Raffi Hovasapian

Spin Quantum Number: Term Symbols I

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Table of Contents

Section 1: Classical Thermodynamics Preliminaries

The Ideal Gas Law

46m 5s

Intro

0:00

Course Overview

0:16

Thermodynamics & Classical Thermodynamics

0:17

Structure of the Course

1:30

The Ideal Gas Law

3:06

Ideal Gas Law: PV=nRT

3:07

Units of Pressure

4:51

Manipulating Units

5:52

Atmosphere : atm

8:15

Millimeter of Mercury: mm Hg

8:48

SI Unit of Volume

9:32

SI Unit of Temperature

10:32

Value of R (Gas Constant): Pv = nRT

10:51

Extensive and Intensive Variables (Properties)

15:23

Intensive Property

15:52

Extensive Property

16:30

Example: Extensive and Intensive Variables

18:20

Ideal Gas Law

19:24

Ideal Gas Law with Intensive Variables

19:25

Graphing Equations

23:51

Hold T Constant & Graph P vs. V

23:52

Hold P Constant & Graph V vs. T

31:08

Hold V Constant & Graph P vs. T

34:38

Isochores or Isometrics

37:08

Physical Chemistry Spin Quantum Number: Term Symbols I

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Section 19: Spin Quantum Number and Atomic Term Symbols: Lecture 1 | 59:18 min

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1 answer

Last reply by: Professor Hovasapian
Sun Feb 17, 2019 1:56 AM

Post by Kimberly on February 15, 2019

Hi professor Hovasapian,

When you did the carbon term symbol, why didn't you include the J term in the final term symbol?

2 answers

Last reply by: Professor Hovasapian
Wed May 11, 2016 2:43 AM

Post by Tram T on April 23, 2016

Dear Prof. Hovasapian,

If Energy En of Hydrogen atom only depends on the Principal QN, then why 2p orbitals have higher Energy than 2s orbital? I thought they are all have E sub 2 energy.

Thank you!

1 answer

Last reply by: Professor Hovasapian
Fri Apr 10, 2015 12:02 AM

Post by dulari hewakuruppu on April 9, 2015

in the multi electron atoms section, where you considered 2P1 of Boron, if we know L we know about m sub L as well right? you mentioned that we dont know about Ml nor Ms so this kind of got me confused.. I dont know if I am wrong though.. could you kindly explain? :) thank you

Spin Quantum Number: Term Symbols I

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Intro

Quantum Numbers Specify an Orbital

Spin Orbitals

Term Symbols

Russell-Saunders Coupling & The Atomic Term Symbol

Example: Configuration for C

Intro 0:00
Quantum Numbers Specify an Orbital 0:24

n
l
m
4th Quantum Number: s

Spin Orbitals 7:03

Spin Orbitals
Multi-electron Atoms

Term Symbols 18:08

Russell-Saunders Coupling & The Atomic Term Symbol

Example: Configuration for C 27:50

Configuration for C: 1s²2s²2p²
Drawing Every Possible Arrangement
Term Symbols
Microstate

