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In our learning objective number nine,

Â we're going to start looking at the shapes of these orbitals.

Â So I want you to know the shapes of the s, the d, the p.

Â And I don't know why I said it in that order.

Â The s, the p, the d orbital, the f orbital.

Â And we are going to be looking at the energies of these orbitals for

Â a multi-electron system.

Â So we know that the orbitals are defined by our SchrÃ¶dinger equations.

Â They are defining regions in space that have a high probability of

Â locating an electron.

Â 0:31

This picture here represents an s orbital.

Â So it's shaped like a sphere.

Â When l equals zero, we have got the s sub-level.

Â And for that sub-level, we have an m sub l,

Â which could be anywhere from a negative l up to a positive l.

Â So it only has one choice.

Â There's only one orientation in space of an s orbital, and that's this sphere.

Â It doesn't matter how you look at a sphere, it looks the same.

Â So, if you were dealing with the 1s sub-shell, you would have an orbital that

Â looks like this, that would be a certain distance away from the nucleus.

Â You could also have a 2s subshell.

Â In that 2s subshell you would have a orbital that looks like this,

Â only it would be larger.

Â It would be further away from the nucleus.

Â 1:20

Now the p orbitals, we know that when p, is a subshell that the l value is one.

Â And when l is 1, the n sub l's can be a negative 1, 0, and 1.

Â Now what I told you in our lessons of these quantum numbers is that

Â this tells you that there are three orientations in space of the p orbitals.

Â So let's look at those three orientations.

Â The first orientation is along the x axis, so it is

Â 1:52

where you have a density about the orbit.

Â So the electrons can be located here.

Â That probability drops off as you approach the edge of this, okay?

Â So it's just diminishing as you go by, at some point, you say, okay,

Â we'll call the boundary here.

Â Where there is a beyond that there's a diminished probability out here in

Â this space, a diminished probability of finding electron, but

Â a high probability of finding it in here.

Â And then they typically just kind of clear it up and

Â just give it a instead of seeing that diminishing, it's getting less and

Â less probable as you move further away, they just choose to draw this.

Â And they call it a dumbbell shape,

Â though I don't know if dumbbells are really shaped like that.

Â But thinking about weights that you're lifting up.

Â So we've got the px, which is oriented along the x axis.

Â Well there's three of these, so the other one would be the py,

Â would be oriented along the y axis, and pz, where it's oriented along the z axis.

Â So those are your three orientations of space of those three orbitals.

Â Now you need to understand that these are overlapping each other.

Â So let's look at this space down here in the bottom right hand corner.

Â And we will overlap these orbitals the way they really are.

Â You've got an orbital along the x axis.

Â You've got an orbital along the y axis.

Â And you've got one coming up and below the axis along the z axis.

Â So those are the three orbitals overlapping their space.

Â 3:23

So if an electron has the right values of m, l and m sub l,

Â they would be located in, you know, maybe this ori, orientation.

Â They'd be the x ax, the xp orbital.

Â We call it p sub x, okay?

Â 3:42

Now there is also, you know, overlapping all of this space, an s orbital.

Â So this might be the 2s.

Â It is the 2s orbital.

Â This would be the 2px, the 2py and the 2pz.

Â And the electrons move about in their space where they will have

Â a high probability, but there's a lot of overlapping space that they are occupying.

Â 4:08

Let's move on to the ds.

Â Now when l is equal to d, to 2, we are talking about d subshell.

Â That is the d subshell.

Â These define the five orientations in space.

Â The five different ways that you will find these orbitals.

Â So let's look at each one of them.

Â This is the dyz.

Â We have got our, lobes in-between the y and the z axes.

Â M'kay, so look at your y and your z,

Â and we see that those lobes are in between those axes.

Â And we are representing that over here in that more solid shape look.

Â 4:46

Now we see areas where you have nothing.

Â Okay, there's nothing here.

Â There's nothing here.

Â There's no probability of finding those electrons, okay.

Â We can kind of draw a little plane right there, a little plane right here.

Â Here you're not going to find the electrons.

Â There's a very low probability of finding those, actually, it's where the probably

Â for electron density, according to the equations, drops all the way to zero.

