 Hi, I'm Zor. Welcome to Inizor Education. We continue talking about structure of atom. Now, previous lecture was just kind of a historical essay, I would say. There are many different people who participated in basically contemporary view on the atom structure. And it's not finished. I mean, it's still continuing. There are certain details which are still coming up, but we are not talking about contemporary level of this knowledge. We are going back to end of 19th century, maybe beginning of the 20th century, that probably would be the next lecture. And we will basically talk about how people progressed in their knowledge about atom. This lecture is part of the course called Physics 14's presented at Unizor.com. If you found the video for this lecture somewhere on YouTube or somewhere else, well, you will have just this particular video, obviously, but if you will go to the website all the videos and textual presentation, which accompanies every lecture, are organized into a course. So there is a menu. There are chapters, if you wish, topics, and it goes progressively from one topic to another, and I'm always using something which I have already covered before in subsequent lectures. So I do recommend you to go to Unizor.com and watch this and every other lecture from there and read the textual notes for every lecture, which is basically like a textbook. The site is completely free, by the way. There are no advertisement, no strings attached, so pure knowledge, use it as well. Right, so we are, right now, at the end of the 19th century, like 1880 something, 82 maybe. People did know at that time about electromagnetic fields. Maxwell equations have already been published and generally accepted, so light is the oscillations of electromagnetic field. That was the general opinion at that time, and people were actually studying how light behaves under different circumstances. One of the very important experiments which basically led to some kind of atomic structure was examining the light emitted by hydrogen when it's activated in some way. Like, for instance, you have electricity or heat or something like this when you are agitating the atoms of hydrogen, it emits light. Well, as many other things, if you have a piece of iron and start heating it up, eventually it will start glowing red, right? Okay, so light is emitted when well, we can say right now that electrons are agitated and their movement within the atomic structure actually causes this particular effect of glowing. So people were studying the very simple, the simplest atom of hydrogen. And they were knowledgeable enough to understand that the light can be spread into a spectrum and by that time many experimental physicists have uncovered what kind of light actually, what kind of components of the light emitted by hydrogen do exist and they could even measure the wavelengths. So at that time people basically came up with certain experiments which gave concrete wavelengths of the light emitted by hydrogen. And it wasn't just one particular monochromatic light. It was a few. So first was Johan Ballmer who basically measured the wavelengths of the different components of a spectrum emitted by hydrogen when it's agitated in some way, like he did, for example. And he had numbers. Numbers were the wavelengths. So let me just give a few of them. I have it written here. 656 nanometers 486 434 410 397 389 and 383. These were just few spectrum lights which spectrum components, these are wavelengths of certain lights emitted by agitated hydrogen, heated or electrified, whatever. And they correspond to certain colors. I think this one is red. This is something like... I don't remember. Maybe cyan. These are definitely violet. And these are all violet. I'm not sure about this one. Now experiment is one thing. But the theory, the real physical theory is another. So what was the first step when you have certain number of numbers which you don't know why they are this particular way? I mean the theory actually, the real theory came up much later. That was at the time of Bohr Adams model, which will be a subject of the next lecture. And that's the 20th century, beginning of 20th century. But at that time, 1880 something, people just had these numbers. They did not really know about planetary model of atom and electrons jumping from one orbit to another, emitting certain amount of energy as electromagnetic oscillations light. So at that time they didn't really know. But they had to build the theory. So what the first thing which comes up is to have some kind of a formula which basically combines these numbers together. And then if there is such a formula to be able to maybe explain why is such and such. I'm not sure, but quite probable some very known formulas, like for example, the Newton's gravity formula. Maybe they people came up with this formula before they actually explained why this particular formula is what it is. So in many cases, and this is one of the examples, people have decided to first let me come up with some kind of a formula which combines these numbers. And then I'll think about how to explain it. So Balmer was the one who basically combined these numbers into formula which he himself came up with. And quite frankly, I don't know how he came up with this formula because it's not that simple. It's simple but not very simple. It's not like y is equal to x square or something like this. It's a little bit more complex. I'll write it down. Anyway, he came up with this formula. He was probably thinking a lot about this. He was not really explaining why this formula describes exactly these particular numbers. But anyway, he managed to come up with this formula and it looks like this. Lambda which is this equals some kind of a constant n square divided by n square minus four. Where this is n equals three. This is n equals four. This is n equals five. n equals six, n equals seven, n equals eight, and n equals nine. So if you substitute n's into this formula where b is approximately 364 to 64.5 nanometers. So if you will substitute this into this formula, you will get these numbers where b is a constant. I checked. Yes, it does correspond. So this was a Balmer's formula. And again, he did not really explain why. And let me just jump a little bit forward. Now, since we were talking about planetary model of atom, I can say that n is actually the orbit number. Now, this is also orbit number. It's not really four. It's two square. Yeah, two square is four, right? But two is orbit number for an electron to jump two. And n is a number electron jumps from. So from third to second, that would be the light emitted by this particular jump. If electron jumps to the second level from number four, you will get corresponding light of different wavelengths. So