Physical Chemistry Online Course

Section 1: Classical Thermodynamics Preliminaries
	The Ideal Gas Law	46:05
	Math Lesson 1: Partial Differentiation	46:02
Section 2: Energy
	Energy & the First Law I	1:06:45
	Energy & the First Law II	1:06:33
	Energy & the First Law III	1:02:17
	Changes in Energy & State: Constant Volume	1:04:39
	Joule's Experiment	16:50
	Changes in Energy & State: Constant Pressure	43:40
	The Relationship Between Cp & Cv	32:23
	The Joule Thompson Experiment	39:15
	Adiabatic Changes of State	35:52
Section 3: Energy Example Problems
	1st Law Example Problems I	42:40
	1st Law Example Problems II	1:00:23
	1st Law Example Problems III	44:34
	Thermochemistry Example Problems	59:07
Section 4: Entropy
	Entropy	49:16
	Math Lesson II	33:59
	Entropy As a Function of Temperature & Volume	54:37
	Entropy as a Function of Temperature & Pressure	31:18
	Summary of Entropy So Far	23:06
	Entropy Changes for an Ideal Gas	25:42
Section 5: Entropy Example Problems
	Entropy Example Problems I	43:39
	Entropy Example Problems II	56:44
	Entropy Example Problems III	57:06
Section 6: Entropy and Probability
	Entropy & Probability I	54:35
	Entropy & Probability II	35:05
Section 7: Spontaneity, Equilibrium, and the Fundamental Equations
	Spontaneity & Equilibrium I	28:42
	Spontaneity & Equilibrium II	34:38
	The Fundamental Equations of Thermodynamics	30:50
	The General Thermodynamic Equations of State	34:06
	Properties of the Helmholtz & Gibbs Energies	39:18
	The Entropy of the Universe & the Surroundings	19:40
Section 8: Free Energy Example Problems
	Free Energy Example Problems I	54:16
	Free Energy Example Problems II	31:17
	Free Energy Example Problems III	45:00
	Three Miscellaneous Example Problems	58:05
Section 9: Equation Review for Thermodynamics
	Looking Back Over Everything: All the Equations in One Place	25:20
Section 10: Quantum Mechanics Preliminaries
	Complex Numbers	34:25
	Probability & Statistics	59:57
	SchrÓ§dinger Equation & Operators	42:05
	SchrÓ§dinger Equation as an Eigenvalue Problem	30:26
	The Plausibility of the SchrÓ§dinger Equation	21:34
Section 11: The Particle in a Box
	The Particle in a Box Part I	56:22
	The Particle in a Box Part II	45:24
	The Particle in a Box Part III	48:43
Section 12: Postulates and Principles of Quantum Mechanics
	The Postulates & Principles of Quantum Mechanics, Part I	46:18
	The Postulates & Principles of Quantum Mechanics, Part II	39:28
	The Postulates & Principles of Quantum Mechanics, Part III	35:32
	The Postulates & Principles of Quantum Mechanics, Part IV	29:55
Section 13: Postulates and Principles Example Problems, Including Particle in a Box
	Example Problems I	54:25
	Example Problems II	46:58
	Example Problems III	44:11
Section 14: The Harmonic Oscillator
	The Harmonic Oscillator I	35:33
	The Harmonic Oscillator II	43:04
	The Harmonic Oscillator III	26:30
Section 15: The Rigid Rotator
	The Rigid Rotator I	41:10
	The Rigid Rotator II	30:32
	The Rigid Rotator III	35:19
Section 16: Oscillator and Rotator Example Problems
	Example Problems I	33:48
	Example Problems II	46:43
Section 17: The Hydrogen Atom
	The Hydrogen Atom I	40:00
	The Hydrogen Atom II	35:58
	The Hydrogen Atom III	36:18
	The Hydrogen Atom IV	33:55
	The Hydrogen Atom V: Where We Are	51:53
	The Hydrogen Atom VI	51:53
	The Hydrogen Atom VII	34:29
Section 18: Hydrogen Atom Example Problems
	Hydrogen Atom Example Problems I	43:49
	The Hydrogen Atom Example Problems II	1:01:57
	The Hydrogen Atom Example Problems III	48:33
	The Hydrogen Atom Example Problems IV	48:33
	The Hydrogen Atom Example Problems V	48:33
Section 19: Spin Quantum Number and Atomic Term Symbols
	Spin Quantum Number: Term Symbols I	59:18
	Spin Quantum Number: Term Symbols II	34:54
	Spin Quantum Number: Term Symbols III	38:03
	Term Symbols & Atomic Spectra	57:49
Section 20: Term Symbols Example Problems
	Example Problems I	1:01:20
	Example Problems II	56:34
Section 21: Equation Review for Quantum Mechanics
	Quantum Mechanics: All the Equations in One Place	18:24
Section 22: Molecular Spectroscopy
	Spectroscopic Overview: Which Equation Do I Use & Why	50:02
	Vibration-Rotation	59:47
	Vibration-Rotation Interaction	46:22
	The Non-Rigid Rotator	29:24
	The Anharmonic Oscillator	30:53
	Electronic Transitions	1:01:33
Section 23: Molecular Spectroscopy Example Problems
	Example Problems I	33:47
	Example Problems II	1:01:05
	Example Problems III	33:31
Section 24: Statistical Thermodynamics
	Statistical Thermodynamics: The Big Picture	1:01:15
	Statistical Thermodynamics: The Various Partition Functions I	47:23
	Statistical Thermodynamics: The Various Partition Functions II	54:09
Section 25: Statistical Thermodynamics Example Problems
	Example Problems I	48:32
	Example Problems II	57:30

Transcription: Spin Quantum Number: Term Symbols I

Hello, welcome back to www.educator.com, and welcome back to Physical Chemistry.0000

Today, we are going to start talking about something called term symbols0004

and we are going to be spending 2 or 3 lessons on this.0009

Before I discuss terms symbols, I want to discuss a 4th quantum number, it is called the spin quantum number.0011

We will introduce that and then we will get into the topic of term symbols.0018

Let us go ahead and just get started.0023

I think I will go ahead and stick with blue today.0026

Three quantum numbers specify an orbital, a wave function.0034

A wave function represents an orbital for the hydrogen atom that we saw.0048

We can also call it a quantum state if we want.0055

Again, like I said we can just go ahead and call it a wave of function which is exactly what it is.0063

