0:00

We are ready for learning objective number seven.

Â And in this learning objective,

Â we're going to be examining, the Schrodinger Equation results.

Â We won't look at the equations themselves, but

Â we're going to be looking at quantum numbers.

Â And we're going to see how these quantum lum, numbers tell us

Â information about where the electron is located, and how much energy it has.

Â As well as what the electron is doing, how it spins.

Â So we're going to be examining quantum numbers.

Â 0:29

So those complex mathematical equations that define the regions in space,

Â that define the orbitals, have these four quantum numbers.

Â There's a principal quantum number n.

Â The angular momentum quantum number l.

Â Magnetic quantum number m sub l.

Â And the spin quantum number m sub s.

Â Now as we go through and we are examining these four quantum numbers,

Â I will use addresses as an analogy for what I'm talking about.

Â We use addresses that define where we live, and

Â we can get more and more pec, specific with where we live, with the address.

Â The first address might be what country you live in.

Â 1:12

And then maybe you're into a state, or, and then narrow it down to a city, and

Â then a street address.

Â Or maybe we could think about a college campus, as a, a broad address.

Â And then you could talk about what dormitory you live in,

Â and then you could narrow it down to what room, what is your room number.

Â And so the first three quantum numbers are giving us the address, getting more and

Â more specific of where the location of that electron is.

Â Now, the fourth quantum number, the spin is, it's, spin quantum number is,

Â what is that electron doing?

Â The electron is spinning and it can spin one clockwise or counterclockwise.

Â And so I, you see, statements that the first three tell me where it is,

Â and the fourth tells me what it's doing.

Â So we're going to be examining those locations as we go through these four

Â quantum numbers.

Â 2:02

Let's begin with the first principle quantum number, n.

Â These values of n can go from n equals 1 up to larger and

Â larger values by whole numbers, integral, integer steps.

Â One is the smallest.

Â This is a number we saw with Bohr's model, he called his orbits by these numbers,

Â n equals 1, n equals 2, n equals 3 and so forth.

Â And the farther away you got, the higher the n.

Â 2:39

So the larger the value of n, the further away the electron is.

Â So if n equals 1 it's close by, nearer the nucleus.

Â And if n equals 2,

Â they're a little farther away, n equals 3, they're a little farther away yet.

Â Now, the farther away the electron is, the higher the energy of that electron.

Â So as, as n gets larger,

Â the value of the energy of that electron gets higher as well.

Â 3:10

So all electrons with the same n value are in the same principal shell.

Â So if n equals 1, every electron that has n equals 1 lives in the same shell,

Â called shell n equals 1, okay.

Â Principal energy level 1.

Â Then we can move further away, we have any electron that's located in

Â principle energy level with an n equals 2, we say they're in the same shell.

Â 3:37

Now, for a hydrogen atom, okay, this mathematical equation applies.

Â If n equals 1, we are located down here and

Â the electron has this amount of energy down here, 'kay.

Â So if an electron was sitting here, we would have this much energy.

Â If n equals 2, it's a little further away, electron is located here and n equals 2.

Â Or we could have the electron in the n equals 3.

Â Now, in hydrogen, thereâ€™s only one electron.

Â But if the electrons are located in these different energy levels,

Â they would have this amount of energy.

Â And that energy can be, be defined by this equation, what we see here.

Â The energy, and this is the energy of the electron,

Â 4:23

is equal to the Rydberg constant, R sub H times 1 over n squared.

Â Now, the value of the R sub H is 2.18 times 10 to the minus 18,

Â and let me get the word out of the way here for you.

Â 10 to the minus 18 joules, and if you

Â take that value times 1 over n squared, you would have the energy of the electron.

Â Now we have to have a minus sign here.

Â Let me def, talk about that a little bit.

Â It seems weird to have a negative energy.

Â As we move further and further away, the value is getting less and

Â less negative, but it is growing in magnitude.

Â 5:04

Eventually, you would get up here to where a value of E, the energy, is equal to 0.

Â Now, at that point, you have just disconnected the electron

Â from the atom and it is not moving, it has no movement to it.

