130
So the binding energy
for the electron

00:05:09.130 --> 00:05:11.237
is minus the ionization
energy-- that's always

00:05:11.237 --> 00:05:12.320
going to [INAUDIBLE] true.

00:05:12.320 --> 00:05:13.990
The binding energy
is always going

00:05:13.990 --> 00:05:16.720
to be equal to minus the
ionization energy, which

00:05:16.720 --> 00:05:19.790
is equal to minus
Z. But now we have

00:05:19.790 --> 00:05:23.630
a different Z. We
have Z effective,

00:05:23.630 --> 00:05:27.910
which is abbreviated Z eff.

00:05:27.910 --> 00:05:32.940
So this is the effective
charge, not the actual charge.

00:05:32.940 --> 00:05:34.350
And that's squared.

00:05:34.350 --> 00:05:37.660
And then we have Rydberg
constant and n again.

00:05:37.660 --> 00:05:43.230
So Z effective is
not the same as Z,

00:05:43.230 --> 00:05:48.010
and it's not the same
Z because of shielding.

00:05:48.010 --> 00:05:49.800
So we talked about
shielding a little bit,

00:05:49.800 --> 00:05:51.684
and I made this
point that you need

00:05:51.684 --> 00:05:53.600
to think about shielding
a little differently.

00:05:53.600 --> 00:05:58.820
It's not just about the
average size of the orbital.

00:05:58.820 --> 00:06:01.960
It's more about the
likelihood-- the probability--

00:06:01.960 --> 00:06:03.750
that they're going
to be electrons close

00:06:03.750 --> 00:06:07.140
to the nucleus that will
participate in-- that

00:06:07.140 --> 00:06:09.660
will be affected by shielding.

00:06:09.660 --> 00:06:12.180
So let's look at
some extreme cases

00:06:12.180 --> 00:06:15.410
now and think about
what's happening

00:06:15.410 --> 00:06:18.600
in terms of this shielding.

00:06:18.600 --> 00:06:20.140
So extreme case one.

00:06:20.140 --> 00:06:21.770
Extreme shielding.

00:06:21.770 --> 00:06:23.947
Maximum shielding.

00:06:23.947 --> 00:06:24.780
So we have the case.

00:06:24.780 --> 00:06:26.270
We have the helium nucleus.

00:06:26.270 --> 00:06:28.280
We have moved far in
the periodic table.

00:06:28.280 --> 00:06:31.740
We've left hydrogen. And
so what is the charge going

00:06:31.740 --> 00:06:36.370
to be on helium nucleus?

00:06:36.370 --> 00:06:37.910
Plus 2.

00:06:37.910 --> 00:06:39.820
So now we have
this electron one.

00:06:39.820 --> 00:06:42.140
We're interested in how
much this electron is

00:06:42.140 --> 00:06:46.830
shielded by electron two
because we've got two electrons.

00:06:46.830 --> 00:06:50.170
Now say electron two
is close to the nucleus

00:06:50.170 --> 00:06:53.700
and it's maximally
shielding electron one

00:06:53.700 --> 00:06:56.620
from this positive
charge down here.

00:06:56.620 --> 00:06:58.340
So think about this electron.

00:06:58.340 --> 00:07:01.450
I like to think about
this electron two

00:07:01.450 --> 00:07:05.300
as kind of the
elasti-girl of electrons.

00:07:05.300 --> 00:07:08.600
So elasti-girl electron
is shielding everywhere,

00:07:08.600 --> 00:07:12.350
stretching everywhere
around that nucleus.

00:07:12.350 --> 00:07:15.800
Just completely shielding
it from electron

00:07:15.800 --> 00:07:21.720
one, using the full negative
charge to really shield.

00:07:21.720 --> 00:07:29.390
So in that kind of exaggerated
case, the Z effective is not 2.

00:07:29.390 --> 00:07:30.520
It's 1.

00:07:30.520 --> 00:07:33.330
So this electron
basically cancels

00:07:33.330 --> 00:07:36.480
the whole positive
charge of this nucleus.

00:07:36.480 --> 00:07:38.890
Really shields that away.

00:07:38.890 --> 00:07:42.740
And so this is the effective
charge with total shielding.

00:07:42.740 --> 00:07:46.350
Maximal shielding
that you can get.

00:07:46.350 --> 00:07:52.310
So now we can calculate what
the binding energy-- or if we

00:07:52.310 --> 00:07:55.290
wanted, what the
ionization energy would

00:07:55.290 --> 00:08:01.180
be for this case, given that
particular effective charge.

00:08:01.180 --> 00:08:03.970
So again, the binding
energy of electron one

00:08:03.970 --> 00:08:08.700
is equal to minus its ionization
energy equal to minus the Z

00:08:08.700 --> 00:08:12.780
effective squared
R H over n squared.

00:08:12.780 --> 00:08:14.670
And we can plug
in those numbers.

00:08:14.670 --> 00:08:16.040
Don't forget the minus.

00:08:16.040 --> 00:08:22.540
We can have Z effective 1 over
1 and we calculate this value,

00:08:22.540 --> 00:08:24.990
which is, of course,
just the Rydberg constant

00:08:24.990 --> 00:08:29.880
or minus the Rydberg
constant minus 2.18 times 10

00:08:29.880 --> 00:08:32.020
to the minus 18th joules.

00:08:32.020 --> 00:08:35.980
So this is just like
it was a hydrogen atom.

00:08:35.980 --> 00:08:37.720
A one electron system.

