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Professor Cima: So now what do the wave functions look like?
So I hope you've all-- this is probably a review for you.
When l equals 0, we have what's called an s orbital.
But that means I could have n equals 1, n equals 2, n equals 3.
All of those principle quantum numbers have associated with them an l equals
zero state. All of these guys right here.
And this is what they look like. So this is the 1s, the 2s, the 3s.
What you can see is is that they get bigger. Well, r sub n, it's getting bigger.
But the more interesting thing is, if you look in these wave functions-- so
this is a probability density map. If you look inside here, you get more nodes.
So here's the radial. If I start at the center and move outwards
and plot the probability density of finding an electron, you see one
s that looks like this. 2s, it looks like that.
The 3s, it looks like that. You get these places radially where the electron
could never be. Somehow, it goes from here to there without
being in between. And as n gets bigger, the number of nodes
increases just like the particle in a box.
If I go to the l equals 1, you've all seen this before.
l equals 1 is this p orbital. And here they all are.
They have different magnetic quantum numbers now.
But all that's different amongst them is their orientation, right?
The projection of the angular momentum on the z-axis changes as I change the
direction of the orbital. And the same thing with the d orbitals.
You've all seen this before. Now I have five different magnetic quantum
numbers possible. l equals 2 is the d orbital.
Five different magnetic quantum numbers possible because they got to
go from minus 2 to plus 2 in energetic time. There they are.
Now, the last thing I want to leave you with is this figure.
These are the radial distribution functions for the s.
So you saw that in the first one. You saw that in the slide or two ago.
Here's the p, and here's the d. So this is the probability as a function of
distance from the nucleus of finding an electron in each of these orbitals.
And this is a very important graph for you to study over the weekend.
And the reason why I say that is look very carefully here.
If I'm in the 2s orbital or I'm in the 2p orbital, I have this probability in
the 2s of finding the electron very close to the nucleus.
That doesn't exist in the 2p orbital. In a single electron atom, they have exactly
the same energy. They are degenerate.
But as we'll see, when we start adding new electrons, this difference in
probability of finding the electron near the nucleus plays a significant
role in the multielectron atom.