Raffi Hovasapian

Term Symbols & Atomic Spectra

Slide Duration:

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 Term Symbols & Atomic Spectra

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Section 19: Spin Quantum Number and Atomic Term Symbols: Lecture 4 | 57:49 min

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Term Symbols & Atomic Spectra

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

Lyman Series

Hydrogen Levels

Hydrogen Levels

Term Symbols & Atomic Spectra

Example I: Calculate the Frequencies of the Allowed Transitions from (4d) ²D →(2p) ²P

Helium Levels

Energy Levels for Helium

Transitions & Spin Multiplicity

Transitions & Spin Multiplicity

Intro 0:00
Lyman Series 0:09

Spectroscopic Term Symbols
Lyman Series

Hydrogen Levels 8:21

Hydrogen Levels

Term Symbols & Atomic Spectra 14:17

Spin-Orbit Coupling
Selection Rules for Atomic Spectra
Selection Rules for Possible Transitions
Wave Numbers for The Transitions

Example I: Calculate the Frequencies of the Allowed Transitions from (4d) ²D →(2p) ²P 32:23
Helium Levels 49:50

Energy Levels for Helium

Transitions & Spin Multiplicity 52:27

Transitions & Spin Multiplicity

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: Term Symbols & Atomic Spectra

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

Today, we are going to talk about term symbols and atomic spectra.0004

Let us jump right on in.0008

I'm sorry if my voice is a little scratchy today, I hope that I'm still well understood.0011

We talked about term symbols and let us see what the association is with term symbols with these atomic spectra.0017

Let us actually go to blue, I think.0024

Term symbols are also called spectroscopic term symbols or spectroscopic symbols0030

because the lines we see on atomic spectra,0055

like the one that you see below, which we will talk about in just a minute.0070

They represent transitions between electronic states.0073

Electronic states as we saw on the previous lessons, they are represented by term symbols.0097

We have seen a spectra like this before and we saw it earlier on in the course,0122

when we are talking about some of the early evidence for the quantum theory.0126

Let me go ahead and take an atom, we excite the energy to a higher level and then we allow0133

and it falls back down to, the excited electron fall back under to the ground state.0139

When we fall back down, they emit that particular excess energy as a photon of light.0146

They emit certain frequency that is what we see here.0152

The higher they go, they fall down, the higher the energy.0155

Of course at some point, it is some upper limit.0159

That is all these are, it absorbs light and energy at a certain frequency0162

and it spits it back out when the electron falls back down to the ground state.0167

This particular one is the Lyman series for atomic hydrogen.0172

Let me do red now.0182

This right here is the Lyman series for atomic hydrogen.0188

The Lyman series represents transitions from higher N values, the first quantum number N = 1, 2, 3, 4, 5.0213

Let me continue it down here.0237

These higher N values, you remember N is the primary quantum number, down to the ground state which is N = 1.0240

This represents transitions from level 2 to level 1, level 3 to level 1, level 4 to level 1, and so on.0262

Level 2 to level 1, that line.0272

Level 3 to level 1, that is that line.0278

Level 4 to level 1, that is that line.0279

We knock the electron, the electron of the 1S by the electron configuration 1S1.0280

We knock it up to our 2P and draws back down the 3P, drops back down we got the 4P, drops back down.0286

It is getting higher and higher energy but when it draws back down, it emits a photon of light.0296

Higher and higher energy, that is all that is going on here.0300

That is what spectra represent.0303

These names, do not worry about it.0305

Lyman α, Lyman β and Lyman gamma, that is just first level, second level, third level.0306

Or in this case, N = 2, N = 3, N = 4, that is unimportant.0311

Here, we have the wavelength given in angstroms.0316

Oftentimes, we will see spectra given in inverse cm.0320

For our purposes, we would be working mostly in inverse cm which is the wave number.0324

In other ways of converting between the two is not important.0328

What is important is the numerical value and the qualitative information that we get so far.0331

When we look at the first line, let us go ahead and take a look at this line.0338

When we actually look at that line under a higher resolution, in other words when we magnify it.0342

When we look at the first line and the second and the third actually, not just for the first,0354

when we look at these lines for the Lyman series, when we look at the first line under a higher resolution,0362

