In this video, we're gonna talk
about how quantum mechanics and
chemical bonding are related.
And this is gonna eventually
lead us to something called,
molecular orbital theory.
So, if we look an s, a p, and
a d orbital and their three-dimensional
representations, sometimes we'll
shade each of these orbitals.
And the question is, why do we shade
these orbitals the way that we do?
And what are the shapes really relate to?
So, the shape of an atomic orbital,
which are shown above,
corresponds to the probability,
of finding,
the electron in a certain location.
And sometimes chemists refer to these
as probability density functions.
So where is this electron in
this particular orbital
most likely to be found?
Okay, Heisenberg has his
uncertainty principle.
And he talked about how we don't
know the exact location and
momentum of a particular electron, and
this is because our electrons
act as waves and particles.
We have to keep both of these in mind.
And Heisenberg, no, sorry,
Schrödinger came up with an equation
that said H psi is equal to E psi.
And this psi part right here
is called wave function.
And this wave function is gonna
describe the path of the electron.
And we can relate this to
differential mathematics.
When we solve this equation,
there's something called a node,
and a node is an intermediate point at
which the probability function,
Goes to zero.
So there's a zero probability
of finding that electron at
a particular node, and if we look
back up to the p and d orbitals.
The nodal plane for the p orbital is
right here, and the d orbitals for
this particular d orbital are going
to lie right along the axis.
Okay?
So when we look at nodes,
there are two types of nodes
that we have to look at.
And those nodes are radial and angular.
We can look at the various
probability density functions to
determine our radial nodes.
So, if we look at the radial
nodes of an s orbital,
we can get something like this,
where if we
put the probability of finding
the electron on the y axis,
and the distance from
the nucleus on the x axis.
For a 1s orbital,
that probability function
is going to look something like this,
where there's a main
probability of finding
that electron fairly
close to the nucleus and
there are no nodes here.
For a 2s orbital, if we plot
the probability versus the distance.
We're gonna see a graph that looks
something like this.
And at this point right here,
we have a node.
For a 3s orbital, if we plot
the probability versus the distance,
we're going to find that
there's two nodes there.
And the probability
of finding hat electron
farther from the nucleus
is going to increase as we increase
n with the principle quantum number.
We also have angular nodes, and
actually if we wanted to
look at a picture of this,
before we get on to that, if we have our
various s orbitals the 1s the 2s and
the 3s, these two radial nodes will
correspond to these lines
right here in the 3s orbital.
So the 3s orbital,
if we represent it over here on
the right, will have two radial nodes.
Another type of node is
called an angular node.
And the angular node is related
to the azimuthal quantum number
which we abbreviate with an l.
And we say that the azimuthal
quantum number l for s, p,
d and f orbitals is zero,
one, two, three respectively.
If we have a s orbital,
it's completely spherical.
There are zero angular nodes.
For a p orbital, we have one angular node.
And for a d orbital,
there are two angular nodes.
And the number of angular
nodes is gonna be
corresponding to the l quantum number,
or the azimuthal quantum number, okay.
And all of these properties are related
to the fact that the electron
can act as a wave.
