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

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

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## Table of Contents

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### Spectroscopic Overview: Which Equation Do I Use & Why

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
- Spectroscopic Overview: Which Equation Do I Use & Why
- Lesson Overview
- Rotational & Vibrational Spectroscopy
- Frequency of Absorption/Emission
- Wavenumbers in Spectroscopy
- Starting State vs. Excited State
- Total Energy of a Molecule (Leaving out the Electronic Energy)
- Energy of Rotation: Rigid Rotor
- Energy of Vibration: Harmonic Oscillator
- Equation of the Spectral Lines
- Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections)
- Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections)
- Vibration-Rotation Interaction
- Centrifugal Distortion
- Anharmonicity
- Correcting for All Three Simultaneously
- Spectroscopic Parameters
- Summary

- Intro 0:00
- Spectroscopic Overview: Which Equation Do I Use & Why 1:02
- Lesson Overview
- Rotational & Vibrational Spectroscopy
- Frequency of Absorption/Emission
- Wavenumbers in Spectroscopy
- Starting State vs. Excited State
- Total Energy of a Molecule (Leaving out the Electronic Energy)
- Energy of Rotation: Rigid Rotor
- Energy of Vibration: Harmonic Oscillator
- Equation of the Spectral Lines
- Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections) 28:37
- Harmonic Oscillator-Rigid Rotor Approximation (Making Corrections)
- Vibration-Rotation Interaction
- Centrifugal Distortion
- Anharmonicity
- Correcting for All Three Simultaneously
- Spectroscopic Parameters
- Summary 47:32
- Harmonic Oscillator-Rigid Rotor Approximation
- Vibration-Rotation Interaction
- Centrifugal Distortion
- Anharmonicity
- Correcting for All Three Simultaneously

### Physical Chemistry Online Course

### Transcription: Spectroscopic Overview: Which Equation Do I Use & Why

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

*Today, we are going to start our discussion of molecular spectroscopy.*0004

*I had a little difficulty deciding on how to actually present molecular spectroscopy.*0013

*What I decided to do was to start with a lesson which gives an overview of primarily the rotational and vibration spectroscopy.*0017

*The reason I want to do this was the lessons that come after this are actually going to discuss in detail, what it is that I present here.*0026

*But I wanted to give a big picture of what it is that is going on*0036

*because you are going to be sort of swimming in this ocean of equations.*0041

*And a lot of it is like where is this coming from and when do I use this?*0043

*I want to let you know why we are choosing the equations we are choosing and*0047

*how to actually choose when you are faced with a specific problem.*0052

*Again, this is the big picture so you have an idea of what is going on with the details,*0055

*when we get to the details of subsequent lessons.*0059

*Let us get started.*0061

*Let me go ahead and write that down and repeat that.*0064

*This lesson intends to provide a concise and broad overview of rotational and vibrational spectroscopy.*0067

*There is nothing in this particular lesson that you actually have to like know for sure in terms of an equation because again,*0110

*all of this is going to be discussed in detail for the next lesson and the lessons that follow.*0116

*This is just a big picture.*0121

*Just get an idea of what is going on before you get down to the nitty gritty.*0123

*What you see here will be discussed in detail in the next 4 lessons.*0128

*In the lessons that follow and in your book, it can appear that you are swimming in an ocean of equations.*0158

*This lesson here hopes to answer the question which equation and why, which equation do I use and why.*0200

*Very important equation, which is a very important question.*0228

*The discussion that we do for all spectroscopy is only going to concern diatomic molecules.*0237

*This discussion concerns diatomic molecules.*0246

*When a molecule absorbs radiation of a given frequency of transitions to a higher state,*0267

*you know this and you are reasonably familiar with spectroscopy from your work in organic.*0289

*The transitions to a higher rotational, vibrational, or electronic state.*0293

*Microwave radiation tends to affect only the rotational state.*0320

*The infrared tends to affect the vibrational state but with vibration you also get rotational changes.*0326

*The visible ultraviolet region of the electromagnetic spectrum tends to promote electronic transitions.*0339

*Along with electronic transitions, you also get vibrational changes and you also get rotational changes.*0347

*The higher the energy, the more it does.*0359

*The frequency of this absorbed radiation or emission, emission is just the other way, excited state down to lower state.*0366

*There is no real difference but for our purposes emission.*0404

*The frequency is given by, we have is relation that you remember from early on.*0409

*If there is a change in the energy, the energy of the final state - the initial - the energy of the initial state.*0416

