PROFESSOR: When more than one
electron is around an atom,
those electrons have a set
of four quantum numbers.
And they'll occupy the available
orbitals around an atom,
but they'll do it in
very specific ways,
they'll follow very
specific rules.
One of those rules is of the
four quantum numbers, n, l, m
sub l, and m sub
s, each electron
must have a unique set.
No two electrons can have
exactly the same quantum
numbers.
That's called the Pauli
exclusion principle.
Now, there's other
rules that they follow.
For instance, if there's
degenerate energy levels--
and we know when we
have the p orbitals,
there's three that are
of the same energy.
How do the electrons
choose to occupy those?
Well, there's several
possibilities.
They could go into the same
orbital, spin-up and spin-down.
That would give them
different quantum numbers.
m sub s would be different,
although n, l, and m sub l
would be the same.
They could have different m sub
l values and different m sub
s values.
So they could go in
spin anti-parallel,
or they could go
in spin parallel.
So the difference would be
in the value of m sub l only.
M sub s would be the same,
they'd go in parallel.
Now, you might think that the
parallel orientation would
be favored, because
the electrons,
remember, behave like
they're little magnets.
So if one goes in this way,
having one go in this way
would have them anti-parallel,
and a lower energy orientation
is to have them lined
up with each other.
And indeed, if you have
electrons anti-parallel,
that's a little
bit higher energy.
They like to be parallel.
So it turns out
that the electrons
like to spread out in space.
That makes sense, because
they have negative charges.
You wouldn't want to cram
them both in the same orbital
if you didn't have to.
So they spread out
as far as possible,
and they go in spin parallel.
So these two possibilities
don't happen.
These are higher
energy situations.
They're not disallowed by
any quantum mechanical rules,
but they're higher in energy.
So this is called Hund's rule.
And it turns out
electrons enter degenerate
orbitals the same way
people get on a bus.
You know, if you get on a
bus, there's a lot of seats
and they each hold two people.
But if there's someone
sitting in one seat,
do you go in and sit right
next to them in the same seat?
[LAUGHS] No.
You go sit in a seat
far away from them.
Do you go and sit in a seat
near them and face them?
No.
You go and sit in the
same direction facing away
on the bus.
Electrons enter
orbitals the same way
people enter seats on a bus.
Let's look at that.
I've chosen to use as
my model for electrons
the universal eating
implement, the spork.
I do that because sporks
have a preferred orientation.
I can tell this
spork is pointing up,
and this spork is pointing down.
So let's bring in some
sporks as electrons
to these two energy levels.
The first one can go in
either spin-up or spin-down.
If there's no other spins
there, then it doesn't matter.
The space is what
we call isotropic,
there are no other
fields involved,
so the magnetic field
can be either up or down.
But the way the
first one goes in
determines how the
second one goes in.
Now, the second electron
comes in, he says,
no, I don't want to sit there.
I want to sit here far
away and spin-parallel
to the first spin.
The next spin that
comes in now is
forced to sit next to
somebody, because these
are the only degenerate
energy levels.
There may be higher
energy levels up here,
but these are lower energy.
It's cheaper in energy
to pair spin-up,
spin-down than go to
a higher energy level.
So the next electron
will go in anti-parallel.
And I go in anti-parallel
because if I go in parallel
here, these electrons will
have exactly the same quantum
numbers.
And the Pauli exclusion
principle says I cannot do
that.
Electrons are fermions.
They're spin 1/2, and fermions
follow this Pauli exclusion
principle, where no two can
have exactly the same quantum
numbers.
They can't occupy the same
space at the same time.
You can think of that m sub
s quantum number as a time
quantum number.
It says, I'll occupy the
same space, the same orbital,
but I'll do it at
different times.
M sub s is different, so
we can both sit there,
we just won't see
each other in time.
It's interesting,
there's another class
of particles called bosons,
that can have the same quantum
numbers.
They can all collapse into
exactly the same quantum state.
And when that happens--
and this has been
proven, a Nobel Prize
was awarded for this--
where a Bose-Einstein
condensate occurs.
All the quantum
particles collapse
into exactly the
same quantum state.
They exist in the same
space at the same time.
Matter collapsed upon itself.
And you can Google
this on the web
and see some
beautiful animations
of a Bose-Einstein condensate.
Particles existing in the
same space at the same time.
It's a quantum
feature of particles.
They're wavelike, they can
exist in the same space
in the same time,
if they're bosons.
They have an integer spin.
Our particles have non-integer
spin, they are spin 1/2.
The final electron in
this set of energy levels
will go in spin
anti-parallel here.
So this set of energy levels
is full, I can occupy no more.
I have a spin-up
and a spin-down,
my two time coordinates in
each of the spatial, n l
and m sub l, three
dimensional coordinates.
This fills up this
set of electrons,
and this is how electrons
fill energy levels,
fill orbitals, fill wave
functions about an atom.