We have N which is the primary quantum number and it takes on the values 1, 2, 3, and so on.0070

When we have L, it is the angular momentum quantum number and it takes on the values of 0, 1, 2, all the way up to N -1.0081

L depends on N and we also have this one, we have the M.0093

Or I'm going to start occasionally putting a subscript of L on there.0098

M or M sub L is the magnetic quantum number and it is dependent on L, which is why we have this subscript L.0103

It is going to take on the values of 0, + or -1, + or -2, all the way up to + or – L.0111

There is a 4th quantum number.0124

I’m not going to spend a lot of time here or talking about where this 4th quantum number comes from.0126

I’m just going to introduce it, tack it on to the three quantum numbers that we have.0135

If we need to go a little bit deeper into what this 4th quantum number is, we will.0144

But I do not want to just unload a bunch of information that is unnecessary at this point.0150

For right now, just know that there is this 4th quantum number and its designated s and is called the spin.0155

In your books or, in any discussion you see online, they are going to talk about how the electron has this intrinsic property called spin.0175

If you want to correlate with why we chose the word spin, you can think of a electron as a ball and a ball is spinning.0186

A ball can spin in 2 directions if you are holding it like this and either spin to the right or it can spin to the left.0195

If you spin it to the right using the right hand rule that you remember from physics,0202

as it spins to the right, your thumb is pointing up.0207

It is up spin.0209

If it is spinning this way and if your fingers going to the direction of the spin, your thumb is pointing down.0211

It is down spin.0215

Now, the electronic is not actually spinning but you can think about it that way, if it helps you.0217

Spin is an intrinsic quality of the electron like its mass.0222

It is just its quality so spin is the 4th quantum number, it has only one value.0227

It has only one value for the electron and that is ½.0236

The actual quantum number that we are going to use and we often see are the M sub S.0244

Sort of like L and M sub L, we have S and we have M sub S.0268

This is the one that has the two values that you have probably seen before.0274

The + ½ and the -1/2, for up spin and down spin, respectively.0279

This is a spin quantum numbers.0286

An electron with a given set of N, L, and M sub L can have M sub S = + ½,0296

which we call up spin or M sub S = -1/2 which we call down spin.0323

I’m not going to hop on this whole idea of the spinning top or spinning electron, things like that.0333

It is not altogether important, it is an intrinsic quality of the electron.0338

When we have just N, L, and M sub L, we have an orbital.0344

We have a quantum state and a wave function.0366

When we add the 4th quantum number to it, when we add M sub S,0371

when we the 4th quantum number M sub S, I would call it something else.0378

Instead of an orbital, we would call it spin orbital.0393

We call these spin orbitals.0399

A spin orbital is just an orbital that actually includes the 4th quantum number.0410

Let us go ahead and change here.0424

Each orbital, each choice of N, L, and M sub L, has 2 spin orbits.0427

We know this already from general chemistry.0446

We know that each orbital that we come across is going to have 2 electrons in it in maximum.0448

One with up spin and one with down spin.0454

Each orbital has 2 spin orbitals.0456

There was 2 places for an electron to go.0461

Again, we already know that an orbital can hold at most 2 electrons of opposite spin.0473

It is not a problem to go ahead and use the things that we learned in general chemistry.0482

I know that that stuff actually comes from this, it comes from the quantum mechanics.0490

It is okay take to use this information, things that we already know to help us understand what is happening.0496

We already know that at least at this level, each orbital can hold at most 2 electrons of opposite spin.0504

For example, we have the 2P.0529

In this particular case, N = 2, L = 1, and M sub L = 1, 0.0536

I’m not going to use comma, if you do not mind.0546

It is 1, 0 and -1.0549

M sub L is, from –L to L passing through 0.0553

We already what this is, this is the P sub X, P sub Y, P sub Z.0557

This is the 2 P sub X that is N = 1.0563

The 2P sub Z is N = 0.0570

Notice, I’m putting the Z before the Y.0572

And because we decided to label it that way.0575

When N sub 0 and M or M sub L is equal to 0, it is actually the Z orbital.0578

0, and we have 2 P sub Y, this is M = -1.0586

1 orbital, 2 orbitals, 3 orbitals.0597

3 orbitals, each orbital can hold 2 electrons of opposite spin.0601

We have a total of 6 spin orbits.0609

Again, nothing strange here.0613

In other words, there are 6 places for electrons to go.0616

In the case of a single electron in the 2P orbital, there are 6 possible places for it to go.0628