Â But as soon as the electron starts moving, then it's going to have

Â energy associated with its kinetic energy there, and its energy will grow above.

Â So any time an energy is a positive value for

Â electrons, that means it's not associated with an atom.

Â Any time it's a negative value, it's associated with an atom, and

Â as it gets closer and

Â closer to the ne, to the nucleus, it has a smaller and smaller energy.

Â 5:51

Okay. All right.

Â Now this Rydberg constant in this equation,

Â you must understand only applies to a hydrogen atom.

Â It doesn't apply to anything else, only a hydrogen atom.

Â It's a much more complex equation and

Â solution once you put more than one electron in

Â there because of the interaction the electrons have with each other.

Â 6:57

All electrons that have the same n and l value.

Â Okay, so you have an electron and you tag it.

Â You say this is where you live.

Â Okay, n and l, and eventually n sub l.

Â For every electron that has the same n and

Â l value, we say that they are in the same subshell.

Â So if I had one electron that had an n of 2 and an l of 1,

Â and I had another electron that had an l, n of 2.

Â Let me write that down, n of 2, and an l equal to 1.

Â So I have one electron with that established locator, and

Â I have another electron with that established locator.

Â We would say those two electrons are in the same subshell.

Â 7:56

If an l equals 0, the name of that subshell is s.

Â If l equals 1 the name is p.

Â 2 is d, 3 is f, and

Â after that, they go alphabetically, g, h, i, j, k, l, so forth.

Â You will, as we work through these, not see anything above an f.

Â But they do exist beyond that.

Â 8:19

So these are the names.

Â So what we would say is, let's say we again have

Â this electron with an n equal to 2 and an l equal to 1.

Â Well since the l is equal to 1,

Â that's called a p subshell, and the p sub, we would say that the electron,

Â if the n equals 2 and l equals 1, are in the 2p subshell.

Â 8:42

All electrons that have n equals 2 and l equals 1 are in the subshell called 2p.

Â If I had another set of electrons where the n equals 3 and

Â the l equals 1, then we would say that those are in the 3p subshell.

Â So all electrons that have the same n and l are in the same subshell.

Â 9:20

So each principal level has its own allowable values of l,

Â because that l can only go up to n minus 1.

Â You can't have every subshell in every shell, in other words.

Â So let's look at the possibilities here.

Â In the shell n equals 4, what are the names of the subshells it has?

Â Now I want you to stop for just a moment after I do this explanation.

Â And I want you to think about this.

Â If n equals 4, the question is, what are the values of l?

Â Go back and look at how l relates to n.

Â And once you've done that,

Â associate names with those, and then choose the right answer.

Â Pause and resume when you think you know the answer.

Â 10:10

Did you pick 4?

Â Well, if you did, that is correct.

Â Now, why is that correct?

Â Let's make sure we're all on board here.

Â If n equals 4, than we know that l can be 0 up to 1 less than that.

Â So these are the values of l.

Â 10:27

If these are the values of l, this is an s, this is a p,

Â this is a d, and this is an f, so those, that doesn't look like an f.

Â Let's try that again.

Â This is an f.

Â So those are the four subshells that are in the n equals 4 shell.

Â So we would call this subshell 4s.

Â We would call this one 4p.

Â This one would be 4d, and this one would be 4f.

Â Those are the four subshells in the fourth shell of any atom.

Â 11:23

Now what this piece of information,

Â it finally gets us down to the actual orbital the electron is in.

Â Remember, the principle quantum number n,

Â tells you that general distance away from the nucleus.

Â 11:51

Now this is going to give you basically the orientation in space.

Â So the l gave us the general shape and the m sub l is going to say,

Â okay, how is that in space for that orbital?

Â We're going to see that here in just a little bit, but let's con,

Â do our connections.

Â All electrons with the same n, l, and m sub l are said to be in the same orbital.

Â 12:15

So the n is telling you which shell the electron is in.

Â The l is saying, this is the subshell it's in, and now the m sub l says,

Â I have narrowed it down to which exact orbital the electron is in.

Â 12:31

So we're going to stop here now that we've seen these three quantum numbers n, l,

Â and m sub l,

Â and we're going to divine, derive all the possible quantum numbers in a table.

