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- [Teacher] To figure out
how we use semiconductors

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to build all these
awesome computing devices,

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we're going to start from scratch,

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all the way down to even understanding

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why semiconductors are semiconductors.

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I mean, why is it that certain materials

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behave like conductors,

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which are very good at passing electricity

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through them while others are not?

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To understand this, we need
to look at the atomic level.

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Now we might have some
intuition about these atoms,

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but guess what?

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Turns out that our knowledge

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of the atomic structure is not enough.

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And so in this video, we're
just gonna recapitulate

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all the stuff that we might already know

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from the previous videos.

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And we'll see why the current knowledge

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or the current theory of the atoms

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is not sufficient to talk
about solids in general,

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which we'll be interested in.

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For starters, you may
already have some intuition.

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For example, you may know that
all matter is made of atoms.

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And if you were to pick any
one of them and zoom in,

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then you might know that
the atoms themselves

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are made of even smaller things.

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At the center, we have this
thing called as the nucleus,

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which have a positive charge,

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and the electrons which
are negatively charged

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are attracted by the nucleus

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and end up going around the
nucleus in different orbits

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just like the solar system

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and how the planets go around the sun.

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Now this is not a very accurate model,

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we'll get back to that.

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But as of now, let's use this model.

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But the important thing is
there are some electrons

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like these, which are
tightly bound to the nucleus.

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We call them as bound electrons.

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Bound electrons, and
these are not responsible

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for conduction.

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Whereas there are other electrons

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which are not strongly
attracted by the nucleus

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and they are free, as
in, they're free to move

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from one atom to another.

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And it's these electrons which we call

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as conduction electrons or free electrons,

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which are really
responsible for conduction.

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And in some materials,

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it's very easy to get
these free electrons.

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And so they end up having a lot of them,

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and we call these materials
as good conductors

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or conductors.

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On the other hand, some materials,

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well, it's extremely difficult
to get these free electrons.

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And as a result, you have
extremely negligible amount.

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And as a result, they are
bad conductors or insulators.

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And of course we have
the intermediate ones

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which we end up calling semiconductors.

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So I think the most important question

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that we have to ask ourselves over here,

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is how does an electron become free?

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I mean, what makes it free
and what does that depend on?

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That's the thing that
we need to figure out.

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And we have to look at,
look at this whole thing

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for a solid, because our
semiconductors are solids.

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So we need to find out,
or we need to figure out

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what makes an electron free in solids.

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And to do that, we need to get past this

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solar system model of the
atom, as I mentioned before,

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it's not very accurate.

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And we need to look at
a more accurate model

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of the atomic structure.

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So let's do that.

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Now, you may have already
learned about this in chemistry.

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It turns out that instead of thinking

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of where the electrons are and what orbits

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or what path they take,

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it's much better to think about
them in terms of energies.

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It's better think about
what are the energies

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that the electrons can take up.

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And you may have already
studied in chemistry

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that the inside of any atoms,

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so if I draw over here energies,

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inside any atom, electrons
can have only some

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specific energy values,

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only some specific energy values.

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And so maybe the lowest energy

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that electron can have
maybe somewhere over here.

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We're not gonna write down
the numbers over here.

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We're not gonna look at
it very quantitatively,

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don't worry about it.

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So maybe this is the lowest energy

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that an electron can possess.

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The next higher energy
an electron can possess

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might be somewhere over here,

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and maybe next higher might
be somewhere over here,

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and so on and so forth.

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And we give names to these energy levels.

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We call the lowest one
as the 1S energy level.

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The next higher one becomes 2S,

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the one that comes above that would be 2P.

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Then we have 3S and 3P
and so on and so forth.

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And again, if this looks very new to you

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and you have no idea what S and P are,

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it would be a great idea
to pause this over here,

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go back and watch the
electron configuration videos

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on chemistry, and then
come back over here.

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But anyways, it turns out
electrons cannot take up

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these energy levels randomly.

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There's a particular rule
using which electrons

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sort of fill up these energy levels.

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And that rule, again, you
may have studied about them.

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We call that as the Pauli's
exclusion principle.

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Pauli's exclusion,

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exclusion principle, or rule.