For multi electron atoms, so we have dealt with hydrogen now0667

we are going to start dealing with helium, lithium, boron, and so forth.0671

For multi electron atoms, we simply add 1 electron at a time to successive orbitals,0678

within the confines of the exclusion principle.0710

An individual orbital can only hold 2 electrons maximum of opposite spin.0712

In general chemistry, what we did is we fill them up one at a time.0723

Like for oxygen, 1S2 S22 before, we ended up feeling 1 electron here up spin and 1 electron here parallel spin.0731

Another electron here parallel spin and then we went back and filled another one down spin0738

and work our way up until we close the shell.0745

For multilevel atoms simply add 1 electronic time to successive orbitals.0748

You know this from general chemistry.0756

The order of filling is, we have 1S2 and 2S2, 2P6, 3S2, 3P6, 4S2, 3D10, 4P6,0762

that just in a higher and higher energy levels.0785

We just throw electrons into it.0787

5S2, 4D10, 5P6, and so on.0791

I’m filling up the F orbitals.0798

Let us take a configuration like 1S2, 2S2, 2P1, this is boron.0800

Let us examine the 2P1 electron.0829

We have N which is right here and we have P, which means that we have L.0842

N is equal to 2, L is equal to 1.0854

We have information on N and L, but notice the 2P1 does not say anything about the M sub L.0858

It does not say anything about the M sub S.0874

In other words, this one electron has 6 possible places for it to go.0877

The M sub L, this can be either 1, 0, or -1.0880

In each of those cases, M sub S can be + or – ½.0886

M sub L = 0 can be ± ½ and the M sub L -1 can be ± ½.0893

This electron configuration that we know from general chemistry does not really give us a lot of information.0900

It does not tell us what primary level it is and gives us an angular quantum number0905

but it does not really give us much more information that we want to know where the electron are.0911

Are they up spin or the down spin, which orbitals they are in?0917

What suborbital they are in?0921

What is the N, what is M sub L, what is the M sub S?0922

I will repeat that by writing it down.0926

Notice that 2P1 says nothing about M sub L or M sub S.0928

We do not know if the electron is in 2 PX, 2 PY, or 2 PZ.0956

We do not know where this spin on this electronic is + ½ or -1/2.0981

This is important information.0995

There are 6 places for it to be.1000

We need a notation that gives us more information than standard electron configuration.1007

This 1S2, 2S2, 2P1, we need a notation that gives us more information than our standard electron configurations1033

about where an electron is exactly that come from the M sub L and what spin state it is in.1055

That comes from the M sub S.1081

Here is where we introduce term symbols.1085

The topic of term symbols.1090

The quantum numbers that you know the N, L, M sub L, and M sub S, notice that they are small letters.1101

Term symbols, we decide use capital letters, that is the difference.1108

When you see a capital letter, it refers to a term symbol.1112

How do we introduce term symbols?1120

That was the challenge, we will do our best here.1122

For a given configuration, when we talk about configuration, we are talking about a general state configuration.1125

For a given configuration, we will determine three things.1139

We will determine L, this will be the total angular momentum also called the total angular momentum quantum number.1150

Notice, small L is angular momentum quantum number.1168

Capital L is the total angular momentum quantum number.1171

Again, this is for more than 1 electron.1174

For hydrogen, it was just 1 electron.1176

L represents the angular momentum quantum number for the electron.1178

L represents adding up all the l for each electron in a multi electron atom.1182

Lithium for example, it has 3 electrons, so each one has an l value.1188

We are going to add those up and it is going to give us the L.1194

We will go into details just a little bit.1197

We are also going to calculate the total angular momentum.1199

S this is the total spin angular momentum.1204

Let me go back and talk about why it is called the spin.1222

An electron, by virtue of its orbital motion, imparts a magnetic field.1225

In other words, it is angular momentum that comes from the fact that the electron is spinning around the nucleus.1238

L represents the total orbital angular momentum.1245

The angular momentum that comes from the fact that these electrons are spinning around the nucleus.1256

This is the total orbital angular momentum.1260

An electron, by virtue of its existence, also has an angular momentum component1266

that it adds to the angular momentum of the total atom.1275

By virtue of its orbital motion, the electron has angular momentum.1283

And by virtue of its spin state, it has angular momentum.1286

The total orbital is L, the total spin angular momentum is S.1290

Of course we have something called J, that is the total angular momentum.1294

It is going to be the sum of the L + S.1298

J is going to be L + S, this is the total angular momentum.1301

The angular momentum that come through orbital motion.1309

The angular momentum that comes from spin state.1311

The scheme in adding up all the small l, adding up all the s, adding up the L + S is called Russel Saunders coupling.1324