Let us actually spell things properly here.0371

It is getting a little ahead of myself.0374

Under a higher resolution, we end up seeing 2 separate lines.0376

This single line that appears in the spectra is actually made up of two individual lines that are close together.0384

We end up seeing two separate lines.0391

The question is, what is going on?0408

We excited from level 1 to level 2 and then it drops back down to the ground state.0411

It emits energy that is what we see here.0419

Given it is the photon of a certain frequency and that frequency in this particular wavelength happens to be that.0422

It jumped up from 1 state ground state to a higher state and it drop back down.0430

We should only see one line, why are we seeing two lines?0435

When we see two lines, each line represents the energy level.0438

Basically, what is happening is its jumping up and it is dropping back down but it seems like they are two different levels.0442

Either it is jumping up to two different levels and each of those level is dropping back down.0453

If this is the ground state, it is either jumping up to here and jumping up to there.0457

When it fallback down to the ground state, you are getting two lines0462

because there are two different energy levels very closely spaced,0467

that ends up looking like one line under a lower resolution or we have a double level jumping up to a single like that.0470

But these are going to end up being the same energy.0478

More than likely, what is happening is that you have the ground state and you have two higher energies0482

but what is it that is actually going on?0489

Let us take a look, we ask ourselves what is going on.0492

This is what is going on.0502

This is an energy level table for atomic hydrogen, this is pretty much what you are going to see0505

when you look at the standard table.0519

There is other information that could have been put in here but I have blocked out all that other information.0521

I just want you to concentrate on the information that absolutely is important.0526

Let us go through this very carefully and see what is that we have on this table.0530

This first column is the electron configuration 1S, 2P, 2S, 23P.0534

When you do not see a number here that just means it is 1 electron there.0540

This is actually the 1S1 configuration.0544

The term symbol, remember this is electron configuration.0548

In the previous lessons, we said that electron configuration is not enough.0551

We need more information than just the primary quantum number and the angular momentum quantum number.0554

We want to know what the spin states are.0561

We want to know as much information as we can.0564

We came up with this thing called term symbol.0567

For the 1S configuration 1S1, the ground state, the term symbol is a doublet S.0571

Its J value is ½, the term symbol for this is doublet S ½.0577

The energy level is 000, that is the ground state.0583

All ground states are listed as 0 energy.0587

Let us go to the second level N = 2.0593

Very interesting thing here.0596

The level 2 has a 2P and 2S.0600

And the 2P itself actually consists of, it has a term symbol.0608

It is a doublet P ½ and also a doublet P 3/2.0612

The 2P state, in other words, if I keep this 1 electron to the 2P1 configuration,0619

there are two possible energies that it can represent.0625

It can be the doublet P ½ which is this energy and it could be the doublet P 3/2 which is this energy.0630

The N = 2 there is also 2S.0637

That is the doublet S ½, that has this energy.0640

Notice that level 2 actually consists of 3 closely spaced energy levels.0646

We have the doublet P ½ which is this one right here, doublet P ½ which is 82258.9191 and this is in inverse cm.0677

Another one has the doublet P 3/2 that is energy 82259.2850.0691

And then we have the doublet S ½ which is the ground state.0699

Let me make this ½ a little bit clearer, that is 8258.9543.0704

Interesting is not it?0716

You got this 2589543, notice that I have arranged this table in term order not in energy order.0719

On the web site that I got this, the National Institute of Science and Technology0731

has this database of spectral lines and spectral energy tables, and things like that.0734

The way I arrange this particular table, I want it to be in term order.0741

I did not necessarily say energy order.0746

Notice that this energy 258.95 is actually higher than the 258.919, which is the 2P.0748

Of course, the highest is the 2P but it is the doublet P3/2 which is the highest energy, that is the 259.2850.0756

The level 2 actually consists of 3 closely spaced energy levels.0766

I will talk about this in just a second.0770

Let us spend a little bit more time on this energy table and just sort of getting accustomed to what it is that is going on here.0777

What you want to concentrate on what this is, once you have a particular configuration,0784

notice 2P 2S, this gives the full breakdown.0791

If you just want to consider the level 2 on its own without worrying about the individual breakdown into energy levels,0795

you can just go ahead and take this number right here.0801

That is all that number means.0804

This two is just sort of a combination, if you will, of all of these.0806

We are going to be concerned about is the breakdown.0811

The 2P level has a doublet P ½ and doublet P 3/2.0816

The 3P level, notice the 3P is the same thing.0821

The 3P this is 3P1, this is 2S1 2P1.0823

Again, if there is no number there it just means that 1 electron.0828

If there is an electron in the 3P1 energy level, it is been kicked up from the 1S1 and the 3P1.0832