00:08:37.720 --> 00:08:41.620
So it had two electrons but
one of the electron shielded

00:08:41.620 --> 00:08:45.660
so completely it was like
a one electron system.

00:08:45.660 --> 00:08:50.540
Again, this is an exaggerated
case of total shielding.

00:08:50.540 --> 00:08:53.840
So now let's go to
the other extreme

00:08:53.840 --> 00:08:56.720
and consider zero shielding.

00:08:56.720 --> 00:08:59.150
No shielding at all.

00:08:59.150 --> 00:09:01.630
So here we have
the helium nucleus.

00:09:01.630 --> 00:09:04.330
We have electron
one is now close

00:09:04.330 --> 00:09:07.570
and electron two
is pretty far away.

00:09:07.570 --> 00:09:11.800
So again, we're asking, how
much is this electron one going

00:09:11.800 --> 00:09:14.840
to shielded by electron two?

00:09:14.840 --> 00:09:19.180
And in this extreme
scenario, electron two

00:09:19.180 --> 00:09:22.150
is not participating
in shielding at all.

00:09:22.150 --> 00:09:23.470
It's far away.

00:09:23.470 --> 00:09:25.310
I'm not sure what it's doing.

00:09:25.310 --> 00:09:27.706
Maybe it lost its super
suit and can't find it.

00:09:27.706 --> 00:09:29.080
It might be at
the dry cleaner's.

00:09:29.080 --> 00:09:30.610
We don't know what's going on.

00:09:30.610 --> 00:09:33.040
In any case, it is
out of the game.

00:09:33.040 --> 00:09:34.410
It is not involved.

00:09:34.410 --> 00:09:38.730
It is not shielding at all.

00:09:38.730 --> 00:09:42.940
So in this extreme
case, electron one

00:09:42.940 --> 00:09:46.810
feels that full
force of the nucleus.

00:09:46.810 --> 00:09:52.720
So its effective charge is
the full complete plus 2.

00:09:52.720 --> 00:09:57.040
So we can plug that
in now and calculate

00:09:57.040 --> 00:09:59.330
what the binding
energy is going to be.

00:09:59.330 --> 00:10:01.620
Again, binding energy
for electron one

00:10:01.620 --> 00:10:05.290
equals minus the ionization
energy for this electron.

00:10:05.290 --> 00:10:06.730
Same equation.

00:10:06.730 --> 00:10:11.130
We put this in but now
the Z effective is 2

00:10:11.130 --> 00:10:13.690
and we can calculate that.

00:10:13.690 --> 00:10:17.710
And now we get a value
of minus 8.72 times 10

00:10:17.710 --> 00:10:20.250
to the minus 18th joules.

00:10:20.250 --> 00:10:22.940
And this is actually
the same as you

00:10:22.940 --> 00:10:27.840
would get for the scenario
of helium plus, which

00:10:27.840 --> 00:10:30.590
is a one electron system.

00:10:30.590 --> 00:10:32.810
Then, in a one
electron system you

00:10:32.810 --> 00:10:36.080
can use a formula of
just Z where Z is 2

00:10:36.080 --> 00:10:37.770
and get your value.

00:10:37.770 --> 00:10:40.510
So here are the two
extreme cases for helium.

00:10:40.510 --> 00:10:44.200
One it's like a hydrogen atom
one electron system, and one

00:10:44.200 --> 00:10:45.320
it's like helium plus.

00:10:45.320 --> 00:10:48.060
And one case is like it
just has one electron,

00:10:48.060 --> 00:10:52.520
and in the other case
you have zero shielding.

00:10:52.520 --> 00:10:57.090
So extreme case one
the Z effective is 1,

00:10:57.090 --> 00:10:59.430
and we have the
binding energy that's

00:10:59.430 --> 00:11:04.680
very similar to hydrogen. And so
this is a total shielding case.

00:11:04.680 --> 00:11:09.110
It's shields so much it's
like a one electron case.

00:11:09.110 --> 00:11:12.250
Extreme case two you
have the full force.

00:11:12.250 --> 00:11:13.540
So there's zero shielding.

00:11:13.540 --> 00:11:15.190
No shielding at all.

00:11:15.190 --> 00:11:19.090
And then, this is
like helium plus case

00:11:19.090 --> 00:11:21.509
where you've actually
lost that other electron.

00:11:21.509 --> 00:11:22.300
It's not shielding.

00:11:22.300 --> 00:11:24.060
It's not even there.

00:11:24.060 --> 00:11:26.150
So no shielding.

00:11:26.150 --> 00:11:30.900
And the reality in most cases
is that you're in between,

00:11:30.900 --> 00:11:33.720
and you can determine
this experimentally.

00:11:33.720 --> 00:11:37.070
You can measure
ionization energies.

00:11:37.070 --> 00:11:40.720
So if we measured the
ionization energy for helium

00:11:40.720 --> 00:11:46.200
we would find that it's 3.94
times 10 to the minus 18th.

00:11:46.200 --> 00:11:53.130
So it's greater than the
2.18 and less than the 8.72.

00:11:53.130 --> 00:11:57.450
So it's in between, and that's
what you find most of the time.

00:11:57.450 --> 00:12:00.692
The Z effective is in
between zero shielding

00:12:00.692 --> 00:12:01.525
and total shielding.

00:12:04.030 --> 00:12:08.920
So we can calculate what
the Z effective is actually

00:12:08.920 --> 00:12:12.970
in this case if we know
the ionization energy.