*It is energy final - energy initial and that was equal to H × ν.*0425

*We have this equation already.*0432

*Therefore, the frequency of this transition is going to be the final energy - the initial energy*0435

*divided by planks constant, in terms of frequency, in terms of hertz.*0442

*The energy of the final state - the energy of the lower state, or the arrival state to the departure state.*0449

*However you want to say it, how it started and where it ended divided by planks constant.*0454

*That gives you the frequency that we see on the spectrum.*0459

*That is all that is happening.*0461

*Or we can say, we can call it energy upper - energy lower divided by that.*0464

*This is going to be important for us because these frequencies are what we going to see on the spectrum.*0475

*That is what we are reading off is this.*0480

*Any time you want to know what the frequency of the spectral line is,*0483

*take the higher energy - the lower energy divide by planks constant.*0486

*In spectroscopy, we usually work in wave numbers not Hz.*0492

*In other words, inverse cm.*0514

*A wave number is anything with a ̃ symbol on top of it, means it is in inverse cm.*0519

*The definition is very easy to state whether frequency you have divided by the speed of light,*0525

*that will give you the wave number.*0531

*It is also equal to 1/ the wavelength λ.*0534

*In cm then, in inverse cm then the frequency of the spectral line that we see*0544

*is going to be the final energy - the initial energy divided by HZ.*0558

*That was going to be important for us.*0564

*What we are going to try to do, we will try to find equations that explain, that predict the experimental spectra that we see.*0567

*We run an experiment, we get some lines on the spectrum.*0589

*We try to come up with equations that explain those lines, that is all we are doing.*0604

*It is really all we are doing.*0608

*The ν above, the wave number above are the frequencies that we see on the spectra.*0612

*In other words, they represent the differences in energy between the starting state and the final state.*0638

*I’m going to say the starting state and excited state.*0687

*How is that, it is probably a little bit better.*0692

*Usually, we can really be going from ground stage to excited state.*0696

*We are going to be seeking equations for the energy of a given quantum state.*0702

*We, then form energy final - energy initial to give us the frequency that we observe.*0721

*This is really what we are doing here, for the next 4 or 5 lessons all we are really concerned with,*0737

*we want to find an expression for the energy of a given quantum mechanical system.*0741

*We subject that quantum mechanical system to the radiation, microwave, infrared, visible UV.*0747

*The rotational, vibrational, electronic transitions that take place taken from one level to another.*0755

*One rotational level to another rotational level.*0761

*One vibrational level to another vibrational level.*0764

*One electronic state to another electronic state.*0767

*We can find the energies of those two states.*0770

*We want to find equations that will give us the energy for those two states.*0773

*We actually have them, that is what we did and what we have been doing for the last 30 or 40 lessons in quantum mechanics,*0776

*finding energies for the different quantum mechanical systems that we are dealing with,*0782

*particle in a box rigid rotator harmonic oscillator, whatever it was.*0786

*If I take the difference between the ground state or the beginning state and the excited state,*0790

*what I get are the frequency that I see on the spectra.*0795

*We want to find equations for those.*0799

*We find the equations for the energies, that is what is important.*0801

*And then, we take the difference between the lower and the higher energy level and*0803

*that gives us the frequency that we see on the spectra.*0807

*We just want equations for E and for ν.*0810

*Let us see, I’m going to leave off the electronic energy for right now.*0817

*Just know that it is actually there and in the subsequent lessons where we introduce it.*0826

*But for right now, I just want to talk about vibration and rotation.*0831

*If you understand those well, everything else after that is very very simple because it is the same thing.*0833

*I’m just adding one more term for the electronic energy.*0838

*Leading out the electronic energy of an atom for the moment,*0843

*the total energy of a molecule is equal the energy of the rotation of the molecule +*0865

*the energy of the vibration of the molecule.*0892

*Let me stop for a second.*0895

*A molecule has 4 types of energy.*0898

*A molecule is translational energy, it is moving.*0900

*It has electronic energy, the energy of the electronic states.*0904

*It has energy of vibration, it is vibrating.*0911

*It has the energy of rotation, it is rotating.*0913

*Notice that I have left off the electronic energy.*0916

*We have also just automatically left off the energy of translational because*0918

*the energy of translation is not affected by spectroscopic interaction, by radiation interaction.*0922

*Basically, we will deal with the translational energy a little bit later when we talk about statistical thermodynamics.*0928

*But for spectroscopy, we are only concerned with electronic, rotation, and vibration.*0935

