 Hi, I'm Zor. Welcome to a new Zor education. Today I would like to talk about the model of Atom, developed by Nils Bohr, very famous physicist. He lived in Copenhagen. Actually, I was once in Copenhagen and I saw the house where he lived. Okay, so this lecture is part of the course called Physics for Teens, presented on Unisor.com. The website Unisor.com is totally free and it contains other courses as well, Maths for Teens, which is a prerequisite for this course and some others. I do suggest you to watch the lecture from the website, because every lecture has notes, very detailed notes like a textbook. So you have a video and you have basically the same explanation, but in a more like textual format. Okay, now the Bohr's model of Atom has been developed based on whatever the previous knowledge was about it. Primarily the planetary model of Rutherford, which we talked about before. So Bohr and other physicists, obviously, saw the problems with planetary model as it was presented by Rutherford. Now, what was the problem? Well, the first problem was, you see, Atom contains nucleus and electrons which are rotating around nucleus. That's the classic planetary model of Rutherford, which he came up with because he saw that Atom is practically empty. The particles can bomb body and go through the Atom. So Atom cannot be like a flung pudding, if you remember. That was the earliest model. So now when the electrons are rotating around the nucleus, they must be under certain force which forces them to go around the nucleus. And whenever you have something like a circular orbit, you have some triple acceleration. So the force between the nucleus and the Atom, nucleus is positively charged, electron is negatively charged. So this force of attraction makes electron to accelerate centripetally. Accelerated electron, according to a classical theory of electromagnetism, must emit electromagnetic waves, oscillations of electromagnetic field. Now, but if that's the true, now the electron is supposed to have certain energy if it rotates in certain radius. And whenever the energy is lost, the electron must actually get closer to the nucleus and eventually it will fall. So as it rotates, it's supposed to emit electromagnetic oscillations all the time and lose energy and eventually reduce this orbit and fall, which is obviously not the case because I mean that would destroy the structure of the of the matter basically. Okay, so we needed to correct this planetary model, not to completely reject it at all, because really the structure of nucleus and electrons around it was kind of beneficiary for the physics. It looks like it experimentally was proven. So how can we improve this? Well, so one problem is that electron would lose the energy and fall on the nucleus, which is not the case. There is another problem. Now, if electron is just floating on any orbit whatsoever, then it must actually move from one orbit to another. If we give some energy boost to an electron, it should go to a higher, more energetic orbit. Or if it loses energy, it will emit certain electromagnetic oscillations of certain wavelengths. Now, if that's basically the case and that said, there are no other rules, so to speak, then if we will supply energy to let's say hydrogen atom, the electrons will move from one orbit to another, emitting certain light. If they go from higher to lower orbit, so we first give some energy, they move to a higher orbit electrons and then after we move, after we give more energy, they cannot move any further. So they will spontaneously move down and emit certain amount of electricity, certain amount of energy in the way of electromagnetic oscillations. So we will see some light, which is true. We do. I mean, whenever we have something like a tube with hydrogen and we put some electrodes in it and supply some energy after a certain amount of time, the tube will start emitting light. But the light which it will be emitted would have a continuous spectrum, so to speak. So if we will go with this light through a prism, it will give all the different colors without any kind of a preference or whatever, which contradicted different sets of experiments, experiments which were analyzing the spectrum of the light emitted by, let's say, hydrogen. Now the spectrum was not continuous. There were distinct separate lines which basically, specific for hydrogen atom, let's say for some atoms of another gas, it was different items, but still distinct separate monochromatic lines in the spectrum, specific for each particular element. So that cannot be explained by a plane, plane-tree model as it was suggested by Rutherford. So Bohr has suggested certain things. I mean, it was not like theoretically derived from certain other principles. So let me just suggest what Bohr suggested. So first of all, he suggested that there are certain orbits for each element, its own set of orbits, which he called stationary. Now, being on a stationary model, being on a stationary orbit, or within a stationary shell, because we are talking about three-dimensional world, so within this stationary shell, electron is rotating or doing something, whatever it's doing on this orbit or within its shell, but it does not emit an energy. Don't ask why, it just does not, basically. That's it. That's a suggestion. It's a hypothesis. So now that's number one. Number two, when it jumps from one stationary orbit to another, it cannot be on any other orbit but on stationary. And when it jumps from one stationary orbit to another, it either emits electricity if it's from a higher orbit to a lower, or consumes certain amount of electricity whenever a certain amount of energy, I should say, when it goes from a lower orbit to a higher orbit. So that's basically, so if this is the nucleus, these are stationary orbits. So whenever it jumps from here to here, it's supposed to consume certain quantum of energy. If it goes from here to here, it emits it. Now, there are other so it can jump from here to here, let's say. Then amount of energy would be equal to the difference between the energy level. So energy high. That's the energy level on the higher orbit, minus energy low. When it moves from higher to low is equal to amount of energy emitted by this particular jump. And now we're going into some kind of a theory which was developed before by Max Planck and then used by Einstein in photoelectricity effect. It's equal to H times frequency of light emitted. And this is Planck's constant. So whenever it moves from energy level to energy level, it emits light of this particular frequency. Frequency is equal one over period. And period is equal to down to the right. See the speed of light, now this wavelength. So this is basically its frequency. This is the period. This is the wavelength. And this is the speed. Okay. So that was a proposition. But that's not it. It was another proposition which were made. And I'll just put it as textbooks usually presented. And I don't like it at all. However, that's how it is presented by textbooks. He suggested that there is something which is called angular moment of the electron. It's basically mass of electron times its speed times radius of its orbit. It's angular