00:12:12.970 --> 00:12:15.800
So if you know the
ionization energy

00:12:15.800 --> 00:12:17.770
you can calculate
the Z effective,

00:12:17.770 --> 00:12:19.700
or if you're given
a Z effective you

00:12:19.700 --> 00:12:21.820
can calculate what
the ionization

00:12:21.820 --> 00:12:24.100
energy should be for that case.

00:12:24.100 --> 00:12:29.160
And so I told you that it
was measured at 3.94 times 10

00:12:29.160 --> 00:12:31.030
to the minus 18th.

00:12:31.030 --> 00:12:33.820
And so in that case
the Z effective,

00:12:33.820 --> 00:12:40.040
if you plug the numbers
in would be 1.34.

00:12:40.040 --> 00:12:44.870
And so this number is in fact
in between the two cases.

00:12:44.870 --> 00:12:49.960
With total shielding you
would have a Z effective of 1

00:12:49.960 --> 00:12:53.280
and with no shielding you
have a Z effective of 2.

00:12:53.280 --> 00:12:55.180
And so in reality,
we're somewhere

00:12:55.180 --> 00:12:58.740
in between in this case.

00:12:58.740 --> 00:13:02.200
So thinking about this
now, let's try your hand

00:13:02.200 --> 00:13:05.320
at a clicker question and
see if you can tell me

00:13:05.320 --> 00:13:11.680
which of these is a possible
Z effective for an element

00:13:11.680 --> 00:13:12.917
with a Z equals 3.

00:13:40.164 --> 00:13:41.655
I'm doing good time wise.

00:14:18.381 --> 00:14:18.880
OK.

00:14:18.880 --> 00:14:19.546
10 more seconds.

00:14:39.520 --> 00:14:44.060
So does someone want to say why
the other ones are not correct?

00:14:44.060 --> 00:14:47.500
Why don't you run up there and
you can give them this pen?

00:14:47.500 --> 00:14:49.400
American Chemical Society pen.

00:14:49.400 --> 00:14:50.230
Hand up there.

00:14:54.600 --> 00:14:56.442
AUDIENCE: Who had their hand up?

00:14:56.442 --> 00:14:57.900
CATHERINE DRENNAN:
I think it's on.

00:15:01.100 --> 00:15:02.860
AUDIENCE: So in the
case of no shielding

00:15:02.860 --> 00:15:06.420
the charge should be 3, and in
the case of maximum shielding

00:15:06.420 --> 00:15:08.750
there's only two electrons
in the 1s so it would be 1.

00:15:08.750 --> 00:15:11.430
So anything below 1 would
be beyond maximum shielding,

00:15:11.430 --> 00:15:13.120
so it's gotta be
between 1 and 3.

00:15:13.120 --> 00:15:14.703
CATHERINE DRENNAN:
Yeah, that's right.

00:15:18.410 --> 00:15:21.580
So now we're going
to talk more about

00:15:21.580 --> 00:15:24.900
why shielding is important.

00:15:24.900 --> 00:15:29.260
And shielding really has
to do with this order

00:15:29.260 --> 00:15:37.250
of orbital energy that we all
know and are very fond of.

00:15:37.250 --> 00:15:40.040
So when I show you this we
want to ask the question,

00:15:40.040 --> 00:15:45.060
why is 2s lower than
2p or 3s lower than 3p?

00:15:48.130 --> 00:15:49.850
So let's take a look
at this, and we're

00:15:49.850 --> 00:15:52.385
going to go back to our radial
probability distribution.

00:15:52.385 --> 00:15:54.510
I told you I wasn't going
to leave it for very long

00:15:54.510 --> 00:15:57.680
and we're back again.

00:15:57.680 --> 00:16:01.410
So here, again, if we're
considering 2s and 2p--

00:16:01.410 --> 00:16:04.020
so we'll consider
this case here--

00:16:04.020 --> 00:16:08.050
the maximum probable
radius is longer.

00:16:08.050 --> 00:16:11.530
It's greater for 2s than for 2p.

00:16:11.530 --> 00:16:13.190
But what we really
care about when

00:16:13.190 --> 00:16:17.262
we're talking about shielding
is this part right here.

00:16:17.262 --> 00:16:19.470
And so there are different
ways you can express this.

00:16:19.470 --> 00:16:22.200
You can say that the electrons
in the orbital with lower

00:16:22.200 --> 00:16:26.780
values of l, like 2s
is lower than 2p--

00:16:26.780 --> 00:16:30.250
those electrons penetrate
closer to the nucleus,

00:16:30.250 --> 00:16:35.030
even though we have this trend
where the radius decreases

00:16:35.030 --> 00:16:36.250
with increasing l.

00:16:36.250 --> 00:16:39.340
So despite this size
difference, when

00:16:39.340 --> 00:16:42.570
you compare this dotted
line with this line here,

00:16:42.570 --> 00:16:44.150
there's more
probability that they're

00:16:44.150 --> 00:16:47.570
going to be electrons
near the nucleus with 2s.

00:16:47.570 --> 00:16:52.030
And that results in
this lower energy.

00:16:52.030 --> 00:16:55.940
So there's less shielding
for the s orbitals

00:16:55.940 --> 00:16:58.090
than for the p orbitals.

00:16:58.090 --> 00:17:00.880
And as a result of that,
with less shielding

00:17:00.880 --> 00:17:04.359
because their probability
is that they're closer,

00:17:04.359 --> 00:17:07.859
that they're bound more tightly,
you have this lower energy.