*For right now, I'm leaving off the electronic just to concentrate on rotation and vibration.*0938

*I think that gives us the best big picture.*0942

* For our purposes, the total energy comes from the energy of rotation and energy of vibration.*0946

*Let us deal with the rotational energy first.*0952

*The energy of rotation, the model for that is our rigid rotator.*0956

*We pretend that a diatomic molecule is just two bodies stuck together and it is rotating,*0968

*that gives us a model for this.*0975

*Now rotator, the energy sub J we said was equal to H ̅² / 2I × J × J + 1.*0979

*J was equal to 0, 1, 2, and so forth.*0991

*I was the rotational inertia, it was the reduced mass × the bond length².*0996

*It had degeneracy as a function of J is equal to 2J + 1.*1003

*This is energy in Joules.*1012

*We want to express the energy in wave numbers.*1025

*Basically, then take any energy in Joules and just divide by HZ and that will give you an energy in wave numbers.*1053

*In inverse cm, our energy sub J, we are going to express this now in terms of wave numbers.*1078

*We will get a new symbol F of J and we write it this way BJ × J + 1,*1089

*where B is equal to planks constant / 8 π² C I.*1101

*The rotational energy in inverse cm is given by this equation B × J × J + 1.*1109

*I’m not going to get into great detail here about what each of all the stuff is because*1117

*I will discuss it again in the subsequent lesson, in the next lesson.*1121

*In fact, we are going to start off with vibration and rotation.*1124

*We will talk about all of this in great detail.*1127

*Do not worry, I just want to show you again what is happening with the equations,*1129

*why we are choosing the equations we are choosing.*1133

*This gives us the equation for the rotational energy of a molecule.*1136

*For the vibrational energy, for E sub V vibration, this is from the harmonic oscillator.*1146

*That is our model so we are going to begin with that equation to represent the vibrational energy of the molecule.*1155

*The energy sub R was equal to ν × R +, it was H μ + ½ values of 0, 1, 2, 3, and so on.*1164

*Again, these are the vibrational quantum numbers.*1180

*Here, ν was equal to 1 / 2 π K / μ ^½.*1183

*In inverse cm, our expression is energy sub R given new symbol G of R is equal to ν ̃ × R + ½.*1193

*Here, ν~ is equal to ½ π C / μ ^½.*1210

*Again, do not worry about it this is just big picture stuff.*1218

*Now, I have the vibrational energy, it is given by this thing.*1221

*I have the rotation energy given by what you saw.*1225

*Our total energy is equal to the vibrational energy + the rotational energy.*1228

*We have that the total energy is equal to, total energy is a function of R,*1241

*the vibrational quantum number and J the rotational quantum number.*1251

*It is equal to G of R + F of J.*1255

*E sub RJ is equal to this thing ν × R + ½ + B~ × J.*1266

*Let me make this J a little bit more clear here.*1279

*J × J + 1.*1283

*R takes on the values 0, 1, 2, and so on.*1287

*J takes on the values 0, 1, 2, so on, independently.*1291

*This, under the rigid rotator harmonic oscillator approximation for the energy of a molecule,*1299

*this equation gives me the energy of a molecule who is in vibrational state R, rotational state J.*1312

*ERJ is equal to ν~ R + ½ + B × J × J + 1 under the harmonic oscillator rigid rotator approximation,*1327

*because molecules are not rigid and they are not harmonic.*1354

*The first approximation, I’m going to make one correction for this.*1358

*Under the harmonic oscillator rigid rotator approximation, this equation gives the energy.*1361

*Very important.*1375

*The frequency of absorption because the energy of the molecule in vibrational state R and rotational state J.*1376

*That is very straightforward.*1399

*To find the equation of the spectral line, find the equations of the spectral lines.*1402

*In other words, the transitions from one energy level to another.*1428

*To find the equations of the spectral lines, we take the energy R upper J upper - the energy R lower J lower.*1437

*The upper energy - the lower energy, whatever those happen to be.*1460

*For example, if I would want the equation for the observed, for the ν of the spectral line*1465

*for the 0, 2 to 1, 3 transition, this is R lower and this is the J lower.*1500

*This is the R upper, this is the J upper.*1511

*I would form the Δ E.*1519

*In other words, I would form the energy of the 1, 3 - the energy to 0, 2.*1523

*That will give me an equation for the spectral line.*1534

*The equation that predicts where it should be.*1538

*Running the experiment tells me where actually is.*1541

*The extent to which is a good match depends on my equation.*1544

*This is an approximation that is going to be off when I start making corrections to*1548

