So let's go back down here.

So you might say well the the Y one at

zero one corresponds to p zed orbital you're all familiar with.

And it's it's natural to say, well, do these correspond to p x and p y orbitals.

And they do, but it's not, they're not simply derived from them.

What you have to do is the p x and the p y are actually combinations of these two.

The p x is the addition combination.

So if you do y minus 1 1.

So let's, let's, let's write that down.

So you have the p x is Y 1 minus

1, plus Y 1 plus 1.

And the the p y is the difference between them, so

that would be the Y 1 minus 1 minus the Y 1 plus 1.

And I am not going to go into it, but

to show that and it's not that difficult to show it

you need to be familiar, or you need to know,

that this e to the i phi is this Euler's relationship.

Let's put it down here.

So Euler's relationship says that e,

say to the plus or minus i phi, that's equal to

cosine of phi and then plus or minus i sine of phi.

So, if you expand them that way, you should be able, or you would

be able to show that the p x actually corresponds to the addition,

and the p y corresponds to the to the subtracting the two.

So as I say, you can do that perhaps as an exercise.

I'm not going to develop it here.

But hopefully this little snippet has has shown you if you like, the origin

of the shapes that you, you see for orbitals in general chemistry textbooks.

And you can explain how the, how the s-orbital shape comes along,

and you can also explain how the p z orbital shape comes along.

And for some of you should also be able to probably work out the p x and the p y

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