00:17:07.859 --> 00:17:12.130
So that explains this
energy difference.

00:17:12.130 --> 00:17:14.849
So we can look at this
now for the three system

00:17:14.849 --> 00:17:17.319
again for n equals 3.

00:17:17.319 --> 00:17:21.810
And here we see that p
electrons are also less shielded

00:17:21.810 --> 00:17:25.579
than the d electrons,
despite the fact if you look

00:17:25.579 --> 00:17:30.890
that the most probable radius
over here is longer for p

00:17:30.890 --> 00:17:32.120
than for d.

00:17:32.120 --> 00:17:36.120
But now, if we look near the
nucleus at the probability

00:17:36.120 --> 00:17:39.022
that they're going to be
electrons near the nucleus,

00:17:39.022 --> 00:17:40.730
there's a higher
probability that they'll

00:17:40.730 --> 00:17:44.690
be electrons near the
nucleus with p than with d.

00:17:44.690 --> 00:17:49.380
So these are going to be less
shielded and lower in energy.

00:17:49.380 --> 00:17:52.940
And if I throw s
on there now we see

00:17:52.940 --> 00:17:56.320
s has the most probability
here of being closer.

00:17:56.320 --> 00:17:58.592
Then p then d.

00:17:58.592 --> 00:18:03.660
So for a multi-electron
atom, the order of energy--

00:18:03.660 --> 00:18:09.080
we have s lower than p, p lower
than d, d lower than f due

00:18:09.080 --> 00:18:11.000
to this shielding.

00:18:11.000 --> 00:18:15.390
So again, we want
to be able to draw

00:18:15.390 --> 00:18:19.070
some version of these diagrams
with appropriate features

00:18:19.070 --> 00:18:22.360
to explain answers.

00:18:22.360 --> 00:18:24.600
And this all leads
into what we're

00:18:24.600 --> 00:18:28.686
doing next, which is
electron configurations.

00:18:28.686 --> 00:18:30.060
So we're going to
think about how

00:18:30.060 --> 00:18:32.590
we're going to write the
electron configurations

00:18:32.590 --> 00:18:38.140
and this indicates how
you build up in energy.

00:18:38.140 --> 00:18:40.006
So electron configurations.

00:18:43.160 --> 00:18:50.210
So first, we're going to fill
our electrons in to the energy

00:18:50.210 --> 00:18:51.770
states that are our lowest.

00:18:51.770 --> 00:18:53.440
Nature doesn't want
to do a lot of work,

00:18:53.440 --> 00:18:56.030
so it's going to put
them in the lower states.

00:18:56.030 --> 00:18:59.260
And again, where those
energy levels are

00:18:59.260 --> 00:19:04.930
depends on, for multi-electron
atoms, both n and l

00:19:04.930 --> 00:19:08.300
And we're going to put them
in one electron at a time,

00:19:08.300 --> 00:19:10.690
starting with the
lowest energy state

00:19:10.690 --> 00:19:12.860
and heading the following rules.

00:19:12.860 --> 00:19:16.380
So there are some rules in
doing this, and most of you

00:19:16.380 --> 00:19:18.550
have probably heard
some of these before.

00:19:18.550 --> 00:19:20.442
And if you haven't I'm
sure you'll like them.

00:19:20.442 --> 00:19:22.650
I know you heard this because
I already just told you

00:19:22.650 --> 00:19:24.120
about that a few minutes ago.

00:19:24.120 --> 00:19:26.440
We have Pauli's
Exclusion Principle,

00:19:26.440 --> 00:19:30.050
which says that you can't have
the same four quantum numbers.

00:19:30.050 --> 00:19:34.240
So if you put one electron in
and it's spin up the next one

00:19:34.240 --> 00:19:37.360
has to be spin down.

00:19:37.360 --> 00:19:41.950
And Hund's Rule, which is one of
my favorite rules in chemistry,

00:19:41.950 --> 00:19:46.060
and that is when you're adding
electrons to the same state

00:19:46.060 --> 00:19:48.300
you're going to put them
in singly, when there's

00:19:48.300 --> 00:19:52.590
degenerate energy orbitals,
before a second one enters

00:19:52.590 --> 00:19:53.870
the same orbital.

00:19:53.870 --> 00:19:58.130
And the spins remain parallel
as you're adding them across.

00:19:58.130 --> 00:20:02.370
So let's consider these and
put some electrons into these.

00:20:02.370 --> 00:20:07.360
And we'll do this for oxygen,
which is a Z equals 8 system.

00:20:07.360 --> 00:20:11.140
So first, I want to put them
in the lowest energy state.

00:20:11.140 --> 00:20:12.960
So that's 1s.

00:20:12.960 --> 00:20:15.700
So I'll put one
electron in there.

00:20:15.700 --> 00:20:17.990
And then I'm going to put
the second electron in there

00:20:17.990 --> 00:20:21.070
because it's the
lowest energy state,

00:20:21.070 --> 00:20:22.410
so I'm going to fill it up.

00:20:22.410 --> 00:20:25.930
But I'm going to pay attention
to Pauli's Exclusion Principle

00:20:25.930 --> 00:20:27.790
and put it in spin down.

00:20:27.790 --> 00:20:28.980
One electron spin up.

00:20:28.980 --> 00:20:30.460
One electron spin down.