*this harmonic oscillator rigid rotator approximation, that gives me a better and better predictions until it is almost exact.*1552

*That is what is happening here.*1559

*It is the energy equation that is important.*1570

*The spectral line equation, the observed frequency or the predicted frequency,*1582

*that I can derive just by taking the energy / - the energy lower.*1586

*It involves a lot of algebra but it is doable.*1590

*It is the energy equation that is important.*1594

*The equations for the absorption emission frequencies can be derived with algebra, energy upper - energy lower.*1601

*A lot of the mess that you see, as far as all these equations, all the derivations that you see*1646

*in the spectroscopy, that is the stuff right here.*1651

*We are taking upper energy - lower energy.*1659

*We are coming up with different equations.*1662

*The thing is we have the harmonic oscillator rigid rotator approximation.*1664

*You will see in a minute that would give us one set of equations.*1668

*When I start making corrections to that, for different phenomenon that I observe*1672

*to make my equations match more of what the real spectra look like give me the different equations.*1676

*It is not really 150 equations that you have to know, you have to know just one.*1683

*The corrections to that one can where everything else comes from.*1690

*That is what I'm trying to do with this lesson.*1693

*I’m trying to show you which one or two equations are important.*1695

*And then from there, depending on what corrections you make, you can derive everything else.*1699

*That is what you are seeing is the derivations.*1703

*Do not get lost in the ocean.*1706

*That is why this is probably the most important lesson of spectroscopy, the overview to the big picture,*1708

*the forest before we get into the trees.*1713

*Let me go back to black here.*1721

*The harmonic oscillator rigid rotator approximation is precisely that, just an approximation.*1726

*Approximation is just that.*1733

*It is an approximation.*1746

*We will now make corrections to the vibrational term, rotational term,*1750

*to make the equations more closely match what we see in experiment.*1774

*To make the equations better match and predict what we see in reality.*1780

*We are going to correct for three things.*1805

*We will correct for three things.*1815

*The lessons, each one, we will talk about a different correction.*1818

*We will correct for three things, we will talk about what they are.*1821

*This is all big picture stuff.*1825

*It is actually really important.*1829

*I wish that more people would spend more time on the big picture stuff because it will make all the details*1831

*and you will know exactly what is going on because I can see the big picture.*1835

*It is better to see from the outside in than it is to be the inside trying to look out, that is the idea.*1842

*Any time you find yourself lost in science or math or whatever it is,*1851

*99% of the time it is going to be because you are inside trying to look out.*1856

*Try to find someone or some book or some other way to get yourself on the outside looking in the big picture.*1862

*All the details are not irrelevant but are secondary.*1868

*If you have the big picture, you really understand, then science becomes a beautiful thing that really is.*1873

*We will correct for three things.*1883

*The first thing we are going to correct for, we would be correcting for something called vibration rotation interaction.*1884

*We are also going to correct for something called centrifugal distortion.*1900

*We are going to correct for anharmonicity.*1910

*Each correction will modify our basic equation, our basic energy equation E sub RJ is equal to ν ̃ R + ½ + B~ × J × J + 1.*1916

*This is our basic equation, it is a rigid rotator harmonic oscillator approximation to the energy of a molecule.*1959

*Each correction we make is going to modify this equation and give us a new energy equation.*1968

*I can do one correction.*1973

*I can correct for 1, I can correct for 2 of them, any two.*1975

*Or I can correct for all three, depending the equation becomes more and more complicated.*1977

*That is all that is happening.*1983

*The three corrections above R will be discussed in the lessons that follow.*1995

*Let us talk about our first one which is vibration rotation.*2019

*Let us talk about the vibration rotation correction.*2032

*We are making a correction for something called vibration rotation interaction.*2049

*Let us talk about our basic equation E sub RJ is equal to ν~ R + ½ + that × J × J + 1.*2058

*B itself, the correction that we are going to make B actually depends on R.*2079

*We symbolize that with a B sub R.*2096

*B sub E - Α sub E × R + ½.*2099

*We take this expression and we have to put into here for the correction.*2105

*When we do that, we get the following modified basic equation.*2112

*We get E sub RJ is equal to ν × R + ½ + B sub R - Α sub E × R + ½ × J × J + 1.*2118

*We now get a slightly more complicated, slightly more complicated equation for the energy of a molecule.*2138