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And it simply says that no two electrons,

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no two electrons

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can have identical,

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can have identical energies.

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Now, again, this is not the
accurate statement of Pauli,

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but this will help us,
this is enough for us.

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So let's take a concrete example.

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Suppose we take, say, a sodium atom,

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then it has, it has 11
electrons inside it.

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There are 11 electrons.

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And now these 11 electrons

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can only have these
specific energy levels.

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And the way these electrons

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are going to fill up the energy levels

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will be using the exclusion principle.

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So the first electron, well, remember,

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electrons always want to take
the lowest energy possible.

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So the first electron would
go over here, over here,

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and then you might think,
well, the next electron

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can't go over here because
that's what Pauli's telling us.

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No arguing with Pauli.

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Second electron, if it comes over here,

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it might have identical
energy, but not really,

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because it turns out
that electrons can have

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up spin and down spins.

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So if the first electron
goes into the 1S tier,

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and suppose it takes up the up spin,

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then another electron can actually take up

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the same energy level and now be down spin

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because turns out these two spins

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have slightly different energy.

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So these two electrons
are strictly speaking,

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still being Pauli, because
they're not exactly identical

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because of their spins.

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But the next electron, the third electron,

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well, it cannot take up the
1S energy level anymore,

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because if it does and then up spin,

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then it'll be identical to this one.

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If it does with a down spin,

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then it'll be identical to this one.

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So it can't take the that up anywhere.

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So it has to take up now

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the next higher energy level
available that's over here.

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It can take up anywhere
in between as well.

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The energy levels in
between are inaccessible

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to these electrons.

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So the next energy it
will take up would be 2S,

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again, it might take up with an up spin.

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The fourth electron might
go over with a down spin.

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The next electron will
take up over here, up spin,

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and the next one will be down spin.

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Now here's the thing.

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It turns out that in P, in P energy level,

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there are three ways in which electrons

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can occupy that energy level.

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We call them as orbitals, right?

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It turns out that in the S energy levels,

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there's only one way.

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So there's only one orbital,

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but in P there are three orbitals.

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So another electron can
take up the 2P energy level

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by being in a different orbital.

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So this electron and this electron

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will be in different orbitals,

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or different configuration, we could say,

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don't have to worry about it too much.

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And so they'll still not be identical.

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And so another electron can
take up that same orbital

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with a down spin.

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Another electron, the third
orbital of P with an up spin,

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and then down spin.

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And now the 2P is completely filled.

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There are no more orbitals available.

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And so the last electron,

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we're down to one, two,
three, four, five, six, seven,

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eight, nine, 10, the last
electron will be over here

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in the 3S up spin.

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But this is for a single atom of sodium.

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What if we have say, two atoms of sodium,

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very close to each
other, what happens then?

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Somewhat like this,

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what if they form some kind of a molecule?

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How would the electrons of this molecule

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fill up the energy levels?

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Can we say that now each atom
will have something like this.

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Each atom will have electrons
filled up accordingly.

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Well, that won't work,
that can't be possible.

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And the way we can think about it,

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is we can say that, if you do it this way,

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Pauli's rule will be violated.

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Remember, Pauli says no two electrons,

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and when we say no two electrons,

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it can be no two electrons inside an atom,

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or no two electrons inside a molecule,

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or maybe no two electrons
inside an entire solid.

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No two electrons can
have identical energies.

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So if the two atoms have
these electron configurations

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then I hope you can see that this electron

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and this electron will,
they will be identical.

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This one, and this one will
be absolutely identical.

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And so all of them will
have identical pairs

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and Pauli will be very, very
sad, so that can't be possible.

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And if we have an entire solid,

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which is made of sodium, where
we have like 10 to the 23

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atoms packed very close to each other,

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and if we used this model for each atom,

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then there would be about 10
to the 23 identical copies

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of electrons in each level.

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And that would make Pauli
extremely sad, extremely sad.

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So the key takeaway is that this structure

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that we have learned for a
single atom cannot be extended

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when we go all the way to the solids.

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We require a new theory to
understand what's going on

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and how electrons are arranged
or how to think about them

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when it comes to solids.

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And we'll explore them
in the future videos.