How Do You Calculate Atomic Orbital Energy?

You might’ve heard about what an atomic orbital is in your chemistry class.

If you need a refresher, an atomic orbital is a mathematical term used in quantum mechanics that can describe the position and wavelike behavior of an electron in an atom.

In this video, you’ll learn how to calculate atomic orbital energy using the periodic table.

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Video Transcript

Now we’re gonna tie together orbitals with the periodic table. This is okay. I keep saying is this is my favorite. Okay. Everything’s my favorite line. <laugh> but this whole idea that we have electrons that are in the orbitals and that the orbital are shaped in a certain way. And these electrons in these orbitals, they also have energies that differ from each other in predictable ways. And I wanna draw up here. It’s a, it’s a type of pneumonic device.

I don’t don’t know if pneumonics the right word for it, but, um, it’s one method. Some people use to remember which orbitals are lower in energy versus other orbitals. But I want to, I wanna challenge this, this technique. I’m gonna show you in a second, um, with just using the PR table. So let’s do that. How was everyone, did you have a good break?

Okay. So here we go. Orbital, we just saw that if we’re gonna be talking about electron in specific orbital, we give the principle quantum number and then we give what type of orbital it is. And so if we look at the lowest energy possible orbital, there is, it’s a one orbitals that’s where principle quad number N equals one and L equals zero.

So in terms of, again, thinking about the bore model of the atom and other ideas like that, that’s gonna be the lowest energy orbital. So I’m gonna draw this at the bottom. If we think about this in terms of high energy being up here, lower energy down here, one as orbital is there.

There are no other possible orbitals that exist where N equals one because of what we just talked about with the rules of quantum mechanics, and that L can only equal zero when N equals one. So there’s one S orbitals and that’s it.

There’s no one P orbitals or one D orbitals or anything like that because of that rule. So that means that the next possible orbital that there is, is the two S orbital. So we’re gonna put that, that is higher in energy than the one S orbital. I’m going to move this ever so slightly like camera over. Okay.

So two orbital, little bit higher in energy than the one else. Are there two P orbitals that exist? That would be N equals two. And if L equals one giving a P orbital, yes, those do exist again, based on those rules of quantum mechanics. So there are two P orbitals.

So energy wise, there are gonna be, at least for hydrogen, they’re gonna be in the same level. So I’ll just draw ’em like that. And then we’re done, there’s no two, two deep orbitals for those reasons we mentioned before. And so this pattern follows, uh, now that we have principle quantum number three, we now are allowed to have L equals two, which is a de orbital. And then when we get to four, we have all four of them as orbitals, P, D, and F are now all allowed four S four P four D and four F.

And if we continue on from here, we’re just gonna stop at F orbitals again, because G orbitals are not seen in practice. Okay. So four S now we have five S so I’ll fill this out. Five P five D five F six S six, P 66 F. And I think I will stop there. Okay. So there is a trick you can use it sometimes called the diagonal rule, where once you have draw all these orbital up like this, you can now draw diagonal lines in this way.

You start down at the bottom and you draw it going up like that, and diagonal, diagonal, diagonal. And you might be wondering why the heck do I wanna do this?

And I’ll tell you why. Okay. It goes on from there is that this is the order of the energy of orbitals that exists in the universe. This is the, or this is the orbital energy order for any, any atom that isn’t hydrogen, just a hydrogen atom by itself. Okay.

Hydrogen atom floating around by itself. Pretty rare in nature. You can see them up cosmic rays and, and in labs and things like that. But for all intensives purposes for everyday life, following this order is telling us the energy of those electrons of all the, in all the possible orbitals. So this let’s see what this would, um, what this would tell us.

So that means that, one S orbital lowest energy followed by two S followed two P followed by three S followed by three P. So there’s nothing too wild or unexpected happening yet.

But look at this, the energy of a three P orbital is followed by four S and then we go back to 3d. And so now we’re out of order and then to four P then five ass, so five inserts itself, and then we go back and there’s four again.

So you can see that there’s this MIS mash, mashing up of order. That’s, that’s seemingly really hard to predict. And so that is why it is taught to write out this order in this way, and then draw these diagonal lines. And then you are able to compare different orbital energies to each other. Okay. Uh, why would you wanna do, what is an example of why you would even ever want to do this? Okay.

This is, if you were trying to figure out, given an element, where are the electrons, how many electrons are there and where are they in? What orbitals are they? So let’s use carbon, for example. Okay. So looking at a carbon atom, where are those electrons?

So carbon, how many electrons does carbon have? Okay. If you’re like off the top of my head, I don’t know. Um, so you could just always grab your handy Dany periodic table and take a Gander and find carbon. And then you would say, all right, carbon element six. So there are six protons. If it’s neutral, there are six electrons. All right. So we can start out there and we say, all right, carbon six electrons.

And now you’re trying to designate where the heck are those electrons? Okay, well, electrons are always going to start out and will exist in the lowest energy orbitals that are available.

They’re not gonna be hanging out at high energy orbitals. All of nature will go towards spontaneously, go towards the lowest possible energy configuration. And that’s what electrons do. Naturally. They will fall down into the lower level orbitals. So that means that we will have

Two electrons in a ones, orbital, each orbital is allowed to hold two electrons. So this ones, orbital, we could designate that. How well is this purple coming? Ah, that’s pretty good. Okay. So the one S orbital is allowed to have two electrons in it. And so we can designate that with a super script. Okay. So that takes care of two of the electrons, but there are six total. So what’s next.