00:20:30.460 --> 00:20:32.670
I can't put them both
spin up because they would

00:20:32.670 --> 00:20:34.590
have the same four
quantum numbers,

00:20:34.590 --> 00:20:38.430
and that would violate
Pauli's Exclusion Principle.

00:20:38.430 --> 00:20:41.510
So next I'm going to put
electrons in 2s because that's

00:20:41.510 --> 00:20:44.150
the next lowest energy state.

00:20:44.150 --> 00:20:46.900
I'll put one in spin up.

00:20:46.900 --> 00:20:52.250
And then, because of Pauli, I'll
put the other one in spin down.

00:20:52.250 --> 00:20:55.100
Next, we come to the 2p system.

00:20:55.100 --> 00:20:57.770
And I'm going to put
the first electron in,

00:20:57.770 --> 00:21:00.240
but I'm not going to
pair the second one.

00:21:00.240 --> 00:21:04.300
I'm going to put electron
in the second orbital, both

00:21:04.300 --> 00:21:06.540
being spin up.

00:21:06.540 --> 00:21:08.370
And then I'm going
to do that again.

00:21:11.250 --> 00:21:13.130
Most people kind of
refer to the Hund's Rule

00:21:13.130 --> 00:21:16.740
as kind of the rule
of seating on a bus,

00:21:16.740 --> 00:21:19.190
where it always seems
that one person goes in--

00:21:19.190 --> 00:21:21.830
and even though there are two
seats, one person takes it.

00:21:21.830 --> 00:21:23.580
The next person gets on the bus.

00:21:23.580 --> 00:21:26.530
Doesn't sit next to the
person who's already there.

00:21:26.530 --> 00:21:29.440
They take another empty
seat and so on and so on.

00:21:29.440 --> 00:21:33.830
And so you fill up the bus
with one person per bench

00:21:33.830 --> 00:21:36.240
before all those
seats are taken.

00:21:36.240 --> 00:21:37.490
Then the next person comes on.

00:21:37.490 --> 00:21:40.030
Sadly has to sit
with someone else.

00:21:40.030 --> 00:21:42.710
So if you think about that,
that's the Hund's Rule.

00:21:42.710 --> 00:21:44.850
You'll always
remember to do that.

00:21:44.850 --> 00:21:48.970
And once you put one in each,
then the next person on the bus

00:21:48.970 --> 00:21:51.360
has to sit next to
someone and they're

00:21:51.360 --> 00:21:54.360
going to do that spin down.

00:21:54.360 --> 00:21:56.210
Because if it was
spin up again you'd

00:21:56.210 --> 00:21:59.990
have the same four
quantum numbers.

00:21:59.990 --> 00:22:03.210
So these are the rules that you
need to know to put these in.

00:22:03.210 --> 00:22:06.730
And then, after you do that
you can write an electron

00:22:06.730 --> 00:22:10.590
configuration that
says what you did.

00:22:10.590 --> 00:22:15.270
So here we can
write it this way.

00:22:15.270 --> 00:22:17.540
We'll say we have 1s two.

00:22:17.540 --> 00:22:19.670
There are two
electrons in the 1s.

00:22:19.670 --> 00:22:20.640
2s two.

00:22:20.640 --> 00:22:22.580
Two electrons in 2s.

00:22:22.580 --> 00:22:23.870
And 2p four.

00:22:23.870 --> 00:22:27.570
We have four electrons
in the 2p orbitals.

00:22:27.570 --> 00:22:29.670
And if for some
reason the question

00:22:29.670 --> 00:22:35.130
asks you to specify m sub
l, you can do that too.

00:22:35.130 --> 00:22:41.230
So then instead of just saying
2p4 then you would say 2px2.

00:22:41.230 --> 00:22:44.490
So there were two
electrons in px.

00:22:44.490 --> 00:22:49.900
And then to 2pz1 and 2py1.

00:22:49.900 --> 00:22:53.190
And if you don't
write 1, 1 is implied.

00:22:53.190 --> 00:22:54.830
So you will see this both ways.

00:22:54.830 --> 00:22:57.270
You will see the 1
indicated and then

00:22:57.270 --> 00:23:00.050
you'll see the orbital
just listed with nothing.

00:23:00.050 --> 00:23:03.310
If you do that you are implying
there is one electron in there.

00:23:03.310 --> 00:23:06.090
If you don't mean to imply
there is one electron in there

00:23:06.090 --> 00:23:07.870
don't write it that
way because that's

00:23:07.870 --> 00:23:10.710
what is implied if
that's the way it is.

00:23:10.710 --> 00:23:12.565
So now let's do a
clicker question.

00:23:46.380 --> 00:23:46.880
OK.

00:23:46.880 --> 00:23:48.000
10 more seconds.

00:23:48.000 --> 00:23:50.954
I think we can get at
least 93% on this one.

00:24:07.370 --> 00:24:08.380
That's not bad.

00:24:08.380 --> 00:24:09.400
90.

00:24:09.400 --> 00:24:10.690
That was a decent guess.

00:24:10.690 --> 00:24:13.430
That was a decent guess.

00:24:13.430 --> 00:24:17.370
So I think the trick
here was just counting.

00:24:17.370 --> 00:24:19.810
So the bottom one
that some people

00:24:19.810 --> 00:24:24.640
liked-- there are only six
electrons and that has more.

00:24:24.640 --> 00:24:25.680
AUDIENCE: Question.

00:24:25.680 --> 00:24:26.638
CATHERINE DRENNAN: Yep.

