 Hi, I'm Zor. Welcome to Unisor Education. I'd like to talk about certain dynamics of electron which is rotating around the nucleus of hydrogen atom. Why hydrogen? Because it's only one electron. The simplest model. Now this lecture is part of the course called UNIX, called Physics for Teens, presented at Unisor.com. There are some other courses. There is a prerequisite course which is math for teens, which I do suggest you to take, or at least familiarize yourself with whatever material is there, because I'm using it all the time, obviously. Now the website contains basically courses, which means if you found this lecture somewhere on YouTube or somewhere else, it's just one singular lecture. On the website it's a course. So there is a menu, there are certain sequence of lectures. Also every lecture on this website is supplemented with a textual description, which basically like a textbook. There are problems solved, there are exams, which you can take as many times as you want. Nobody is actually forcing you to certain grades or anything like that. Just try to do it until you feel perfectly comfortable. And the site is totally free. There are no advertisements, nothing to distract you from getting knowledge. So today we'll talk about orbiting electron. So we are assuming at this particular moment the model presented by Rutherford, the planetary model of the atom, and further developed by Bohr with certain improvements, I would say, and we will talk about this separately. So basically we are assuming, well, purely mechanical electrical problem that there are two masses. One is a nucleus, another is an electron. They have certain charge, electric charge. Electric charge attracts them. Nucleus is positive, electron is negative. We ignore the gravitational component of this because the particles are very small. It's not like planets. So we are talking only about electrical interaction between them, and we will try to calculate the characteristics of the electron's movement around a nucleus, which allows this electron to stay on a station orbit and not fall onto the nucleus. So it's like in the mechanical equivalent of this whenever we are talking about satellite orbiting the planet. Satellite, if it's on a certain radius, it must have certain speed. Here we have exactly the same thing. If there is a certain radius of rotation, radius of the orbit, electron is rotating around the nucleus, it must have certain speed. And let's just calculate the speed and whatever else we can. Okay? Now, first of all, what we have if we have an electron, we are assuming its mass is M and its electrical charge is negative E. Now, these are known constants. I mean, it was measured. Somehow, there are experiments. We know how to measure the mass of the electron and its charge. Now, incidentally, since we are not interested in gravitational interaction between electron and nucleus only in electrical, we don't need the mass of the nucleus, but we do need the electric charge of the nucleus. And what is electric charge of the nucleus? So if this is electrons, the nucleus is supposed to be plus E. Why? Because the atom is supposed to be electrically neutral. So there is minus E charge on an electron. That's why there is a plus E charge on the nucleus. And then we have the Coulomb's law, basically, right? So that gives us the force. The force between nucleus and electron, positive and negative, is supposed to be K. K is Coulomb's constant, also known, think, charge of the one, which is E, charge of another, which is also E. This is nucleus. This is electron divided by square distance between them. Now, it's supposed to be actually with a minus sign or plus sign. It doesn't really matter. I'm talking about magnitude of this force, which is K E squared divided by R squared. Okay. On one hand, we have this force, which is pulling electron towards the nucleus. Now, since we are talking about rotation and we're assuming it's a circular orbit, there is a centripetal acceleration. So from purely mechanical viewpoint on this particular rotational movement, the electron is supposed to be accelerating all the time towards nucleus. Now, without the force, it would just fly away without the electric force. So since electric force pulls it back towards the nucleus, there is an acceleration, centripetal acceleration, which as we know, equals to V squared divided by R, where V is a linear speed of the electron on the orbit, the one which we're supposed to find. And since we have the second Newton's law, this same force, which on this hand from the electrostatic viewpoint is expressed as such, it's supposed to be equal to M A. That's the second law, which is M V squared divided by R. And since it's exactly the same force, so this force is supposed to have this acceleration. So it's the same force just calculated through different laws of physics. So that's equal to R squared. Or, let me just put R squared here, it will be M V squared R equals to K E squared, from which V is equal to square root of K D squared divided by M R, or E squared root of K divided by M R, where M is a massive electron, R is radius of orbit, K is Coulomb's constant, and E is charge of the electron. Now, from this incidentally, kinetic energy of the electron and anything else is equal to M V squared divided by 2. That's the definition, right? So from this we can actually define what is kinetic energy of electron. It's K E squared divided by 2 M R, right? M V squared, no, no M here. Just to R, R, and divided by 2, yes. So now we have a kinetic energy of the electron. And obviously we can add the potential energy since we know the parameters and have the full energy of electron. So this is a very, very simple view based on a very, very simple atoms model. In reality, when we will introduce something which is related to quantum of energy, which we did address before, that complicates the whole picture. So the Bors-Atom model combines the Rutherford model, which is planetary model, which we are talking right now, with quantization. And that kind of complicates it, but it corresponds to experiments. And no matter how maybe strange or weird or whatever, the whole principle of quantization of energy or momentum, et cetera, sounds like nothing we can do about it. Since it corresponds to experiments, then that's what nature actually gives us. As suggested to read the notes for this lecture, it's a very short, it's a real problem if you wish, but it's a very short one and very simple one. But still read the notes for this lecture. It's on unizord.com courses called Physics for Teens. Then there is a part of this course which called Atoms. And if you click on the Atoms menu, that's the first chapter, which is basic, building blocks of the matter. And then there is this orbiting electron lecture inside that particular chapter. All menu driven, et cetera. Okay, thank you very much and good luck.