Â So don't think that this is an orbital.

Â That's not the orbital.

Â The whole thing is the orbital.

Â And an electron can move about anywhere in that space if it's

Â got the right energy to be located in that orbital.

Â 5:24

Somehow it travels about this orbital without occupying the spaces in between.

Â Or at least, according to the equations, the probability drops down to 0.

Â Now, that's one.

Â Here is the other one.

Â This is the second one.

Â We have the dxz.

Â Now I don't expect you to learn those numbers,

Â those letters associated with them, but

Â the dxz is like the yz except that it is in between the node, the planes.

Â It's on the xz plane as we see here.

Â The next one is the dxy.

Â Now this picture is not very good, because it is showing them on the axes, and

Â they should actually in, be in between the axes, okay?

Â So don't focus on this.

Â We see the axes running through here, and those are in between them.

Â 6:12

Then there is this one.

Â It's very, very similar to the dxy.

Â It's called the x squared minus y squared but

Â those nodes, lobes are actually located on the x and y planes.

Â Okay, so you actually see them there on those planes.

Â I mean, on the axes.

Â So those are the first four.

Â You ought to recognize a d orbital when you see one.

Â So when you see these four lobes like this, as opposed the two lobes of the p

Â orbital, you see these four lobes you know it's a d orbital.

Â But there's one oddball, and this oddball is called the dz squared.

Â It's along the z axis.

Â It has no nodal plane associated with it at all, that is the dz squared.

Â So there's the five orbitals that are the d orbitals.

Â 7:00

Let's look at the f orbitals.

Â When l equals 3 we know that the m sub l's are negative 3 up to a positive 3.

Â There are seven numbers so that means there are seven orientations in space.

Â I'm going to pop all seven up here at once.

Â Four of them look very similar.

Â They have these eight lobes associated with them just oriented differently amou,

Â among the axis.

Â Three of them have this, a different shape along the x, y, and z plane.

Â It's kind of similar to our oddball d orbital except there is

Â a nodal plane between them so in between them, the axis we can

Â see that there is a nodal plane separating the two halves from each other.

Â And those are your seven f orbitals.

Â So I expect you to recognize an orbital if you were to see a picture of that orbital.

Â 7:58

And if you were to have a two dimensional wave, okay,

Â that wave could be above the plane like we see here, and it would have a plus sign.

Â If you have a node in that, and there's a node where it's zero, you

Â can have above and below, of the plane, and so we'd have a plus and a minus.

Â Well, a three dimensional wave would have that very similar thing.

Â So you're going to see when you've got these multi lobes,

Â you might see pictures in the future in which you see multi colors.

Â Those signs may come into play when we start bringing orbitals together to

Â make bonds between atoms.

Â But for now, just know that they do have those signs associated with them, and

Â we don't need to really worry about those signs at this time.

Â I want you to be familiar with the shapes of the various orbitals.

Â And so I'm going to show them to you and move them about so

Â you can see them from different vantage points.

Â You have them in your notes and

Â you can look at them there, but this is an s orbital.

Â It's a sphere, there's only one orientation of a sphere, and

Â we know from the m sub l value that there's only one s orbital.

Â The next one is the p.

Â 9:06

And because of our m sub l's, we have three of them, negative 1, 0, and

Â 1, there are three orientations of the p orbital.

Â And here they are, so we have one along the x axis,

Â we have one along the y axis, and one along the z axis.

Â Now which one's which, I don't know, they usually call this one the z axis.

Â But we see that we have them in the, the three orientations.

Â Now these you need to imagine, in an atom, are actually all over top of each other so

Â they exist in the same, on the same axis, but there are three of them and

Â that's what a p orbital looks like.

Â So these are our five d orbitals, and we know that n sub l gives us five

Â different values for the d subshell, and this is how they're oriented.

Â So four of them look very similar.

Â They have these four lobes that we see here.

Â In the x-y plane, these two are different in that these are between the axes,

Â and this is on the axes, so we see that being different here.

Â This is along the x-z plane, and they're perpendicular to each other, so

Â that's four of them.

Â The fifth one is very unusual.

Â It doesn't look like any of the others.