00:24:26.638 --> 00:24:30.997
AUDIENCE: Are the p and
sub l notations always

00:24:30.997 --> 00:24:33.062
filled in with order
x, z, y or can it

00:24:33.062 --> 00:24:36.950
be x, y, z, or [INAUDIBLE]?

00:24:36.950 --> 00:24:39.950
CATHERINE DRENNAN: Yeah, you
don't have to worry about that.

00:24:39.950 --> 00:24:43.260
That's kind of arbitrary
what you put for that.

00:24:43.260 --> 00:24:46.690
So if it is indicated
then that's fine,

00:24:46.690 --> 00:24:49.210
but we didn't give you an
option that would be different.

00:24:52.530 --> 00:24:56.580
So now you can imagine that if
you were writing these electron

00:24:56.580 --> 00:24:59.190
configurations and you were
asked to write an electron

00:24:59.190 --> 00:25:02.450
configuration for something
way down on the periodic table

00:25:02.450 --> 00:25:06.040
you would be writing for a
very, very, very long time.

00:25:06.040 --> 00:25:11.760
So you can use information
about core electrons and valence

00:25:11.760 --> 00:25:14.130
electrons to make
your life easier.

00:25:14.130 --> 00:25:17.890
Now, sometimes you will be
asked to write the full electron

00:25:17.890 --> 00:25:18.800
configuration.

00:25:18.800 --> 00:25:21.770
It will say don't
use the noble gas

00:25:21.770 --> 00:25:24.136
short hand, then that's
what you have to do.

00:25:24.136 --> 00:25:25.260
Very important on the exam.

00:25:25.260 --> 00:25:27.460
Read questions carefully.

00:25:27.460 --> 00:25:31.080
So let's introduce this concept
of core electrons and valence

00:25:31.080 --> 00:25:32.140
electrons.

00:25:32.140 --> 00:25:38.440
So if we look at the periodic
table we have our 1s1, 1s2,

00:25:38.440 --> 00:25:39.820
and then we come down.

00:25:39.820 --> 00:25:43.810
We have our 2s's and our 2p's,
and then we have a noble gas,

00:25:43.810 --> 00:25:47.800
and then we come down and
we have our first 3s1.

00:25:47.800 --> 00:25:49.940
And so if we're
talking about sodium,

00:25:49.940 --> 00:25:51.910
we have core
electrons, which are

00:25:51.910 --> 00:25:57.850
the electrons that make up
the noble gas element that's

00:25:57.850 --> 00:26:00.260
on the row before.

00:26:00.260 --> 00:26:03.310
And then, those are
usually not very reactive.

00:26:03.310 --> 00:26:05.260
They're held pretty tight.

00:26:05.260 --> 00:26:07.380
And the valence electrons--
the valence electrons

00:26:07.380 --> 00:26:10.725
are the electrons that do all
the exciting chemistry-- lose

00:26:10.725 --> 00:26:12.790
and gain valence electrons.

00:26:12.790 --> 00:26:14.100
They're the fun ones.

00:26:14.100 --> 00:26:17.710
And so those are going to
be beyond that noble gas

00:26:17.710 --> 00:26:18.620
configuration.

00:26:18.620 --> 00:26:20.140
Those core electrons.

00:26:20.140 --> 00:26:24.470
And so here sodium has one 3s1.

00:26:24.470 --> 00:26:29.520
So we can also write sodium
then as bracket neon,

00:26:29.520 --> 00:26:32.220
indicating the noble
gas before, and then

00:26:32.220 --> 00:26:34.480
just put the valence electrons.

00:26:34.480 --> 00:26:36.070
The 3s1.

00:26:36.070 --> 00:26:39.220
And unless it's
clearly specified

00:26:39.220 --> 00:26:43.170
you're not supposed to do
that this will be acceptable.

00:26:43.170 --> 00:26:46.480
So we can go on in that
row of the periodic table

00:26:46.480 --> 00:26:47.920
in the third period.

00:26:47.920 --> 00:26:52.180
And so the next one
we would have 3s2,

00:26:52.180 --> 00:26:56.130
and then we jump over
here to the 3p's and so

00:26:56.130 --> 00:27:00.850
on and so on until we get
to our next noble gas.

00:27:00.850 --> 00:27:02.590
So this is pretty
straightforward.

00:27:02.590 --> 00:27:06.280
There are no exceptions
on the third period.

00:27:06.280 --> 00:27:11.800
But when we get to the fourth
period of the periodic table

00:27:11.800 --> 00:27:14.200
we start to have a
couple of exceptions

00:27:14.200 --> 00:27:17.740
that you will be
responsible for.

00:27:17.740 --> 00:27:20.020
So it's looking good up
here in the beginning.

00:27:20.020 --> 00:27:24.000
We have now our noble
gas, and then we

00:27:24.000 --> 00:27:28.420
have our valence
electrons 4s1, 4s2,

00:27:28.420 --> 00:27:32.770
and then we start down
in the 3d's over here.

00:27:32.770 --> 00:27:37.780
And when we get halfway
through we have an exception.

00:27:37.780 --> 00:27:41.950
So you have exceptions
halfway through and also

00:27:41.950 --> 00:27:44.140
when you're almost at the end.

00:27:44.140 --> 00:27:50.230
So instead of having
4s2 3d4, it really

00:27:50.230 --> 00:27:54.100
wants to have 5 electrons.

00:27:54.100 --> 00:27:58.530
And in this case, instead
of 4s2 3d9 it wants 10.