In other words, we are going to couple the orbital angular momentum1348

with the spin angular momentum to come up with a total angular momentum for a particular multi electron atom.1351

The scheme is called Russell Saunders coupling and gives rise to the atomic terms symbol.1360

Atomic term symbol looks like this.1374

There is going to be and L value and on the left is a superscript is going to be 2 times S +1.1383

It is going to be a number.1391

On the right subscript, there is going to be a J.1393

Notice LSJ, LSJ, this is the atomic term symbol.1397

This is what is going to look like.1402

L represents the total, we call L the total orbital angular momentum quantum number.1405

We call S the total spin angular momentum quantum number.1429

We called J, let us make J a little bit better J here so it does look like something else.1440

We call J the total angular momentum quantum number.1445

The capital letters, they represent quantum numbers for multi electron atoms.1459

A hydrogen atom has N, L, M sub L, M sub S.1464

A multi electron atom has, because we are talking for each electron, it has an L,1471

it has a angular momentum quantum number just like the hydrogen atom did.1481

It has an S spin quantum number and it has a total angular momentum quantum number.1484

These are the quantum numbers that are used for multi electron atoms.1489

That is the correlation.1495

We have the quantum numbers that we have for the hydrogen atom.1497

We have quantum numbers for multi electron atoms.1499

That is the only difference.1501

When you see capital letters, we are talking about multi electron atoms.1503

Here is where it is interesting.1510

Couple of things I would like to say here but I will write them down.1513

The only way to really see what is happening is to manually workout1516

all of the possible arrangements for a particular electron configuration.1547

In other words, I'm going to pick a particular electron configuration and1570

I'm going to actually work out all of the possible ways that however many electrons we choose, going to which orbital.1573

You need to see every single possibility.1581

What we are going to do is we are going to group those into ones that have different energy levels.1583

Those groupings are going to be the term symbols.1589

It is going to give us a very detailed information about exactly where the electron is1592

and what configurations it can possibly take depending on its energy.1597

The only way to make sense of the term symbols, I can go ahead to wrap the process and1601

show you how to come up with a term symbol but you have to work out at least one manually just to see it.1606

It is the only way to do it, you only wrap your mind around.1613

The other way that is happening is to manually work out all the possible arrangement1616

for a particular electron configuration and see how these arrangements fall into groups1620

that is represented by the terms symbols.1643

Let us look to the configuration for carbon, 1S2, 2S2, 2P2.1665

We do not need to look, notice the 1S2, 2S2 are close shells.1700

We do not need to include those electrons in our scheme for coming up with a term symbol.1704

We will talk a little bit about why later on, but just real quickly, notice 1S2.1710

I will talk about that later but just understand that when you are doing terms symbols for a configuration,1718

you do not have to look at close shells.1723

You just have to look at everything that comes afterward, the orbit shells.1725

Let us just go ahead and write that down.1732

We do not need to look at closed shells.1734

In other words, you do not have to worry about these 4 electrons.1746

We only have to worry about these 2 close shells.1747

I will explain why when we actually done the process and wrap our minds around this.1753

2P2, the N itself does not matter.1760

In this particular case, they are all the same level.1767

They are all the same N value.1770

The 2P2, also N does not matter.1775

We are only concerned when we talk about a particular terms symbol is which suborbital they are in, S and P, and electrons and nodes.1784

Those are the one that we are concerned with.1795

In this particular case, we have just the P2 configuration.1797

We have 2 electrons that can be distributed among 6 spin orbitals.1803

2 electrons that can be distributed among 6 spin orbitals.1813

The P suborbital has 3 suborbital.1832

Each orbital has 2 spin orbitals, and 2 times 3 is 6.1839

2 electrons that can be distributed among 6 spin orbitals, because P implies that L is equal to 1.1842

M sub L is equal to 1, 0, and -1 or P sub X, P sub Z, and P sub Y.1855

In other words, I can actually draw out every single possible configuration.1872

Let us draw every possible distribution.1879

I will use the word distribution, let us use the word arrangement.1891

Every possible arrangement of the 2 electrons in 6 different spin orbitals.1895

Let us draw each one out.1904

I’m going to be calculating, once I do the drawings.1906

Next to the drawings I’m going to calculating some numbers.1916

I'm going to be calculating the sum of the individual M sub L and that is going to be M sub L.1919

I'm going to be adding up the individual M sub S.1929

That is going to equal M sub S and I'm going to end up also writing M sub L + M sub S is going to equal M sub J.1936

