00:01
As I mentioned, the shells themselves
can be divided into orbitals,
each of which contains two electrons.
00:08
Orbitals are characterized by shape that is produced
when the region surrounding the nucleus is plotted
in which it’s typically regarded that a
95% chance exists of finding the electrons.
00:22
The orbital shapes that we will
come across are s, p, d and f.
00:29
We’re mostly going to focus on s, p and d orbitals.
00:35
The analogy to use is that each shell unlocks
if you like an additional orbital type.
00:40
So, in other words, for the first shell
you can only get the s-type orbital.
00:45
For the second shell you can get
the s- and the p-type orbitals.
00:49
And for the third shell you can get s, p and d.
00:53
And for the fourth it’s possible
to have access to all four,
bearing in mind each individual
orbital can only contain two electrons.
01:05
And we’ll talk about this in
more depth a little later.
01:08
The orbital quantum numbers are given
for s orbitals as 0, 1, 2 and 3.
01:16
And the nomenclature in quantum mechanics,
where n was for principal quantum number,
is that the orbital quantum
number carries the letter l.
01:26
So, as we’ll see, it’s possible to actually
assign the specific designation of an electron
just using quantum numbers.
01:39
The simplest orbital, as you can see here, is where
l, or the orbital quantum number, is equal to 0.
01:46
And it is spherical.
01:48
Here you can see three particular types of
shells of orbitals: the 1s, the 2s and the 3s.
01:58
Each of these is spherical but, as you can
see, each of these is of a different size.
02:03
As of course we move further away from the
nucleus, of course the electrons themselves
or the probability of finding them is
also more distant from the nucleus.
02:14
Also bear in mind it’s spherical
and so the x, y and z axes there
demonstrate the three dimensionality of this species,
and the fact that there is a 95% probability
of finding electrons within this region.
02:29
Note of course that, if you go back
to the basic quantum mechanics,
the theoretical chance of finding
electrons in the nucleus is, of course, 0.
02:40
So, going from left to right, 1s is an
s orbital, which is a spherical orbital
which actually stands for ‘sharp’ rather than
‘spherical,’ which is rather counterintuitive.
02:52
The 2s is an s orbital in shell 2 and
the 3s is an s orbital in shell 3.
02:59
And each of these – the 1s, the 2s and the
3s – can formally contain two electrons.
03:08
p orbitals – these are ‘principal’ orbitals
and this is where you have an orbital quantum
number of 1 or l equals 1 – are more complex.
03:20
And remember what I said: as you move up the shells,
it’s possible to accommodate more and more electrons.
03:26
The only way to do this of course is to have
more and more different types of orbital.
03:31
And here we can see three of these:
the 2py, the 2px and the 2pz.
03:38
Note that the number prior to the py, px and
pz correlates to the principal quantum number
which, in this case, is the
lowest one for p orbitals of two.
03:52
It is, of course, possible to get 3p and 4p
orbitals but, of course, not possible to get 1p.
03:59
You haven’t unlocked them at that point.
04:02
Note the similarities between these guys.
04:04
They are dumbbell shaped.
04:07
It’s often the shape that’s considered.
04:09
And their orientation is along the three component
axes – that is the y axes, the x axes and the z axes
as shown in this particular slide.
04:26
Crucially, if we look in the
center where the node is formed,
where we have the tiny spot in the
center is where the nucleus is.
04:38
And there we have an electron density of 0.
04:43
Now, the question you may be asking is:
well why are they shaded differently?
And this is what I’m going to come to in a moment.
04:55
A p orbital has two regions where
electrons may be found on either side.
04:59
Note what I’ve done is we’ve got a plane
through the node of the p orbital as shown here.
05:07
And, along that plane, there exists no
electron density as it contains the nucleus.
05:14
But, again, what is the significance of
the negative and the positive charges?
And this is to do with the phase of electrons.
05:26
Now remember what I said: we tried to discount
the idea of treating electrons as particles
because it created a lot of
theoretical problems for us.
05:37
In fact, we understand that electrons exist in
shells and it can only go up or down those shells
by absorbing or giving off quanta of energy.
05:47
Equally, we talked about electrons existing in waves.
05:50
That’s why we can only talk about the probability
of finding them in particular parts of an atom.
05:57
And this is the same analogy because, in this
case, we’re talking about wave coherence.
06:03
We’re talking about whether or not
an electron exists as the peak here
of the trough that we’re showing
here, the sine wave, or as the trough.
06:16
Right. So, as I mentioned, it’s possible for us to
treat electrons as waves as well as as particles.
06:24
And, in the context of the p
orbital, this is very important.
06:28
So, if we look at this wave form here, we can see that
it is analogous to the dumbbell shape of our p orbital
whereas we see in the center node, the
chances of finding an electron are 0.
06:42
but the chances of finding an electron
either side are reasonably high.
06:48
So, if we think of an electron as a
wave with positive and negative regions,
we can think about the ideas of coherence,
i.e. constructive or destructive interference.
07:03
So, as there are three p orbitals, there
needs to be a way of telling them apart
because, if you look here, you
can see that they are degenerate.
07:12
By that, what I’m talking about here is the
idea that you could superimpose one on the other
by a simple rotation, around 90 degrees.
07:21
And so a way of defining an electron in a given p
orbital is via the magnetic quantum number or ml,
Okay, not to be confused with ms.
07:31
That is a different one which
we’ll come onto a little later.
07:34
So this helps us to define the direction
of an orbital as well as its type.
07:42
So here we can see we’ve got the orbital
running along the y axis and across the x axis
and then, finally, along the z axis.
07:52
So, d orbitals.
07:55
These have a more complex set of shapes and
they have the orbital quantum number of 2.
08:02
The d in the orbital stands for ‘diffuse’
and they have two nodal planes
and come in sets of five.
08:11
The ml, or magnetic orbital
number, can be -2, -1, 0, 1 or 2.
08:20
And don’t just take it and accept it as read.
08:22
There is actually an equation which
we’ll come onto in the next lecture
which explains how you can determine this yourselves.
08:31
The lowest energy shell
containing d orbitals is n = 3.
08:36
Prior to that, they haven’t been unlocked.
08:42
Degeneracy.
08:43
This is what I alluded to in the case of the p
orbitals and, as we’ll see a little later on,
in the d orbitals.
08:51
These are orbitals with the same energy.
08:54
When they have the same energy and they have the
same orientation, they’re regarded as degenerate.
09:00
In other words, they’re
superimposable onto each other.
09:04
And this is the case for p and
also some of the d orbitals.
09:09
And degeneracy is based on the idea
that, whilst they have the same energy
and the electrons – or the probability of finding
them – is the same distance from the nucleus,
they point in different directions.
09:23
By rotating them 90 degrees in the three
axes, however, they would all be identical.
09:30
They’re all superimposable and
therefore they’re termed degenerate.