Why atomic theory doesn't work for solids | Class 12 (India) | Physics | Khan Academy

- [Teacher] To figure out
how we use semiconductors

to build all these
awesome computing devices,

we're going to start from scratch,

all the way down to even understanding

why semiconductors are semiconductors.

I mean, why is it that certain materials

behave like conductors,

which are very good at passing electricity

through them while others are not?

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

Now we might have some
intuition about these atoms,

but guess what?

Turns out that our knowledge

of the atomic structure is not enough.

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

all the stuff that we might already know

from the previous videos.

And we'll see why the current knowledge

or the current theory of the atoms

is not sufficient to talk
about solids in general,

which we'll be interested in.

For starters, you may
already have some intuition.

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

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

then you might know that
the atoms themselves

are made of even smaller things.

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

which have a positive charge,

and the electrons which
are negatively charged

are attracted by the nucleus

and end up going around the
nucleus in different orbits

just like the solar system

and how the planets go around the sun.

Now this is not a very accurate model,

we'll get back to that.

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

But the important thing is
there are some electrons

like these, which are
tightly bound to the nucleus.

We call them as bound electrons.

Bound electrons, and
these are not responsible

for conduction.

Whereas there are other electrons

which are not strongly
attracted by the nucleus

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

from one atom to another.

And it's these electrons which we call

as conduction electrons or free electrons,

which are really
responsible for conduction.

And in some materials,

it's very easy to get
these free electrons.

And so they end up having a lot of them,

and we call these materials
as good conductors

or conductors.

On the other hand, some materials,

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

And as a result, you have
extremely negligible amount.

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

And of course we have
the intermediate ones

which we end up calling semiconductors.

So I think the most important question

that we have to ask ourselves over here,

is how does an electron become free?

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

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

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

for a solid, because our
semiconductors are solids.

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

what makes an electron free in solids.

And to do that, we need to get past this

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

it's not very accurate.

And we need to look at
a more accurate model

of the atomic structure.

So let's do that.

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

It turns out that instead of thinking

of where the electrons are and what orbits

or what path they take,

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

It's better think about
what are the energies

that the electrons can take up.

And you may have already
studied in chemistry

that the inside of any atoms,

so if I draw over here energies,

inside any atom, electrons
can have only some

specific energy values,

only some specific energy values.

And so maybe the lowest energy

that electron can have
maybe somewhere over here.

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

We're not gonna look at
it very quantitatively,

don't worry about it.

So maybe this is the lowest energy

that an electron can possess.

The next higher energy
an electron can possess

might be somewhere over here,

and maybe next higher might
be somewhere over here,

and so on and so forth.

And we give names to these energy levels.

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

The next higher one becomes 2S,

the one that comes above that would be 2P.

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

And again, if this looks very new to you

and you have no idea what S and P are,

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

go back and watch the
electron configuration videos

on chemistry, and then
come back over here.

But anyways, it turns out
electrons cannot take up

these energy levels randomly.

There's a particular rule
using which electrons

sort of fill up these energy levels.

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

We call that as the Pauli's
exclusion principle.

Pauli's exclusion,

exclusion principle, or rule.

And it simply says that no two electrons,

no two electrons

can have identical,

can have identical energies.

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

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

So let's take a concrete example.

Suppose we take, say, a sodium atom,

then it has, it has 11
electrons inside it.

There are 11 electrons.

And now these 11 electrons

can only have these
specific energy levels.

And the way these electrons

are going to fill up the energy levels

will be using the exclusion principle.

So the first electron, well, remember,

electrons always want to take
the lowest energy possible.

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

and then you might think,
well, the next electron

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

No arguing with Pauli.

Second electron, if it comes over here,

it might have identical
energy, but not really,

because it turns out
that electrons can have

up spin and down spins.

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

and suppose it takes up the up spin,

then another electron can actually take up

the same energy level and now be down spin

because turns out these two spins

have slightly different energy.

So these two electrons
are strictly speaking,

still being Pauli, because
they're not exactly identical

because of their spins.

But the next electron, the third electron,

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

because if it does and then up spin,

then it'll be identical to this one.

If it does with a down spin,

then it'll be identical to this one.

So it can't take the that up anywhere.

So it has to take up now

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

It can take up anywhere
in between as well.

The energy levels in
between are inaccessible

to these electrons.

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

again, it might take up with an up spin.

The fourth electron might
go over with a down spin.

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

and the next one will be down spin.

Now here's the thing.

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

there are three ways in which electrons

can occupy that energy level.

We call them as orbitals, right?

It turns out that in the S energy levels,

there's only one way.

So there's only one orbital,

but in P there are three orbitals.

So another electron can
take up the 2P energy level

by being in a different orbital.

So this electron and this electron

will be in different orbitals,

or different configuration, we could say,

don't have to worry about it too much.

And so they'll still not be identical.

And so another electron can
take up that same orbital

with a down spin.

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

and then down spin.

And now the 2P is completely filled.

There are no more orbitals available.

And so the last electron,

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

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

in the 3S up spin.

But this is for a single atom of sodium.

What if we have say, two atoms of sodium,

very close to each
other, what happens then?

Somewhat like this,

what if they form some kind of a molecule?

How would the electrons of this molecule

fill up the energy levels?

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

Each atom will have electrons
filled up accordingly.

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

And the way we can think about it,

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

Pauli's rule will be violated.

Remember, Pauli says no two electrons,

and when we say no two electrons,

it can be no two electrons inside an atom,

or no two electrons inside a molecule,

or maybe no two electrons
inside an entire solid.

No two electrons can
have identical energies.

So if the two atoms have
these electron configurations

then I hope you can see that this electron

and this electron will,
they will be identical.

This one, and this one will
be absolutely identical.

And so all of them will
have identical pairs

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

And if we have an entire solid,

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

atoms packed very close to each other,

and if we used this model for each atom,

then there would be about 10
to the 23 identical copies

of electrons in each level.

And that would make Pauli
extremely sad, extremely sad.

So the key takeaway is that this structure

that we have learned for a
single atom cannot be extended

when we go all the way to the solids.

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

and how electrons are arranged
or how to think about them

when it comes to solids.

And we'll explore them
in the future videos.