You see this pattern that is developing.1956

There is an L, there is an S, and there is a J.1959

There is M sub L, M sub S, and M sub J, just like we have the L and M sub L, this is the correlation that we are developing.1964

We are trying to keep things parallel.1976

These three numbers. M sub L is just adding up the individual M sub L for that particular arrangement.1982

Let us go ahead and do that.1989

It is going to take a little bit while here.1990

I'm hoping I can actually get to it solve on one page.1994

I'm going to try my best to.1996

I have got 12345678910.1999

Let us do 123, 123, 123 123, that is 4, 5.2005

123, 123, 123, 123 and 6 123456789 and 10.2018

Make this one a little bit better.2036

Let me go over here and do another set.2039

123, 123, 123,23, 123, that is 15.2041

123, 123, 123, 123, 123, 12345678910.2052

And we need one more, let me write that over here actually.2067

It is not a problem, let go over here.2072

This page, as we move forward, you do not have to keep referring to this page.2079

I, myself, can actually go back but you, yourself can by just rewinding and looking back on this page2086

when you see how is that we are going to take the arrangements.2094

Anyway, let us go ahead and draw out all the possible ways that 2 electrons can be distributed among 6 different spin orbitals.2097

This is PX PZ PY, these are P orbitals.2104

How many different ways can I actually put 2 electrons into this?2108

You just you have to do this, that is one possibility.2114

You have to take your time account for every single possibility.2122

It is going to turn out that they are 21 different ways of doing this.2125

That is another possibility, do not worry about whether it violates the exclusion principle or not yet.2133

We just want to throw all the possibilities out there and we will cross off those that we can use for one reason or another.2141

That is another possibility, 2 electrons can go there, you can have down spin.2149

You can have that, you can have that, you could have that.2155

2 electrons can go there, 2 electrons can go there.2163

You can have one up spin, one down spin.2167

You can have one down spin, one up spin.2170

You can have up down here, you can have down.2174

You can have up, you can have up.2178

You can have down, you can have down.2180

You can have up, you can have done up and down the same or done the same.2183

These are the 21 different ways that you can have 2 electrons and distribute them in among 6 spin orbitals.2195

Let us go ahead and calculate what we said the M sub L and M sub S and the M sub J.2208

This is M sub L1, M sub L0, M sub L-1.2221

We are going to add up the M sub L.2228

In this case, it is 1 to 0.2230

M sub L could be the first number.2233

That is going to equal 1 + 0, it is going to equal 1.2236

M sub S, I'm just going to add up the spins.2241

This is up spin and up spin, ½ + ½, ½ + ½ S= 1.2244

The sum of those 2 M sub J is equal to 2.2252

I’m collecting some numbers here.2260

M sub L M sub L 1, 0, -1.2264

In this particular case, M sub L = 1, + and -1 that is equal to 0.2268

The M sub S is still ½ + ½ because it is up spin and up spin, so it is equal to 1.2277

The sum of these 2, the M sub J is equal to 0 + 1 is 1.2285

Here, I'm going to go ahead and drop the M sub L and M sub S.2298

The first I’m going to calculate is going to be the M sub L and the second numbers M sub S.2303

And the sum is going to be M sub L sub J.2307

In this particular case, I have a 0 and -1.2310

0 + -1 = -1, they are both up spin.2315

½ + ½ = 1.2321

In this particular case, the M sub J is equal to 0.2326

Here we have 2 electrons, they are both in the same orbital and they both have up spin.2331

This is a violation of the exclusion principle.2335

These we can just throw out.2340

The M sub L is 1, 0, -1.2350

1 + 0, the M sub L is equal to 1.2353

The spins, they are both down spin.2359

-1/2 + -1/2 = -1.2362

M sub J is equal to 0.2369

Here 1 + -1 = 0 down spin -1/2 + -1/2 = -1.2371

Here M sub J = -1, 0 -1, I’m just going to start doing these quickly.2388

0 -1 = -1, - ½ - ½ = -1.2395

M sub J = -1 and -1 = -2.2415

Here we have a violation of the exclusion principle.2421

We have a violation, we have 2 electrons of the same orbital of parallel spin.2428