Â We're just seeing connections and then we will go and actually look at these shapes.

Â 12:51

The smallest n, is an n equals 1.

Â Now we know that l can go from zero up to n minus 1.

Â So what are the possibilities for l when n equals 1?

Â Well, 0 is certainly is one, okay?

Â So we have 0, can we go any further?

Â Well, n minus 1 is 0.

Â So that's as far as we can go.

Â 13:14

Now that would be called an s subshell.

Â So we would be in the 1s subshell if an electron had an n equals 1 and

Â an l equals 0.

Â We would be in the 1s subshell.

Â Let's go to the orbitals.

Â What are the quantum numbers m sub l?

Â Now we know that m sub l will go from a negative l

Â by integral numbers up to a positive l.

Â 13:40

Well, if l is 0, I have one choice.

Â Now when I see that number,

Â what it tells me is the number of orbitals that are in the 1s subshell.

Â It doesn't mean that there are zero orbitals, but

Â however many numbers I see here, is how many orbitals.

Â Now, I see one number sitting there, so there is one orbital in the 1s subshell.

Â And we are done.

Â So let us think about what we have just derived.

Â What we have said here is that if we are in the first shell, where n equals 1,

Â there is only one subshell, and that subshell is called the 1s subshell.

Â 14:23

And in that subshell, there's only one orbital, and it's called the 1s orbital.

Â Because they're named the same as their subshell.

Â So this is one orbital.

Â It's called a 1s orbital, and that's it.

Â That's all that's in that first shell.

Â So it's a very, very, very small city.

Â Let's move out.

Â 14:46

Let's move out a little further away.

Â So now let's go to n equals 2.

Â If n equals 2, what can l be?

Â Well, l goes from 0 up to, and let me do it this way.

Â 15:08

This would be called a 2s subshell.

Â This would be called a 2 what?

Â Well it would be a p because when l equals 1, it's a p.

Â So those are the two subshells that you have in this shell.

Â So in the second shell, there's only two subshells, so this is a 2s and

Â the 2p subshell.

Â Now, let's move over to the values of n sub l.

Â For l equals 0, we know that we have only this one.

Â So there's one orbital again, it's called the 2s orbital.

Â And then we move to the p value.

Â The p, when l equals 1, we have from a negative 1 up to a positive 1.

Â So we have negative 1, 0, and 1.

Â Now, how many orbitals do you see there?

Â There are three numbers.

Â Those three numbers tell me that there are three orbitals in this subshell.

Â And they are called the 3p orbitals.

Â I'm sorry.

Â 16:09

Three orbitals are called the 2p orbitals.

Â So I have three of them.

Â So their names of the orbitals are the same as the names of the shell, and

Â let's just think about the second shell for a second.

Â We've come out from the n equals 1, we've moved a little further away.

Â So we're a little further away out here.

Â This is the second shell.

Â In this second shell, there's two subshells.

Â There's the s and there's the p, okay?

Â The s subshell only has one orbital.

Â It's called a 2s orbital.

Â The p subshell has three orbitals, okay.

Â They're each called 2p.

Â They're oriented and spaced differently.

Â We'll see that in a little bit here, but those are the three p orbitals, 'kay?

Â By three, I mean there's three of them.

Â There's three orbitals, each orbital is called a 2p.

Â Now at any time that you're not catching it, back up and

Â listen to it again, because this is important that you see these connections.

Â So, we've gone from the one, first shell to the second shell.

Â Now we're ready to move out to the third shell.

Â The third distance away from the nucleus.

Â Let's do the values of l.

Â L will go from 0 up to n minus 1.

Â So we have 0, we have 1 and we would have 2.

Â 'Kay?

Â So we are going through now,

Â we've done the first shell, the second shell, the third shell.

Â In the third shell, you would have a 3s,

Â you would have a 3p and you would have a 3d subshell.

Â 17:50

In the 3p subshell you would go from a negative 1, 0 and 1.

Â You would have three orbitals there.

Â Now, let's move out to the d, this is the d subshell.

Â We would go from a negative 2, up to a positive 2.

Â So we would negative 2, negative 1, 0, 1, and 2.