00:27:58.530 --> 00:28:01.520
So it like things being
half full or totally full,

00:28:01.520 --> 00:28:04.150
and so you have these
exceptions there.

00:28:04.150 --> 00:28:08.070
So you don't have a d4
and you don't have d9.

00:28:08.070 --> 00:28:10.450
And you're responsible
for these two,

00:28:10.450 --> 00:28:15.060
and then in the period
right below same position

00:28:15.060 --> 00:28:16.720
same exception.

00:28:16.720 --> 00:28:18.590
So you can think
about this-- I don't

00:28:18.590 --> 00:28:23.750
know if it's four exceptions or
really just two in two places,

00:28:23.750 --> 00:28:26.410
but these are the
exceptions you need to know.

00:28:26.410 --> 00:28:30.160
So in the fifth it's the ones
right below are the same.

00:28:30.160 --> 00:28:33.670
You're not going to
have d4 or a d9 here.

00:28:33.670 --> 00:28:36.690
So you bump one up
because it's just happier

00:28:36.690 --> 00:28:41.470
when it has 5 or 10
electrons in the d orbitals.

00:28:41.470 --> 00:28:44.840
You're also responsible
for knowing the orders.

00:28:44.840 --> 00:28:46.260
We have a question way up there.

00:28:46.260 --> 00:28:47.242
Who wants to run?

00:28:51.930 --> 00:28:53.180
Get some exercise.

00:28:53.180 --> 00:28:56.140
I don't always see questions
so yell out my name

00:28:56.140 --> 00:28:58.230
if I don't see people.

00:28:58.230 --> 00:28:59.400
I am wearing my glasses.

00:28:59.400 --> 00:29:00.150
That's good.

00:29:00.150 --> 00:29:00.770
Yeah?

00:29:00.770 --> 00:29:03.190
AUDIENCE: So what happens
when we have an ion?

00:29:03.190 --> 00:29:04.399
Like a titanium [INAUDIBLE]--

00:29:04.399 --> 00:29:05.773
CATHERINE DRENNAN:
Good question.

00:29:05.773 --> 00:29:06.710
I'm getting to that.

00:29:06.710 --> 00:29:07.220
AUDIENCE: All right.

00:29:07.220 --> 00:29:07.520
Cool.

00:29:07.520 --> 00:29:08.020
Thanks.

00:29:08.020 --> 00:29:09.810
CATHERINE DRENNAN:
Hold on a minute.

00:29:09.810 --> 00:29:11.914
Yes.

00:29:11.914 --> 00:29:12.830
We're getting to ions.

00:29:12.830 --> 00:29:14.920
They're right at the end.

00:29:14.920 --> 00:29:17.280
So first, let's
consider what happens

00:29:17.280 --> 00:29:19.420
when we're not doing an ion.

00:29:19.420 --> 00:29:23.240
And there are a couple different
ways that we can look at this.

00:29:23.240 --> 00:29:25.860
This is one way to remember.

00:29:25.860 --> 00:29:29.970
So you just write out 1s,
2s, 2p, threes, your fours,

00:29:29.970 --> 00:29:34.070
your fives, your six, your
sevens, and then draw a line.

00:29:34.070 --> 00:29:44.230
First you fill 1s, then 2s,
2p, 3s, 3p, 4s, 3d, 4p, 5s, et

00:29:44.230 --> 00:29:46.740
cetera, et cetera, et cetera.

00:29:46.740 --> 00:29:47.770
That works.

00:29:47.770 --> 00:29:49.150
That's one way to do it.

00:29:49.150 --> 00:29:50.890
It's kind of time consuming.

00:29:50.890 --> 00:29:54.620
Not sure that's the easiest way.

00:29:54.620 --> 00:29:57.630
The other way that
you can do-- this

00:29:57.630 --> 00:30:00.680
is the periodic table you'll
be getting on the exam,

00:30:00.680 --> 00:30:03.550
and you can just
remember what's happening

00:30:03.550 --> 00:30:05.530
at these different cases.

00:30:05.530 --> 00:30:10.180
So over here we're
filling up our s's.

00:30:10.180 --> 00:30:15.230
Over here we're filling up
our p's, except for helium.

00:30:15.230 --> 00:30:19.230
Over here we're doing our
d's in the transition metals.

00:30:19.230 --> 00:30:22.430
Over here we have f.

00:30:22.430 --> 00:30:26.420
And then in terms of
the period numbers-- so

00:30:26.420 --> 00:30:28.720
we have one over here.

00:30:28.720 --> 00:30:36.550
So we do 1s2, 2s2,
or 1s1, 1s3, 2s.

00:30:36.550 --> 00:30:37.590
Then we come over here.

00:30:37.590 --> 00:30:44.320
We have the two p's, three
s's, three p's, four s's.

00:30:44.320 --> 00:30:51.710
Then we have four d's and go to
four p's, five s's, four d's,

00:30:51.710 --> 00:30:55.290
five p's, and then we
can't forget when we

00:30:55.290 --> 00:30:58.140
get down here that we have f.

00:30:58.140 --> 00:31:00.830
What number goes here?

00:31:00.830 --> 00:31:02.360
Four.

00:31:02.360 --> 00:31:04.640
So when you get to
principal quantum

00:31:04.640 --> 00:31:07.940
number four is when you
start having f orbitals.

00:31:07.940 --> 00:31:09.970
So if you just
remember this, it's

00:31:09.970 --> 00:31:11.950
going to help you
think about what

00:31:11.950 --> 00:31:14.601
the energy levels-- how
you're going to write those

00:31:14.601 --> 00:31:15.226
configurations.