Â Now remember, the mathematical equations,

Â the SchrÃ¶dinger equations are what define these shapes.

Â And so with the right quantum numbers, you end up with this three-dimensional shape.

Â So the five d orbitals are four of them that look very similar with

Â the four lobes, and then the fifth one which is very different.

Â 10:42

There are four that are similar and

Â then three others that have a similar look to each other.

Â These first four here have eight lobes associated with it,

Â so you'll recognize them by their eight lobes.

Â And they're just a little bit oriented.

Â In the x-y-z plane of, a little different from each other.

Â So that's the four that look similar.

Â And then we have the other three.

Â And these other three kind of remind me of the d in that they have, the,

Â well, it's just a similar shape, but there is a no plane between the two sides here.

Â And so this is what the remaining three f orbitals look like, and

Â they're arranged along the x, y,

Â and z plane like we saw the p orbitals aligned along the x, y, and z plane.

Â So remember with the f orbitals, we have got seven, because we would,

Â m sub l values gives me seven values for the f subshell.

Â And four of them have got the eight lobes, and then we have this general shape here.

Â 11:46

Now we've got a couple diagrams here.

Â I want to focus on the left-hand side for right now.

Â This is what the hydrogen atom would be.

Â So we have the 1s orbital.

Â Okay, now what is that, that we're in the first, we're in the first shell.

Â The one.

Â There is one orbital, in the,

Â I mean there's one shell, it's called the s subshell.

Â It has one orbital, and I've represented that orbital with a line.

Â In a hydrogen atom when you go to the second shell,

Â it's higher in energy, there exists the s and the p subshell in there.

Â And there's the orbitals of the s and the p.

Â Then we move up from there.

Â It's not quite a big a climb as from one to two as you go from two to three.

Â In the third shell there's the s orbital, the p orbital, and the d orbitals.

Â There's one s, there are three p orbitals, and there are five d orbitals, and

Â those are represented by the lines.

Â Then we move a little further up in energy, and we have our s, our p, our d,

Â and there are fs, and how many fs would there be?

Â There would be seven of them, so I could draw seven lines out here beyond this, but

Â I ran out of space and I didn't draw the lines, okay?

Â So there does exist the 4f orbitals as well, and

Â they'd be seven lines associated with them.

Â But in the hydrogen atom, where we only have one electron,

Â 13:21

And this is why hydrogen is so much easier.

Â And when we did the electrons, calculations and

Â we did them for hydrogen atoms, we had nice, simple equations.

Â As we move over to the right side of this page,

Â we see that we're dealing with an elec, a multi-electron atom.

Â As soon as you put a second electron in there, because their spins in a,

Â their interactions of their spins the orbitals don't stay, all of them,

Â the dinner, within a shell.

Â What happens is, the p's raise and have higher energy then the s's have.

Â 13:58

And the d's are higher then the p's, so here's a 3s.

Â The 3p is a little bit higher.

Â The 3d is higher yet.

Â Then we have a the force, we have the s, the p, the d, and

Â then the f's would be way up high, somewhere up here, and we'd have the 4f's.

Â So they spread out.

Â Now within a shell, I mean a subshell, okay there's the 2p subshell.

Â Within a 2p subshell, all the orbitals have exactly the same energy.

Â They're degenerate.

Â 14:33

Okay, they have exactly the same energy within a sub-level.

Â But you don't keep the energies within the level all the same.

Â So as soon as you put two electrons in there, as soon as there is more than one,

Â then the energy of the s orbitals will be lower than the energy of

Â the p orbitals of a subshell, which is lower than a d, which is lower than the f.

Â And we have this spreading that occurs.

Â So eventually we need to start putting electrons into these orbitals and

Â assigning them their location in an atom.

Â And that's what our next learning objective would be.

Â But for now we've seen what they look like and

Â we've seen their energies from the lowest energy up to the highest energy.

Â Both within the, let me change the color of my pen.

Â So both within a shell we see that we're going from a 1s.

Â Higher in energy are the twos, higher in the energy are the threes.

Â And then we see also within the actual sub-levels,

Â that we have this increasing of energy from s to p and p to d.

Â Okay, we'll keep that in mind as we move forward to our next learning objectives.

Â