it all depends on the difference in energy levels on level, let's say, three and level two. So the energy level is the one which quant of energy is emitted. And again, you remember we were talking before about energy of the photon equals to h times f. f is frequency of light at h's plant constant. We did talk about this in photoelectricity effect, etc. So since we have a difference between energy levels between, let's say, number three and number two, and then h is a constant that defines the frequency or wavelengths these are related. So he didn't know about that. Now, why is it from two, I mean into two, not into one, let's say, what about level number one, orbit on the first level? Well, the thing is very simple. The larger amount of energy between two different layers the more energy is supposed to be emitted in the photon. So the photon should have higher frequency, which means lower wavelengths. So the lower wavelengths than this would be ultraviolet and bummer just didn't see it. So that's why his formula is everything about jumping to level number two. What about jumping from, let's say, number eight to number five? No, this formula is not about that. So this is only about jumps to level number two, which is probably in his particular case was the most prevalent or I don't know his experiment how it was organized. Here comes Rydberg or Rydberg, Johannes Rydberg, Swedish. Just a couple of years later after Balmer, and he basically knew these results, but then either his experiments were different or whatever else, but he has come up with a different formula. And the different formula combined not only the level electron jumps from, but also the electron jumps to. So here's his formula. And again, he had a lot of experiments, a lot of data, and then he tried to combine these data into some kind of a formula. And you see, considering this formula is about jumping from two, both orbits are involved. Most likely he kind of had in mind the orbital structure. And I'm not sure whether it was really explicitly suggested, but in this particular case, he probably realized that there are two different positions of the atom or electrons within the atom of hydrogen. And these two positions are involved into each other. And he has come up with a slightly different formula, which actually is a generalization of Balmer formula. So the formula which Rydberg came up with is the following. Let's use m here and n here, where n is from and m is two. So m is orbit number. Now, let me use this more contemporary language to describe this. So n is the, maybe Rydberg used a different terminology, I'm not really sure, but from our perspective, n is an orbit number where electron comes from and m is the orbit number the electron comes to. Now, you see, this is slightly different than this, but to tell you the truth, it's exactly the same thing. Because if m is equal to two, so the orbit, it comes two is number two. So what do we have here? 1 over lambda equals R 1 fourth minus 1 n square, which is R n square minus 4 divided by 4 n square, right? Yes, common denominator. From which lambda is equal to n square divided by n square minus 4, 4 divided by R. So 4 divided by R is b and n square divided by square minus 2 is exactly this. So Rydberg formula, which is this one, where Rydberg constant is this one, describes a little bit more general case when electrons are jumping from any orbit to any orbit. And again, I'm not sure Rydberg was using exactly this terminology, but I would like you to understand it as this. So this is directly related to orbital model, which generally started by Rutherford. I don't remember the dates, actually. Maybe it was at the same time more or less, and obviously extended by Niels Bohr, but that was already beginning of 20th century, like 1911, 1913 or something. But anyway, this is the formula which actually somebody like Niels Bohr actually had in his hands. And it described quite well how a hydrogen atom emits light when it's heated or well, supplied some kind of an energy. Now, will it work for other elements, not hydrogen like helium, for instance, or a little bit heavier like metals, for instance, etc. Well, the problem is this formula is good for hydrogen. Why? Because hydrogen has only one electron. Now, whenever you have a more complicated model, I mean, heavier element with many electrons, there are other much more important forces which are participating in this, not much more important, but in addition to jumping from one level to another, there are certain other energy components which are involved in this process. And that's why the formula is good for one electron only. In a more complex case, we need much more complex things. But for one electron, it's a correct formula for hydrogen and a true explanation of why this formula is what it is came much later. It came with development of Bohr's model and basically even Bohr himself had to just postulate certain things which he did not himself explained. It was explained later on and we'll talk about this in the next lecture about Bohr's atom model. But in any case, I think you have to view this as a perfect example of how science is actually developing. First, you have some numbers and you have some kind of a formula which generalize these numbers and you have a better formula maybe and only much later you have an explanation of why formula is such and such based on certain axioms which people basically accept because well it seems reasonable or something like this. I mean obviously every theory should be explained based on some earlier results and earlier results based on some even more earlier results. It goes to certain axioms which we have to accept without the proof, without an explanation. And we do. And that's if it's correct, well if it corresponds to the reality, to the real nature, if our axioms correspond to reality then our subsequent theoretical derivations would also correspond to reality to a certain degree which basically defined by how precise we were with our axioms. So that's the theory of well not the theory it's basically practice of a Reitberg formula. It looks much simpler by the way than this one and quite frankly to me it presents less questions because why is it too square here? I mean just looking at Ballmer's formula you don't realize basically this kind of I don't know how to say it seems to be more natural all right if you wish. So that's what it is. I do suggest you to read the notes for this lecture it's on Unisor.com so if you go to atoms in physics the physics for gene course then you go to atoms and it's building blocks of matter chapter series of lectures and this lecture is about Reitberg formula. Reitberg or Ringberg I'm not sure. All right that's it. Thank you very much and good luck.