For more information, please see full course syllabus of Physical Chemistry

For more information, please see full course syllabus of Physical Chemistry

### 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 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

### 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 symbols*0004

*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 now*0667

*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 spin*0738

*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 number*0905

*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 configurations*1033

*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 component*1266

*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 momentum*1348

*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 workout*1516

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

*In other words, I'm going to pick a particular electron configuration and*1570

*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 is*1592

*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 and*1601

*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 arrangement*1616

*for a particular electron configuration and see how these arrangements fall into groups*1620

*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 page*2086

*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 and*2638

*what the energies of those configurations are and then all of those terms symbols that*2648

*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 orbitals*3210

*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 electronically*3529

*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

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