The term symbol for the P1 configuration is a doublet P.0839

The doublet P has 2 energy levels, 2 states, doubled P ½ and doublet P 3/2.0844

The S and S1 have a doublet S ½.0850

When we solved the Schrodinger equation for hydrogen, we found that the energy of the electron dependent only on N,0858

which is the primary quantum number.0900

Again, level 2 and level 3 and level 4 like what we saw in the energy table.0907

Y then is split into 3 energy levels.0917

It should not be, it should just be 1 energy level based on N2, N3, and N4.0931

That is it, single energy level but it is not.0936

The answer is spin orbit coupling.0939

I will mention it, I will define it, and then we will not worry about it anymore.0943

Spin orbit coupling is the interaction of the magnetic moment caused by an electron’s intrinsic spin with the magnetic field,0960

induced by the electric current caused by the electron’s own orbital motion.1000

In other words, we have orbital angular momentum and we have spin angular momentum.1035

The fact it is orbiting, the fact that this charged particle is orbiting, it is moving around, it is causing a current.1040

That current creates a magnetic field.1050

Do you remember from general physics?1055

The particle itself, the spin of the electron itself also has a magnetic moment.1057

The interaction of those two, the magnetic moment and the magnetic field that is what causes this energy splitting.1063

You do not need to know any more about this spin orbit coupling.1071

Just know that this spin orbit coupling is actually going to take a certain level1074

and split that level into closely spaced energy levels.1080

It is not going to be just 1 energy level, when you jump up a primary quantum number.1084

It is actually going to be several, that is all that is going on here.1089

As we saw level 2 is split into 3 energy levels.1096

I hope you keep referring back to that table, 3 energy levels.1117

Those 3 energy levels were doublet P 3/2, a doublet P ½ and a doublet S ½.1121

The Lyman series under higher resolution shows only 2 lines.1131

The Lyman series shows only 2 lines, why does not it show 3 lines representing the 3 following jumps?1144

Why does it not show 3 lines for the following transitions?1163

We said that the Lyman Series, we are going to take the first line.1184

That is going to be from N = 2 to N = 1.1188

The transition from N = 2 to N = 1.1191

We saw that level 2 was actually split up into 3 energy levels.1194

Basically, we are wondering that means that the 1S1 electron should go to 2S1.1197

They can go to 2P1 here, you can go to 2P1 that term symbol, or it can go to the 2S1 that term symbol.1207

We should see 3 lines but we do not.1220

We only see 2 lines, why is that?1223

Again, technically it should show because we have 3 energy levels, should be the following.1225

It should be the doublet P ½ down to the doublet S ½.1234

The doublet P 3/2 down to the doublet S ½ and the doublet S ½ to the doublet S ½.1244

These represent the transition from the 2P1 configuration to the 1S1 configuration.1259

This one is the 2S1 configuration down to the 1S1 configuration.1263

And again, configuration S1 S1, notice the term symbols are the same.1268

However, they are different primary levels, level 2 to level 1.1276

We should see 3 lines, one for this transition, one for this transition, one representing this transition.1281

But we only see 2, why is that?1286

Here is the answer.1289

The answer is selection rules.1291

They are selection rules that stipulate the allowed transitions1299

that an electron can make from one state to another.1332

These rules are expressed in terms of the changes in the quantum numbers.1349

The selection rules are as follows.1365

For atomic spectra, the selection rules are δ L = + or -1, + 1 for absorption spectra, -1 for emission spectra.1367

We are mostly going to be concerned with emission spectra.1385

We are mostly going to be concerned with higher levels to lower levels.1387

It is the same, except in reverse.1392

You absorb energy of a certain wavelength, you release the energy of a certain wave length.1393

We just had to speak more of emission spectra.1398

Δ S = 0, δ J = 0, or + or -1, and the J = 0.1406

If J = 0 and there is a transition, J = 0.1416

The J = 0, this transition is not allowed.1422

In this particular case, δ J = 0 but if you are going from 0 to a 0 that transition is not allowed.1426