Â How many numbers do you see there?

Â There are five numbers.

Â That tells me that we have five d orbitals in a d subshell.

Â Now this is always true.

Â If you're in a d subshell,

Â there will be five orbitals, because we see five numbers.

Â 18:29

So this third shell is bigger than the second shell.

Â It has three subshells, and how many orbitals total does it have?

Â It hs one, two, three, four, five, six,

Â seven, eight, nine total orbitals in that third shell.

Â 18:47

'Kay, we can move out a little further yet.

Â Let's go to the n equals 4.

Â In the n equals 4, we're going to have 0, 1, 2 and 3 for our l values.

Â That tells me I have a 4s subshell, a 4p subshell,

Â a 4d subshell, and a 4f subshell.

Â Those are the subshells that are in the fourth shell.

Â 19:15

Now let's look at the orbitals.

Â When l is 0, we have one number.

Â When l is 1, we have three numbers.

Â When l is 2, we have five numbers.

Â 19:30

Now, what do we have equal, if l is 3?

Â Well, we can have an n sub l of a negative 3, negative 2, negative 1, 0, 1, and 2.

Â We have all of those values.

Â 19:46

So, that tells me that there are one, oops.

Â Gotta get one more.

Â One, two, three, four, five, six, seven.

Â There are seven orbitals here.

Â 'Kay, so we have in the f subshell, there are seven orbitals.

Â So that is the co, all the connections between the quantum numbers.

Â Now you should be able to keep going further away from that.

Â But let's just, just think about what these numbers.

Â Each, each electron in an atom would have these four quantum numbers assigned to it.

Â It would have an n, an l, and an m sub l assigned to it.

Â Those four quantum numbers would say, this is where the electron lives.

Â 20:32

So lets just pick for quantum numbers that can exist.

Â Can an electron have an n equals 2, all right.

Â An l equals 1, that doesn't look like an n equals 2.

Â Lets try this, can an electron have an n equals 2,

Â an l equal 1 and an m sub l equal to 0?

Â Well, let's see.

Â N equals 2, you can have an l equals 1, and you can, oops, there's 1,

Â you can have an l equals 1, and you could have an n sub l equal to 0.

Â So an electron can have those three quantum numbers, and

Â when you know those three quantum numbers, you know that the electron lives in

Â an orbital of the p subshell in the second shell.

Â 21:32

If n equals 2, can you have an l equals 2?

Â No, because you can only have a 0 and a 1.

Â So, there is no electron that's going to have that set of quantum numbers.

Â There is no electron that can live in

Â a 2d because there's no such thing as a 2d subshell.

Â 22:56

Then the m sub l can only be ze, negative 1, 0 and 1.

Â It cannot be a negative 2.

Â So there's the problem with that one.

Â So you need to know what's allowed and what's not allowed,

Â based upon the connections between n, l and m sub l, okay?

Â So if you've had an electron, and you knew this electron was in the 4p subshell,

Â 23:35

So we see that the right answer is, both 2 and 3, and so

Â if you picked that, you were correct.

Â Let's examine why that would be.

Â This number here tells you n.

Â This number tells you l, 'kay?

Â So we know that n has to be 4.

Â So all of those have an n of 4.

Â We can't narrow any down there.

Â But if l, if it's a p subshell, we know that when l is 0, that's an s.

Â When l is 1, that's a p.

Â So l has to be 1.

Â So that's this guy and this guy.

Â The question is, are those allowable n sub l's for that l?

Â Well, if l equals 1, we know that n sub l could be negative 1, 0, or 1.

Â So either one of these would be fine.

Â There would be one other one that would have been okay to write, and

Â that would be 4, 1, and 1.

Â That would be fine as well.

Â The electron could have that address.

Â So, any one of those values would be acceptable for

Â an electron in a 4p subshell.

Â 24:43

'Kay, so, this is the end of Learning Objective number seven.

Â We've examined the quantum numbers and

Â seen the allowable quantum numbers that tell you the location of your electron.

Â So an electron has these three taggers of n, l, and m sub l.

Â Now we haven't talked about m sub s yet.

Â We will here in a little bit.

Â