*This equation accounts for something called the vibration rotation interaction.*2149

*When we use this equation, when we take the difference of the upper and lower*2153

*to get a new equation for the observed frequency, what we get is closer to what we see.*2157

*It gives us a little bit closer.*2161

*This is the harmonic oscillator rigid rotator corrected for vibration rotation interaction.*2164

*That is one of the corrections that we are going to make.*2183

*Again, I'm going to do each one of these corrections one at a time.*2189

*I took the basic equation, I corrected for vibration rotation interaction.*2194

*Now, I’m going to go back to the basic equation correct for centrifugal distortion.*2197

*I’m going to take the basic equation, I’m going to correct for anharmonicity.*2201

*We can put them all together, 2 at a time, 1 at a time, 3 at a time.*2206

*That is what we do.*2210

*Let us talk about centrifugal distortion basic equation.*2211

*We have E sub RJ is equal to ν × R + ½ + B × J × J + 1.*2227

*Real quickly, centrifugal distortion what is it is when a molecule rotates, the rigid rotator assumes the bond is rigid.*2249

*A diatomic molecule speeds faster and faster, it is not rigid, the things actually pull apart.*2258

*Notice from your experience, if you spin something, it starts to pull apart.*2264

*Because of the bond actually stretches, we have to make an adjustment for that.*2267

*The adjustment that we make gives us the following equation E sub RJ is equal to ν × R + ½ + B × J × J + 1.*2274

*That is our basic equation, the correction is DJ² J + 1².*2291

*This is the new energy equation under a correction for centrifugal distortion.*2301

*Let us go ahead and do our third correction.*2309

*We are going to correct for anharmonicity.*2311

*Once again, we have our basic equation E sub RJ is equal to ν ̃ R + ½ + B~ × J × J + 1.*2318

*As you move to higher and higher vibrational states, as it starts to vibrate more and more violently,*2344

*it starts to deviate from harmonic behavior.*2349

*It does not become harmonic.*2352

*We have to adjust for that.*2355

*The equation that we end up with is E sub RJ is equal to ν sub E × R + ½.*2357

*It is not ν~, it is ν sub E ̃, different set of numbers.*2367

*X sub E ν sub E × R + ½² + B × J × J + 1.*2373

*This is the new equation for the energy of a molecule after we have made a correction for the anharmonic behavior.*2386

*Notice each time the basic equation was corrected for one phenomenon, we can correct for 1, 2, or all 3 phenomena simultaneously.*2396

*Correcting for all three simultaneously gives us the best agreement for what we actually see in the spectra.*2454

*Correcting for all three simultaneously gives us the best agreement for the energies and*2467

*absorption emission frequencies we see in the actual experiments.*2505

*Correcting for all three, the equation becomes this.*2517

*E sub RJ is equal to ν sub E × R + ½ - X sub E ν sub E × R + ½² + B sub E - Α sub E × R + ½ ×,*2520

*I will put it on the second line here because I want to see that it is actually three different corrections.*2550

*+ B sub E - Α sub E × R + ½ × J × J + 1 - DJ² J + 1².*2558

*The correction for anharmonicity correction for vibration rotation interaction, correction for centrifugal distortion,*2583

*this equation gives me the total energy of the molecule that comes from rotation and vibration.*2593

*Adjustments made to account for more of the reality of what is going on.*2604

*In fact that the molecule is not a rigid rotator.*2608

*The fact that the vibration of the molecule does not follow a harmonic model.*2612

*The predicted frequency of absorption and emission, I will call it predicted if you want, equation predicted.*2619

*Let us write predicted or calculated.*2632

*The equation is going to be the ERJ for the upper state - the ERJ for the lower state.*2637

*In other words, one of these whole equations for the upper state and one of these whole equations*2646

*for the lower state depending on what RJR.*2651

*You put those values in here and you get this equation.*2654

*You will do a whole bunch of algebra to reduce it down as an equation*2657

*that will predict what the frequency of the spectral line is.*2661

*Now, the symbols, do not worry about these symbols.*2668

*The symbols ν sub E X sub E ν sub E is actually a single symbol by the way, we will get to that.*2675

*B sub ED, Α sub E are called spectroscopic parameters.*2686

*I have it tabulated for you for a bunch of diatomic molecules.*2710

*In the problems you come across here in your book, on your exams,*2721

*you will be given the spectroscopic parameters and you have to find information.*2727

*Or you will be given certain spectroscopic information and you have to find the spectroscopic parameters.*2730