That does not work, that is not allowed.1432

For the 3 possible transitions that we just listed for the hydrogen atom from level 2 to level 1 and1436

the first line of the Lyman series, we have a doublet P ½ going down to a doublet S ½.1456

The doublet P 3/2 transitioning down to a doublet S ½ ground state.1467

A doublet S ½ that is the 2S1 electronic, it is the 2S orbital following down to the ground state which is also a doublet S ½.1474

Here, your δ L from P to S, = -1.1489

Your δ S22, in this case S is 0, S is 0 δ S = 0.1496

Here our δ J is ½ to ½, = 0.1502

That qualifies, this transition is allowed.1509

Because that transition is allowed, we see that line.1513

Let me put a little separation here.1518

Here, our δ L from P to S, remember S is the top left, L represents the middle, and J is down here.1522

2S + 1 S is 0, because these top numbers are the same, δ S is the same.1532

P to S, we are concerned with δ L.1539

P to S that is -1 δ S = 0, 3/2 to ½ δ J = -1.1541

This qualifies, this is also allowed.1552

Δ L -1, δ S= 0, these are the allowed transitions.1558

For this final one, SS here.1562

Δ L = 0, δ S = 0, and δ J = 0, this is not allowed.1568

This transition is not allowed because δ L = 0.1577

Let us go to red.1587

This one right here, this transition is not allowed.1589

Therefore, we do not see this line.1591

Therefore, 1 electron is jumping up from when we energize the electron.1594

The 1S1 electron of hydrogen.1605

It will jump up to the 2P.1607

It will jump up to this one and it will jump up to this one because there are two energy levels for the 2P.1612

However, the 1S1 will not jump up to the 2S1.1618

That transition is not allowed.1622

Therefore, when the electrons fall back to the ground state, they are going to fall back from the 2P levels.1624

The doublet P ½ to doublet ground state, the double P 3/2 down to the ground state.1629

We would to see 2 lines.1634

2 lines because they are 2 slightly different energies.1636

We do not see a third line because this is a not allowed transition.1638

That is it, that is all that is going on.1643

Let us go ahead and write that out.1648

Only 2 lines appear, the lines for the allowed transitions.1650

We have a doublet P ½ to the doublet S ½ and we have the doublet P 3/2 to the doublet S ½.1666

Do not worry, the numbers will drive you crazy because these are numbers and symbols all over the place.1676

The wave numbers for these transitions are calculated straight from a table.1688

That is it, you just take the higher level - the lower level.1699

The wave numbers for these transitions are calculated straight from a table.1703

These tables are great.1707

They are calculated straight from the table.1709

The doublet P ½, this transition doublet P ½, the wave number frequency1721

for that particular transition is we just look at the table.1740

I find the entry for the doublet P ½ level 2, and I subtract the doublet S ½ the ground state which is 0.1746

It is going to be 82258.9191 -0.00, that transition takes place at 82258.9191 inverse cm.1755

I see one of those double lines at that frequency.1775

The other one, the doublet P 3/2 to the ground state doublet S ½, that frequency = 82259.2850 -0.00.1781

That = 82259.2850 inverse cm.1800

Clearly, these are very close together.1808

It is easy to see how under lower resolution, it is just go look like one line but it is not one line, it is 2 lines.1812

The 1S1 electron of hydrogen jumps up to that 2 level, it is not allowed to jump up to 2S level but it will jump up to 2P orbital.1819

However, the 2P orbital is split into 2 energy levels.1831

This one, the doublet P ½ and the doublet P 3/2, one that drops back down it releases photons.1836

That frequency is going to release a photon of that frequency, of that wave number.1843

We will see these as individual lines, these lines are closely spaced together.1852

It is the first line of the Lyman series.1856

You are going to see doublets for all the lines in the Lyman series because the 3P, 4P, 5P, 6P, 7P, and so on.1858

They all consist of the same doublet P ½, doublet P 3/2.1865

When we fall back down that is what happens.1869

Let us see, the appearance of the greater spectral complexity, in other words the multiple lines does not have to be double.1876

It can be triple, quadruple, whatever, depending on how many levels there are.1908

Multiple lines are called fine structure.1913

It is called the spectral fine structure, I will just say it is called a fine structure of the spectral line.1918