Here we have a violation.2434

Here, we have 1 + 0, the M sub L, 1 + 0 is equal to 1.2437

And here we have up spin and down spin, ½ and ½ at 0.2446

Here MJ is equal to 1.2452

Over here we have the same thing.2456

It is going to be 1 + 0 = 1, this time it is - ½ + ½ that is equal to 0.2460

Again, we have MJ is equal to 1.2472

1 + -1, let me write -1.2477

1 -1 = 0 so that is M sub L.2484

½ - ½ = 0, that is M sub S.2488

Therefore, our M sub J is equal to 0.2494

Same thing here, here we have 1 -1 is equal to 0.2497

Here we have - ½ + ½ is equal to 0.2502

Again, we have an M sub J equal to 0.2507

We have 0 and -1, 0 -1 = -1, that is our M sub L.2510

We have ½ - ½ = 0.2521

Our M sub J = -1.2526

Here we have 0 and -1, 0 -1 = -1.2530

We have - ½ spin + ½ spin = 0.2536

We are left with M sub J = -1.2540

Over here, we have 1 + 1 is equal to 2.2546

½ - ½ is equal to 0.2552

Our M sub J is equal to 2.2556

Here we have, 0 + 0 are both in the Z orbital.2560

0 + 0 = 0, that is our M sub L.2566

Up spin down spin ½ - ½ = 0, that is our M and S.2570

Therefore, our M and J, the sum of those two is equal to 0.2576

Over here, we have -1 -1 which is -2 and then we have + ½ - ½ = 0.2581

Therefore, our M sub J = -2.2602

I will go ahead and erase this.2606

This is it, these are the total number of ways that 2 electrons can be distributed among 6 spin orbital.2609

6 or more violations 123456, 123456.2617

Yes, that leaves 15 possible, 15 viable ways that the 2 electrons that the 1S2, 2P2, that 2P2 configuration, there are 15 possible places for those electrons to be.2624

What we are going to do is we are going to come up with terms symbols to tell us which configurations they can be and2638

what the energies of those configurations are and then all of those terms symbols that2648

we are going to find one that is in ground state, that is where we are interested in.2653

You are going to be referring back to this, I myself once I move forward, I cannot move back.2659

But you, yourself can move back.2664

When I make a statement, just come back here and take a look.2666

The important numbers are going to be M sub L and M sub S.2669

For right now, those are the one that we concern ourselves with in the next set of steps.2674

This 1 and 1, this 0 and 1, this -1 and 1, all of these numbers.2679

The first one is the M sub L, the second one is M sub S.2686

Let us go ahead and see what we can do.2693

We looked on this list and we are going to look for the largest value M sub L.2698

The largest value M sub L is 2.2704

That is what we do, first step.2723

The largest M sub L is equal to 2.2725

This implies that L is equal to 2.2734

The actual values of the M sub L, they are represented, are going to be 2, 1, 0, -1, and 2.2748

Remember, just like we had the L and the M sub L for the hydrogen atom number,2757

if L was 3 then M sub L had the values of 3, 2, 1, 0, -1, -2, -3.2764

This is the same thing, there is a correlation here.2773

There is a L and there is the small values M sub L takes on all of these values.2775

We chose the largest one to account for everything from the largest to smallest.2782

Let me get the largest M sub L that implies L =2.2787

Therefore, all the possible values M sub L are 2, 1, 0, -1, and 2.2794

I hope that makes sense.2799

We have L is equal to 2, we found our L.2805

For this particular ML is equal to 2, the largest MS value for the ML = 2.2812

The largest MS value is equal to 0.2823

This implies, if the MS is equal to 0 that means S is equal to 0, which means that the only value that MS actually has, M sub S has is 0.2837

In other words, the S are 1, we have 1, 0, -1.2850

If S were 2, we have 2, 1, 0, -1, -2.2854

If S were 3, we have M sub S = 3, 2, 1, 0, -1, -2, -3.2858

There is a correlation.2866

L, all the values of M sub L from + L to –L.2868

S, the M sub S, all the values from +S to –S, passing through 0.2875

Let us go, M sub S is equal to 0.2885

S is equal to 0.2888

I’m going to go ahead and before I actually write the term, you remember the L values.2894

Let me draw a little bit of something here.2903

Remember, we set the terms symbol is L 2S + 1 and J, we found that L is 2.2910

We found that S is 0.2918

2 times 0 + 1 is 1.2919

However, instead of writing the number 2 here, we would actually use a letter.2922

The correlation is as follows.2927

If you remember L, the small L from the hydrogen atom 0, 1, 2, 3, 4, we call this S, P, D, F, G, and so on.2928

It was the same correlation.2946

When L is equal to 0, 1, 2, 3, 4, we call this the S term, P term, the D term, the F term, the G term.2948

In this particular case, we found that L is equal to 2 that correspond to D.2965

S is equal to 0, there is that correspondence that we set up because we prefer to use letters.2970

L is equal to 2 means D term.2979

S equal to 0 means 2 times 0 + 1, 2S + 1 is equal to 1, D1 term symbol.2988

We found our first term symbol.3011

There are some arrangements that fall into the D1 level.3014

It is a term that represents the particular arrangements that have the same energy.3018