*It pretty much all comes down to.*2735

*Not always easy but that is what it comes down to.*2737

*That is the big picture.*2740

*When you do your homework problems, you will be told which corrections, if any you need to make to the basic equation.*2745

*You will be told which corrections to account for.*2768

*The particular corrections that they are asking for, that is going to decide which equation you use.*2785

*These will decide which equation you use.*2798

*You might have a problem that says under the harmonic oscillator rigid rotator approximation,*2813

*you know to use the basic equation.*2817

*You might say under the anharmonic oscillator also accounted for centrifugal distortion, you use the appropriate equation.*2819

*That is what is happening.*2831

*Again, the ocean of the equations that you see in your book,*2835

*that is all the various energy upper - energy lower equations that they are driving for you.*2838

*Let us go ahead and turn to our summary.*2847

*Here is our summary, very important.*2854

*For harmonic oscillator rigid rotator approximation, this is the basic equation*2856

*under the harmonic oscillator rigid rotator approximation.*2861

*The vibration rotation interaction, this is a correction to the rotational term.*2865

*This is the correction.*2870

*The centrifugal distortion, this is also a correction to the rotational term.*2873

*That is this one, it is - this thing.*2877

*The anharmonicity, this is a correction to the vibrational term.*2881

*It is this thing we are subtracting from this.*2884

*This is the vibrational term.*2886

*This is the rotational term.*2893

*For the vibration rotation interaction, use and take this thing into here.*2895

*If you are accounting for centrifugal distortion, you subtract it here.*2902

*The vibrational term, you take this thing and you subtract it here.*2910

*The vibrational term and the rotational term.*2917

*These two correct for the rotation and this one correct for the vibration.*2918

*Correcting for all three simultaneously, this is the equation that makes a correction for all three simultaneously.*2926

*Here is a correction for vibration rotation.*2937

*Here is the correction for centrifugal distortion.*2940

*Here is the correction for anharmonicity.*2944

*This gives you the energy of a molecule.*2947

*It is in a rotational state given by J and a vibrational state given by R.*2951

*If that molecule is excited to another vibration and or rotational level, the frequency that we see on the absorption or emission spectrum*2960

*is given by the energy of the upper state - the energy of the lower state.*2972

*All that is happening in the next 5 lessons.*2980

*The difficulty, rather the tedium and the mess, come from working out the algebra for this.*2983

*I hope that helped to see the forest, now we can get into the trees.*2994

*Thank you so much for joining us here at www.educator.com.*3000

*We will see you next time, bye.*3001

3 answers

Last reply by: Joseph Carroll

Mon Apr 4, 2016 1:54 AM

Post by Joseph Carroll on March 30, 2016

Professor Hovasapian, your lectures never cease to amaze me, especially how, this one in particular, relates so closely to the truth of our very existence in correlation with God.

It reminds me of how our lives are like how a basic equation that computes incorrectly/short when it comes to the reality of what is seen in experimentation. The Father, Son, and Holy Spirit are our correction for our sin nature which was caused from the fall in the Garden of Eden by Adam and Eve who disobeyed God and ate of the apple of the tree of knowledge.

Just like the vib-rot, centrifugal distortion, and anharmonicity corrections are needed to provide the truth of what is actually observed in reality with respect to molecular spectra lines, we need the (1) correction of God the Father, whom sent His Son Jesus Christ of Nazareth to atone/correct(2) for our sin

[a "correction" for something that we could never do fully do since the time God established the 10-commandments covenant through Moses on Mt. Sinai to prove to the Israelites, and to the Gentiles (us), that we could not do follow them, not even King David of Israel (reigned as king sometime between c.1040 - c.970 BCE) who loved God with all his heart and tried his best to do God's will]

by sacrificing himself on a cross(c.33AD) for our disobedient hearts. The final and third correction is His Holy Spirit (3) (sent to baptized, repented believers, {first sent to jesus apostles shortly after His death}) to correct for how we should live a life pleasing to God and ultimately obtain resurrection from the dead just like Jesus Christ did 3 days after his crucifixion near jerusalem. All who confess that Jesus Christ is Lord and believe with all his heart that the Father rose him from the dead will be saved from eternal death and rise to eternal life to worship his creator forever.

2 answers

Last reply by: Professor Hovasapian

Thu Dec 17, 2015 2:27 AM

Post by Van Anh Do on December 14, 2015

I'm not sure why E tilda is E/hc. I thought anything with a tilda is just itself divided by c? Thanks!