Let me write this a little bit better, me and my fast writing.1929

Let us take a look at an example.1938

Using the energy table for atomic hydrogen below, calculate the frequencies and1944

wave numbers of the allowed transitions from the 4D level to the 2P level.1949

The transition is going from the 4D to the 2P.1957

This is a notation that you often see.1959

More often than not, I tend to put parentheses around the electron configuration1961

that we remember from general chemistry 3D, 4D, 5D, 3S, 3P, 1S, things like that.1965

I tend to put parentheses around that and then the actual term symbol.1975

The 4D electron configuration, the term symbol for that is double t D.1981

It is going down to the 2P level, that transition.1988

The 2P consists of a doublet P.1993

Let us take a look at those and let us see what transitions are actually taking place.1996

Calculate the frequencies of the allowed transitions.1999

Let us go ahead and go to 4D, that is going to be right here.2002

It is a doublet D, notice the doublet D, the 4D energy and the 4D level also consists of 2 energy levels.2014

We have a doublet D 3/2 and we have a doublet D 5/2.2025

This could be one of the things that we are looking at.2029

This is not the ground state.2033

The state is going to fall down to, it is going to be the 2P and the 2P we see that it has 2.2036

We have 2 coming down to 2.2044

There are going to be 4 possible transitions.2047

Out of those 4, we want to see which ones are actually allowed.2049

It is going to be the doublet D 3/2 down to the doublet P 1/2.2053

The doublet D 3/2 down to the doublet D 3/2.2058

The doublet D 5/2 to the doublet P 1/2.2062

The doublet D 5/2 to the doublet P 3/2.2066

Those are 4 possible transitions, there may be up to 4 lines.2070

4 lines is the maximum that we see for the spectra.2074

We want to calculate the frequencies for those and we want to see which ones are allowed first.2076

These are the values that we are going to take a look at.2081

Let us go ahead and move on to the next page here.2085

The 4D doublet D, that consists of a doublet D 3/2,that is at 1028230.8943inverse cm.2092

And it also consists of a doublet D 5/2 which is at 102823.9095.2110

The 2P configuration which is a doublet P, that is also consists of 2, that is a doublet P ½,2121

that is going to be 82258.9191.2131

And there is a doublet P 3/2 which is going to be 82259.2850.2139

The available transitions are to be, this to this, this to this, this to this, this to this.2150

Possible transitions are therefore, we would have the doublet D 3/2 down to the doublet P ½.2161

For this one, our δ L = -1, our δ S = 0, our δ J 3/2 + 1/2 = -1.2190

This transition is allowed.2203

We will see a line, we will calculate the frequency in just a minute.2204

We will calculate that and we are just going to see which ones are allowed and which ones are not allowed.2214

The next possible transition is going to be the doublet D 3/2 down to the doublet P 3/2.2217

Here, we have a δ L, the D to the P that = -1, that is good.2227

We have a δ S 22 that = 0.2233

3/2 δ J = 0, this one is also allowed, not a problem.2236

The next possible transition we have is the doublet D 5/2 down to the doublet P ½.2249

Here, our δ L D to P = -1, so far so good.2261

Our δ S value 2 2 = 0 and our δ J = -2.2268

This transition is not allowed.2280

This transition is not allowed because our δ J = -2.2283

Δ J can only be + or -1.2294

This line, this transition will not happen.2297

An electron will not go from the 4D configuration whose state is represented by doublet D 5/2 to the 2P configuration.2301

The state is represented by doublet P ½, it is not going to happen.2313

The selection rules would not allow it.2317

The final transition is going to be a doublet D 5/2 all the way down to a doublet P 3/2.2320

Here we have δ L = -1, we have δ S = 0, and we have δ J = -1.2329

This one is allowed.2337

In this particular case, we have 3 allowed transitions.2339

The fine structure is going to show 3 lines.2342

The 4 possible transitions only 3 are allowed.2353

You would be doing this the same way.2365

Always find the possible transitions, check the δ L, δ S, δ J values and see which ones are allowed.2367

That is it when I calculate frequencies.2373

This transition which in this particular case is 4D to 2P, but it could be any D down to 2P,2375

it belongs to the Ballmer series of atomic hydrogen spectra.2390

We have a line in series which was from any N level down to the ground state.2396