00:31:19.490 --> 00:31:24.960
So maybe I'll leave this up and
we'll do a clicker question now

00:31:24.960 --> 00:31:25.870
on this.

00:31:31.000 --> 00:31:34.540
And you have your periodic
table available to look at.

00:31:34.540 --> 00:31:35.920
And then we'll get to ions.

00:31:44.720 --> 00:31:46.186
This should be 93%.

00:31:46.186 --> 00:31:46.686
Yeah.

00:32:02.761 --> 00:32:03.260
OK.

00:32:03.260 --> 00:32:03.760
10 seconds.

00:32:23.730 --> 00:32:25.150
Well, 85.

00:32:25.150 --> 00:32:27.320
That's still pretty good.

00:32:27.320 --> 00:32:32.140
So this one was one of
our exceptions over here.

00:32:32.140 --> 00:32:38.340
And we wanted to have no d9.

00:32:38.340 --> 00:32:41.330
So it just is happier
as d10 system,

00:32:41.330 --> 00:32:42.980
so that's our exception.

00:32:42.980 --> 00:32:47.430
One of the four that you
need to know for this.

00:32:47.430 --> 00:32:52.660
So now we have our two
methods of remembering this.

00:32:52.660 --> 00:32:55.190
And we did the clicker
question, and so I'm

00:32:55.190 --> 00:32:59.560
going to jump to ions.

00:32:59.560 --> 00:33:01.690
There's one question
on problem sets

00:33:01.690 --> 00:33:05.080
and people have been
asking about ions.

00:33:05.080 --> 00:33:11.710
So when we're just here
filling up our 4s ones.

00:33:11.710 --> 00:33:14.260
4s we're putting
in first and then

00:33:14.260 --> 00:33:18.900
we're going to our 3d, which
is what we just learned about.

00:33:18.900 --> 00:33:24.220
But what actually happens when
you start putting electrons

00:33:24.220 --> 00:33:27.700
in your d orbitals is
that the orbital energy

00:33:27.700 --> 00:33:31.320
of the d orbitals
drops below the 4s.

00:33:31.320 --> 00:33:34.380
So once they start
becoming filled you

00:33:34.380 --> 00:33:37.700
have this change that happens.

00:33:37.700 --> 00:33:39.630
And this is really
only important

00:33:39.630 --> 00:33:42.925
when you're talking about ions.

00:33:42.925 --> 00:33:47.800
So if we were asking
here about this one--

00:33:47.800 --> 00:33:53.130
so we would normally say,
OK, we put our two 4s in

00:33:53.130 --> 00:33:57.890
and then we have
two 3d electrons.

00:33:57.890 --> 00:34:02.640
But now, because we've
started to fill the 3d,

00:34:02.640 --> 00:34:05.610
if we're going to really do
this in terms of energy level

00:34:05.610 --> 00:34:07.300
we could reverse the order.

00:34:07.300 --> 00:34:11.380
And we would accept both of
these for the neutral ion.

00:34:11.380 --> 00:34:13.150
You could do either here.

00:34:13.150 --> 00:34:17.590
But importantly, if you
start ionizing it and losing

00:34:17.590 --> 00:34:19.820
electrons, you need
to think where are

00:34:19.820 --> 00:34:21.400
those electrons coming from?

00:34:21.400 --> 00:34:25.210
Which are the electrons
that are easiest to remove?

00:34:25.210 --> 00:34:32.560
And what happens is that you
end up losing the 4s2 electrons.

00:34:32.560 --> 00:34:40.480
And so the configuration for
titanium plus 2 is just 3d2.

00:34:40.480 --> 00:34:42.340
And so this is different.

00:34:42.340 --> 00:34:45.550
Ions behave
differently, and now you

00:34:45.550 --> 00:34:49.139
can go run and finish
problem set two.

00:34:49.139 --> 00:34:51.040
That last question.

00:34:51.040 --> 00:34:57.400
And this is because now we're
at the end of exam one material.

00:34:57.400 --> 00:35:01.500
So one thing I didn't get
to-- it said in the beginning.

00:35:01.500 --> 00:35:04.210
Number 12 on the problem
set we're not going

00:35:04.210 --> 00:35:06.130
to get to until next week.

00:35:06.130 --> 00:35:09.410
So if you've done number 12
already you can turn it in.

00:35:09.410 --> 00:35:12.220
It won't be graded and you can
turn it in again on problem set

00:35:12.220 --> 00:35:14.420
3 so you won't have wasted time.

00:35:14.420 --> 00:35:17.550
But that won't be on
exam one material.

00:35:17.550 --> 00:35:21.630
So this is the end
of exam one material.

00:35:21.630 --> 00:35:26.350
And read your instructions
for the exams very carefully.

00:35:26.350 --> 00:35:28.730
And there's a couple
questions, but I think

00:35:28.730 --> 00:35:30.820
it's too noisy to answer them.

00:35:30.820 --> 00:35:35.310
Note that not everyone is
taking the exam in this room,

00:35:35.310 --> 00:35:37.920
and you need to go to
the appropriate place.

00:35:37.920 --> 00:35:40.300
So please look at
the instructions.

00:35:40.300 --> 00:35:40.800
All right.

00:35:40.800 --> 00:35:43.171
And who won the clicker
competition for today?

00:35:47.330 --> 00:35:49.640
Recitation 12.