We look here, there’s a two S ORs the next highest in energy. And so we can write that here. Two S and then once again, in this two S orbital two electrons are allowed. And so we put them in there and now the two S orbital is full and we go to the next highest energy. Okay. So after the two S now we go to the two P and we can put in the two remaining electrons in carbon into the poral. All right. So this is what we call electron configuration.

All right. Electron configuration telling us where those electrons are. We are also going to be drawing out the orbital energy diagrams, but I wanna show this because I wanna now tie this in with the periodic table and show you what is happening. Okay. So I wanna make sure that this at least, uh, the important parts, which is essentially, um, up here, um, that we can see it. Okay.

So when we think about carbon and that it has these six electrons, we can essentially start with hydrogen and do kind of accounting. And we can see where are those electrons? And knowing that hydrogen has one electron, and that the one S orbital is lowest in energy. And so that means that the hydrogen, that one electron is in L one S orbital, and then we have helium helium. Now has two electrons, neutral helium. We’re gonna just be talking about neutral atoms here.

Um, it’s got two. And so that second electron will go in the one S orbital. And then we can come over here to lithium lithium one S orbitals full. So now we’re in the two, we are now filling the two S orbital here. And then we look at beum and we still have one more space. And the two S orbital, and then that gets filled. And then we come to boron.

The one S is filled, the two S is filled. Now we are beginning to fill the P orbitals, those two P orbitals. Now notice here, how there are six elements across how many P orbitals are there? How many different configurations of PBIS are there different orientations? We saw that there are three at MSL minus one, zero plus one. That was one of my questions for land ail that you answered, right? So there are three different orientations.

There are three different P orbitals and each P orbital can hold two electrons, two to two. That’s a total of 6 1, 2, 3, 4, 5, 6, not a coincidence. Okay. So right here, all these elements are filling the two P orbitals. These elements are filling the one S orbital. These are filling the two S orbital. These are filling the three S four S five S six S seven S. So we call these two and they’re really, um, I would say formally helium should be over here, but it’s just moved over there because it’s so inert.

And it acts like a noble gas. I mean, it is a noble gas. Um, so that’s why it’s over there. But in what we’re talking about, these, all of these elements, their last electrons to be added are all being put into the S orbitals. So this year is called the S block because those last electrons to the editor in the S orbitals over here, all these orbit, all these elements that are here, that are in this block, that’s showing that six across because we have three P orbitals, two electrons, each six, all these are filling the two P in this row or in this period, I should say, in this period, we’re filling the three S I just said, S <laugh>, let me start over.

These are filling the two P orbitals, the three P the four P the five P the six P. Okay. So the periodic table is lining up with what is being filled. First. What’s being filled first. It’s always the lowest energy orbital. Okay. Let me add one more thing in here, cuz we are just looking at carbon was our example. And so far we’ve only talked about the two S and the two P in terms of tying it in with the pure act table. What about the three D orbitals? So remember there aren’t one D orbitals don’t exist.

Two D orbitals don’t exist. Three D is the first orbital that can exist. That is a D orbital. It’s gotta be three D okay. Following all of our rules of quantum numbers and those start getting filled right here. So scandium always next to calcium because after calcium exists with its 20 protons and its 20 electrons, and they’ve just filled the four S orbitals then comes the element scandium is where we now put an electron for the first time into a D orbital into that 3d orbital.

So we’ve seen one S two S three S four S we see on the periodic table, the four S orbital is filled first followed by 3d. It shows it’s right here on the periodic table.

It shows us we don’t need to dry all this mumbo jumbo and go like, oh, four S is filled before 3d. Oh, I better memorize that. No, you just need a periodic table. It’s all there for you. Is that amazing? Periodic table. All right. Four S 3d. Okay. Let’s look at the, the, the 3d period right across here. How many are there?

I’m gonna block it so you can’t count. Okay. How many should there be? How many de orbitals were there? De orbitals L equals two. So what can SAB L equal Bel gives you the orientation and if L equals two, then Bel can equal minus two, minus one, zero plus one plus two. How many is that? Five? There are five D orbitals. So how many electrons can fill those five D orbitals 2, 4, 6, 8, 10?

There are ten one, two three four five seven, eight, nine, ten. Yes. That is where that comes from. So we have just filled up, remember one S two S three S four S and then 3d. And then what’s this. When we get to gallium, what orbital are we filling?

Two P three P four P. So we went from four S 3d to four P, but again, it’s all here on the par table. We didn’t need to do that thing. Okay. And then we go back to here now and, and we would follow the rules. Now, when you get Tolan, you might be like, oh, no. Now what do I do? There’s this double asterisk. <laugh> what’s happening.

This is where we have to jump from here and then go down to here, double asterisk, double asterisks. And the only reason why this isn’t just inserted into the periodic table is because we are a society that lives with either, depending on where you live eight and a half by 11 inch sheets of paper that are either vertical or horizontal, horizontal for a pair table. Um, or there’s the a four size that’s used in your European countries and other countries.

Okay. So we are, we are essentially, we confine ourselves in certain shapes, not these really long banners. Now, if you wanted to include the F orbital elements here, these lanthanide and actinides and insert them into here, you would end up with a pure act table. That was just really long. It’s not a big deal. It’s not a problem.

It would just be really inconvenient for textbooks and for posters like this, et cetera. So that’s the reason why we have everyone jump from and use little asterisks, go, Hey, go down there. Um, element 57 element 58, 59. And so, as long as we’re, we’re just paying attention. When we get down into that realm, then once again, we can see what is the orbital energy of filling? Where are those electrons going to go? Okay.

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