This one is any D level down to the 2P level, that is it.2401

It belongs to the Ballmer series.2408

There are a whole bunch of series for each atom.2413

The hydrogen goes on, the posh and series and things like that.2416

Belongs to the Ballmer series for hydrogen.2421

The line representing this transition, the single line representing this transition result of the 3 lines of the fine structure.2435

Results into 3 lines under higher resolution.2453

Let us go ahead and calculate the frequencies here.2468

We have the doublet D 3/2 transition to the doublet P ½.2471

For this particular case, our frequency is going to be the upper – lower.2482

It is going to be 102823.8943 - 82258.9191.2490

Our frequency is going to equal 20564.9752.2506

We will see a line at that wave number.2514

The next one, I will do on the next page.2525

The next transition we had was the doublet P doublet D 3/2 down to the doublet P 3/2.2533

Our wave number is 102823.8943 - 82259.2580.2544

Our frequency of that particular transition is going to be at 2564.6363.2562

We will see a line at that particular frequency, that particular wave number.2572

Our file transition, we have a doublet D 5/2 to a doublet P 3/2.2577

This one is going to be 102823.9095 - 82259.25802.2585

It is the process that matters.2606

20564.6515.2612

There we go, we have 3 lines.2620

Let us take a look at what is looks like graphically.2622

I think I have to put here, put it here, just put that there.2627

This is the 4D configuration, our doublet D term symbol, our doublet D state.2653

This is the 2P configuration, our doublet P.2661

It consists of 2 lines, this one is the 4D doublet D 5/2.2665

This is the 4D doublet D 3/2.2678

Here we have 2P which is the doublet P 3/2 and we have the 2P doublet P ½.2683

The doublet D is consists of 2 energy levels.2697

The doublet P is consists of 2 energy levels.2702

Here is the breakdown in energy, here are the transitions that we have.2704

The basic transition, when you see a single line it is just the transition from the 4D to the 2P.2709

The doublet D to doublet P.2725

Single line, that is what we see when we see a single line.2727

When we look at the spectra under lower resolution.2730

On higher resolution, what is happening is the following.2732

You have this transition, you have this transition, you have this transition.2735

Notice this transition does not exist when we look at the spectra.2744

We are going to see a line here, we are going to see a line here.2757

We are going to see a line here.2764

This one is the 20504.9572.2771

This one right here is the 20564.6515.2783

That one right there is the 20564.6363.2795

Single line, higher resolution, you are going to see 3 lines for this transition.2807

All of these under lower resolution is just one line.2812

That is it, you just magnify and look at what is going on.2816

Multiple energy levels, multiple transitions.2819

4 possible transitions and 3 are actually allowed so we see 3 lines.2822

The tables are used in these lessons are available from the National Institute of Science and Technology,2833

the comic spectra database.2882

If you have ever taken a look at the National Institute of Science and Technology,2887

anything to do with science and technology is right there.2891

Wonderful databases like a gold mine of scientific information, absolutely wonderful.2895

In any case, if you are interested I will go ahead and put down .2901

It is www.NIST.gov/pmi/data/atomic spectra database asd.cfm.2905

When you go there, you do not need to, all the tables that you need are all going to be provided for you in the book, in the back of a book.2927

On your exams, you do not have to have to go there.2935

But if for any reason you are interested, you want to be around little bit and see what is available to you.2938

You want to play around and see all the different ways you can actually have the output come out.2941

Remember, I said I did it in terms of term order.2946

You can do in terms of energy order, all the different of columns.2948

There are other columns you can have on there.2952

There are fewer columns, just depends on what is it that you want.2955

Check it out, when you go to the spectra database just click help and that will lead you through2957

how to actually choose the information in order to recover a particular spectral data.2964

If you want to do that, you will just go ahead and get in touch with me here at www.educator.com.2971

Send me a question on line and I will be more than happy to lead you through it.2975

Let us go ahead and finish this discussion here.2980

Let us go ahead and take a look at helium, the energy table for helium.2984

This is the energy table for helium, the energy levels of helium.2994

Let us take a close look at this.2997

We have 2 electrons 1S2 in the ground state that is here.3001

Let us go ahead and do this in red.3005

0 energy ground state, 1S2 is the configuration.3007

The term symbol for that is singlet S0.3011

The J value was put in a separate column.3015

This just means singlet S0.3017

We can kick up, we can excite one of these electrons to a higher energy level.3020