Everything is D1 level, all those arrangements they have the same energy.3026

How many are there?3030

Since ML is equal to 2, 1, 0, -1, -2, and M sub S is equal to 0, this comes from L = 2, this comes from S = 0.3034

There are 5 microstates.3057

In other words, arrangements in the D1 level.3067

The number of M sub L times the number of M sub S.3084

This is 5 times 1 = 5.3091

There are five of those arrangements that we drew on the previous page.3097

Five of those arrangements belong to the D1 energy state along the D1 term.3100

We have grouped five of them.3109

Of the 15 viable candidates, they all have the same energy.3111

In other words, the electrons, they are 5 different arrangements of them but all of them have the same energy.3117

That energy is represented by this term symbol D1.3121

In other words, the total angular momentum for those things is going to be 2.3127

The total spin angular momentum for the state is going to be 0.3132

That is what this means.3139

D tells you that L = 2, that is the total angular momentum.3141

2S + 1 is equal to 1.3144

When you solve that equation 2S + 1 = 1, we get S = 0.3147

That means that the spin angular momentum for those states is going to be 0.3152

We will worry about J a little bit later.3157

I hope this last part makes sense.3161

There are five of those arrangements that fall into this category.3166

Let us go ahead and see.3172

Let me just finish up what I want to say here.3176

For each combination of M sub L and M sub S, we choose a microstate.3177

In other words, what you are going to end up actually doing,3205

you are going to go back to the page where we drew out all those individual arrangements.3207

What we call them microstates, the possible arrangements for 2 electrons and 6 spin orbitals3210

and you are going to choose M sub L, 2M sub S0.3215

You are going to choose that microstate, that is going to belong to D1 group.3220

You are going to choose 1, 0.3225

You are going to choose 0, 0.3228

You are going to choose the one with ML =-1 and MS =0.3229

Then, you are going to choose the one with ML = -2 and MS =0.3233

That is what we are doing here.3237

Those all belong to the D1 level.3239

For each combination of ML and M sub S, we choose a microstate.3242

If there is a choice of more than one, in other words if you have 2 microstates that have 1,0 and 1, 0, just choose one of them.3247

It does not matter which one you choose.3266

If there is a choice of more than one for each M sub L and M sub S, it does not matter which you choose.3268

The reason is because that is the same energy.3292

Either what you choose but pick only one.3295

When go back to the H where we draw all those microstates, for every value of M sub L 2, 1, 0, -1, 2, and this equal to 0.3306

2, 0, 1, 0, 0, 0, -1, 0, 2, 0, those that have those numbers, I’m going to choose those microstates.3318

Here is the one that I actually pick out.3327

They have 123, 123, 123, 123, and 123.3330

There is this one, there is this one, there is that one, there is that one, and there is that one.3339

In this particular case, here the ML is equal to 2.3357

Here, the MS is equal to 0.3365

We have taken care of the two 0.3367

In this particular case, M sub L is -2, M sub S =0.3369

Here, M sub L =1, M sub S was 0.3376

Here, M sub L was -1 and M sub S = 0.3383

This one was M sub L = 0, M sub S = 0.3388

These 5 possible arrangements, these all along the D1 energy states.3395

These microstates belong to the D1 level, the D1 term.3401

It is a notation that describes the energy of these 5 states, the D1 level.3421

They have the same energy.3429

We will take care of the J.3441

Now, we have the D1, we still have to figure out what this thing is right here.3455

We still do not know what the J value is.3460

We will take care of the J after we have found the primary terms symbols for the groups.3462

Then, I will go back and fill in the J values after we have grouped them.3473

All those 15 viable microstates, the arrangements, we are able to find 5 of them that fall into a certain category.3488

That category has the term symbol D1.3496

This D1 tells you about what is happening here.3499

The D tells you that the L is equal to 2.3504

The total orbital angular momentum for the state is 2.3507

The 2S + 1 = 1.3510

This one number here tells you that S is equal to 0.3513

It tells you that the total spin angular momentum of these is 0.3516

Up spin down spin 0, Up spin down spin 0, Up spin down spin 0, Up spin down spin 0, Up spin down spin 0.3521

These terms give you information on what is happening here electronically3529

in terms of angular momentum, orbital angular momentum, and spin angular momentum.3534

I’m going to go ahead and stop this lesson here.3540

The next lesson is going to be the continuation of these examples.3542

Just consider one long lesson.3546

I do not want to make it one huge long lesson, I want to break it up.3547

The next lesson is going to be just a continuation of this particular example.3552

Thank you so much for joining us here at www.educator.com.3555

We will see you next times, bye.3557

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