momentum. Now I think angular momentum was actually addressed in mechanics part of this course. But regardless. So this is angular momentum. So he suggested that angular momentum must be equal to, and that's so called quantization, quantization, whatever, quantization of angular momentum. It's supposed to be equal to n which is some positive integer number times so called reduced Planck constant which is Planck divided by 2 pi. Now that is a very, very important equality whatever which Bohr came up with. But just as it is, just quite frankly, I cannot understand how the person can come up with this particular hypothesis. Just doesn't seem to be natural. Well apparently he had some other things. And there are certain suggestions how exactly he came up with this. But eventually he came up with this. So he postulated the quantization of angular momentum of the electron. That's what it is. Now, contemporary, well not even contemporary, like 1920s approximately, level of physics allowed to come up with this particular equality slightly differently. And again I'm not suggesting this was a rigorous proof. Rigorseness is not really something which physicists are very comfortable with. Usually they allow themselves not exactly the rigorous derivation. And I will present how this can actually be derived from more, I would say, fundamental principles like theory of relativity and quantum theory. So here is what was basically presented in one of the sources which I was using some time ago as I should not say a proof of this formula. But at least some explanation of this. First of all we know the most famous formula of physics. Energy is equal to mass times speed of light square. That's the full energy of basically anything. Okay, so that's one thing. On another thing we know that if you have a quantum of light, let's say, then it bears certain amount of energy equal to Planck's constant times frequency of this light, right? So equating these two things results in the following. So h, now frequency is, as I was just saying before, it's speed divided by wavelengths. Why? Because wavelengths divided by speed is the time this particular thing moves for one wave, which is a period. And frequency is a reverse, inverse of period. Okay, now, so that's one thing. So that's one thing. Now, from this we see what mc square equals to this. We can reduce the c, so mc is equal to h divided by lambda. Okay, now, on another hand, let's talk about lambda. You see, that's a very interesting explanation which was actually presented by De Broglie in 1924, probably. He has suggested that electron on the orbit is somehow analogous to a string fixed on both sides. Now, when we pluck the string, it starts vibrating, right? Now, what kind of vibration this particular string can have? Well, it can have this one. It also can have something which is called standing wave. When part of string goes up and then down and the middle part, so it goes either this way or this way. So it goes with this middle part, but basically standing still. That's why it's called standing wave. Now, it can be divided in like four, let's say, pieces. Then it will be like this. So in any case, the length of the string should be equal to n times wave lengths, where n is a positive integer number. Now, well, actually, I think divided by two even, because we can have only one half of the wave. But in any case, when this particular equation, when the integer number of wavelengths can be put into this length, then you will have the real oscillation and the real sound from this string. Because if it's not, then the waves which are reflected from both sides would interfere, negatively interfere with each other. And there will be no distinct node which can be basically obtained from this. That's very important. And Dubroil has suggested that if this is the radius, then 2 pi radius, which is the length of this, which he has suggested should be equivalent to the string, should be equal to n times lambda, is the wavelength of electron considered as a wave. Again, there's this duality between the waves and the particles. What is electron? Is it a particle or is it a wave? Well, contemporary view is that sometimes it's this, sometimes it's that, whether you like it or not. I don't, but nothing you can do about it. It looks like these are theories which have been experimentally confirmed to like 10 to the minus 8 or minus 10th degree in any kind of unit of measurements. So if theory corresponds to experiment, we have nothing to do, but accept this theory at least for a while until the next experiment will contradict it. So if this is the case, then this is the case. h divided by lambda is what? 2 pi r, 2 pi r, and n goes here. And that's it. Because if r goes here, m times c times r is equal to n times h divided by 2 pi. Now this is angular momentum. h divided by 2 pi usually is used as a reduced blank constant. And we basically have derived with the same proposition of Niels Bohr that angular momentum of the electron is supposed to be an integer number of reduced blank constant. Do not consider this as a strict proof, rigorous proof. It's not basically, but it's a certain way which maybe in certain more developed theory can be considered as such. I didn't want you to really consider this to be the last word in this particular thing, not at all. But anyway, it gives you that there is some logic in it. So the quantization of angular momentum suggested by Niels Bohr did have some very important theoretical foundation behind it. And that's it for Atom's model which was developed by Niels Bohr. So he was a very interesting physicist. He left Copenhagen when the Nazi came to the country. And there is some kind of an interesting story about Bohr's gold medal. I think it was a gold medal which he has received as a Nobel Prize. I'm not really sure. Some kind of gold medal which he wanted to take with him. And he was told that the gold cannot be just brought through the border or something like that. And he dissolved it in some kind of a, gold can be dissolved in some liquid, some acid or combination of acids, whatever. And then somehow restored it back. I don't remember the whole story and I'm not sure it's even true. But anyway, it was a very interesting physicist and very famous actual physicist. All right, so that's it for model built by Bohr. It brings us to, you know, not to contemporary, not at all. But to a level of 1920s, something like this. But obviously we did not address the two fundamental things which we were using here, which is theory of relativity, which is this one. And quantum theory, which is this one. So we did not touch this. It's completely outside of this particular course, which are called physics for teens. So this is not for teens. This is for older audience. But in any case, we'll see. That's it for today. I would suggest you to read the notes for this lecture. So you go to unisor.com, physics for teens is a course. It has a part called atoms. And we're talking right now about the chapter called building bricks of model, of matter. So building bricks of matter, I think that's how I called it. And then there is this Bohr's atom model. That's it. Thank you very much and good luck.