Let us say we kick one of the electrons up to the 2P level.3026

We have 1S1 2P1.3031

Something interesting happens, 1S1, 2P1, that is a triplet P state.3034

That triplet P state, I have actually 3 individual states.3041

It is going to be triplet P2, triplet P1, triplet P0, and these are the energies.3045

That all electron can actually go to any one of these.3050

However, notice we not only have a triple in the state but the 1S1 2P1 configuration also has a singlet P state.3053

And that one has just 1, it is a singlet P1.3064

The question becomes which one does it actually jumped to?3069

And if you just take a look at the rest, you will see it is often like that.3072

You will see like over here, we have the 1S 3D 1S 3D.3076

We have a triplet D state, we have a singlet D state.3081

We have the 1S 2S, the 2S there is a triplet state and there is a singlet state.3083

The 3S there is a triplet state and there is a singlet state.3092

For helium, you have triplet states and singlet states.3095

Here it demonstrates helium and that is not the only one that does, other atoms do as well.3101

Helium demonstrates more than 1 spin multiplicity.3109

This number on the top left that is the spin multiplicity.3117

More than 1 spin multiplicity for a given level.3122

For example, we solve the 1S1 2P1, that has a triplet state and has a singlet state.3132

You will know the other levels, they are triplet and singlet.3145

In the transition from 1S to the ground state to the 1S1 2P1 excite state, the possible transitions are 1S2.3153

We can go from a singlet S to a triplet P.3190

I have left of the J values, I’m just speaking using basic terms symbols.3199

Or I can go from the 1S2 state which is a singlet S.3202

I can go to the 1S1, 2P1, I can go to singlet P.3207

The first is not allowed.3213

The first is not allowed because δ S is not equal 0.3227

Let me go to black here.3233

This is 1, this is 3, δ S has to be 0 in order for the transition to take place.3234

Here and here is what is allowed.3247

When this transition takes place, the electron in the S orbital goes up to the single P state.3249

It does not go up to the triplet P state.3251

This means the transitions and we see this for many atoms.3256

This means that transitions are only allowed between states with the same spin multiplicity.3270

We knew that already because δ S have to be 0 but we thought it would be nice to actually to say it again.3297

The spin multiplicity is the 2S + 1, it is the number on the top left of the term symbol.3304

Enclosing the selection rules that we have presented are appropriate3312

and are valid for atoms with relatively small atomic numbers.3337

Say less than 30 or 35, I’m just throwing out a number right there.3360

At higher atomic numbers, as atoms get bigger and bigger,3367

all the selection rules that we threw out this δ S equal 0, these rules have to break down.3370

There are larger atoms where states between singlet or transition do actually occur between singlet and triplet states.3377

With a spin multiplicity, when δ S does not have to be 0.3386

These set of selection rules that we threw in out and at this level is absolutely appropriate.3390

This is sort of where we would be staying.3394

We are not going to be worry about spectra for higher and heavier atoms.3397

This is appropriate mostly for relatively low atomic number atoms.3400

We just thought you should know that these selection rules are not set in stone.3406

It is not like this across the board.3411

As atoms get bigger, the selection rules break down.3413

We just want to let you know that.3415

At higher atomic numbers, these rules start to break down and all kinds of transactions take place.3418

It is very interesting, very complex.3449

I will go ahead and leave it that.3459

Thank you so much for joining us here at www.educator.com.3460

We will see you next time to work on some example problems for term symbols and atomic spectra.3462

Take care, bye.3468

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ISBN: 0935702997

Publisher: University Science Books

Year: 1997

"As the first modern physical chemistry textbook to cover quantum mechanics before thermodynamics and kinetics, this book provides a contemporary approach to the study of physical chemistry. By beginning with quantum chemistry, students will learn the fundamental principles upon which all modern physical chemistry is built. The text includes a special set of ""MathChapters"" to review and summarize the mathematical tools required to master the material Thermodynamics is simultaneously taught from a bulk and microscopic viewpoint that enables the student to understand how bulk properties of materials are related to the properties of individual constituent molecules. This new text includes a variety of modern research topics in physical chemistry as well as hundreds of worked problems and examples."

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