PROFESSOR: Now let's
talk about electrons
grouping around a nucleus.
So they have to occupy
many of the orbitals,
and we've already seen
when they do that.
They occupy the orbitals
in regular ways.
There's rules that
say, no two electrons
can have the same
four quantum numbers.
N l m sub l and m
sub s, at least one
must be different
for each electron.
And we've seen they
always go in spin parallel
to degenerate orbitals.
But another effect occurs, and
that is low energy electrons
will shield the higher
energy electrons.
In fact the three
body problem, that
is one nucleus that's
positively charged
and two electrons, both
negatively charged,
around a nucleus is a
mathematically incredibly
difficult problem to solve.
You can't solve it
exactly like you
can the two body problem,
one nucleus and one electron.
So what we do is we take the one
nucleus one electron problem,
and we say, let
that one electron
define all the orbitals.
And then when we start
putting more electrons in,
they'll serve as just a slight
perturbation to that one
electron system.
It's easier than solving all
the mathematics over again.
So let's look at the
various energy levels
and how an electron
already existing
might perturb the energy levels
of a higher energy electron
so one s electrons.
Now, s electrons are
very good shielders.
That is, they can shield
some of the nuclear charge
from outer electrons.
So here's a big nuclear
positive charge.
An s electron has no
node at the nucleus.
That is, the orbitals
are aligned such
that the electron has
access to the nucleus.
If you're a p electron or a d
electron, if l is one or two,
then you have an angular
node at the nucleus.
You're forbidden mathematically
to exist at the nucleus.
So s electrons, by nature, are
very good shielders of outer p
electrons, because they
have access to the nucleus,
where the p electrons don't.
So even within the
same principle quantum
level, if you have
n equal two, you
have both two s and
two p electrons,
the two s electron will be an
effective shielder of the 2 p.
Now, what do we
mean by shielding?
Shielding means I remove some
of the effective nuclear charge.
So rather than this
electron here seeing
say, a full plus two,
if this were a helium
nucleus, for instance, rather
than seeing a full plus two,
the inner electron
shields some of that.
And it'll seem more
like maybe just
a plus one-ish effective
nuclear charge.
So if it sees a lower nuclear
charge, it's easier to ionize.
Its energy state is
raised, it's closer
to that zero ionized state.
Let's look at that
in more detail.
Here I've plotted the one s,
two s, three s, four s energy
levels.
L equals zero.
Very good shielding electrons,
because l equals 0 means
s, no node at the nucleus.
If you look at how they
affect the p orbitals, those
that have l equal one,
they're shielding them.
These levels are raised slightly
because of the shielding effect
of the s electron.
And that effect continues.
If you look at l equal
two, the d orbitals
are shielded by the internal
s and p orbitals below them,
so they go to higher energy.
And the effect is
pretty dramatic.
When you get a lot of s
and p orbitals, this d,
for instance, the first
d that you encounter,
3 d actually becomes
higher energy, easier
to ionize than the four s in
many electronic configurations.
So it's a significant effect,
this shielding effect.
S electrons that
have this inner state
don't shield each
other very well.
All s electrons have equal
access to the nucleus.
It's no node, so
two electrons that
have equal access to
the nucleus pretty much
always see the full
nuclear charge,
and they don't shield
each other very well.
But s electrons are great
shielders of p and d electrons.
So you get two p energies
that are higher than 2 s,
and you get d energies that
are even higher than four s.
So let's look at ionization
energies more carefully,
and see if we can
understand this phenomenon.
