 Hi, I'm Zor. Welcome to Unisor Education. We continue talking about a structure of atom, electronic structure of atom, how basically electrons are positioned around a nucleus. This lecture is part of the course, Physics for Teens, presented on Unisor.com. I suggest you to watch this lecture and everything else from the website, because it's a course which means there is a manual, there is a certain sequence, order of lectures, because if you just found it on YouTube, let's say, it's just one singular lecture and I might refer it to something else, and you don't know where it is. From the website you have all the lectures at your disposal. Now the website is totally free, there are no advertisements, no strings at age, you don't even have to sign in if you're just learning by yourself. There is a prerequisite course on the same website called Math for Teens. Math is absolutely necessary to study physics and at least something like calculus and vector analysis are definitely the part, subjects of mathematics which are needed for physics. What else? Now the website has not only lectures but also the textual description of every lecture. So you have a video and you have a text, like a textbook basically. So you can always, after the video, you can read the textual part of it just to re-emphasize certain things and make it a little bit maybe better understanding. Okay, so today we will talk about energy of electrons. Now we did go through Bohr's model of how electrons actually are moving around a nucleus, that there are certain stationary orbits where moving on these orbits, moving along these orbits, electrons do not emit any energy and that's what makes these orbits stable. So we were talking about, instead of the word orbit, we were talking about the concept called shell, which basically means the same thing, it just reflects the three-dimensional world we are in. So electrons are somewhere within certain shells around the nucleus. Now we were also talking that it's not just shells, every shell has certain sub-shells and it was a pretty good, like mathematically even very nicely looking theory about sub-shells. So sub-shells have numbers, numbered let's say 1, 2, 3, 4, 5. They have been assigned letters, I think it's S, P, I don't remember, something like F maybe, no D, first G I believe and then F and then G and then by alphabetically. There are some historical reasons for these letters, so sub-shells are called with the letters and every sub-shell has certain maximum number of electrons it can hold. So this one is 2, then 6, then 10, then 14, then 18, every time we are increasing by 4. So this is number of electrons per shell. Now per sub-shell, I'm sorry, so these are sub-shells. Now the shells have certain number of sub-shells. The shell number 1 has 1 sub-shell, shell number 2 has 2, shell number 3 has 3 sub-shells. So this one has S, this one has S and P, this one has S, P and I guess D. If I'm not mistaken, I think that's what it is, etc. So these are shells, these are number of sub-shells and as you see number of sub-shells is equal to shell number and then these are sub-shells which are included, which means that the first shell has only 2 electrons, the second shell has 2 plus 6 equals 8 and this one has 2 plus 6 plus 8 equals 18. So these are structures of the first layers around the nucleus. Now let me just exemplify it with this configuration for a few elements which we do know about. Okay, let's start from hydrogen. Now hydrogen has atomic number 1, which means it has only one proton and one electron. Now obviously this one electron should be on the first sub-shell of the first shell because it's only one electron, there is nothing else, right? So what I can say is that the electronic structure of the hydrogen is first shell has only one single sub-shell and there is only one single electron in it. So this is the shell number, this is sub-shell letter, well, letter and number basically correspond to each other, but it's traditionally the letters and the superscript with the shell tells how many electrons it holds. Okay, let's go further. Helium has atomic number 2, which means it has 2 protons and 2 electrons. Okay, now shell number 1 has sub-shell, which can hold up to 2 electrons and that's the only thing which we need, we have 2 electrons. So they go to the first sub-shell of the first shell and that's it. Next one, lithium. Lithium has atomic number 3, which means it has 3 protons and correspondingly 3 electrons to make the atom neutral. Now how they can actually be positioned? Well, let's just think about it. We have the first shell, now the first shell has only one sub-shell and this is sub-shell S, it can hold up to 2 electrons. Okay, so we have 2 electrons here, but we have 3 electrons. So, where does it go? The first shell doesn't have any more sub-shells. So we need to go to the second shell to its first sub-shell and put electron there. Oh, it's not we actually putting the electron there, it's there. Who puts there, I don't know. Okay, so that's basically how the lithium atom is created. Okay, let's just skip a couple and let's go to carbon. Carbon has atomic number 6. So we have 6 protons in the nucleus, we have 6 electrons in orbits. So let's just position these 6 electrons into shells and sub-shells. Again, let's start sequential. We have the first shell, it can have only one sub-shell, and this sub-shell has 2 electrons. Okay, 2 goes 4 to go. Now, we have the second sub-shell. Now, the second sub-shell has the first sub-shell of it. It can hold also 2, right? No more than 2. So we need to go to the second sub-shell of the second shell. So it's 2. This is the P is the letter of the second sub-shell. And it can hold up to 6 electrons. Now, we need only 2 left, right? Because we need 6, so it's 2, 2 and 2, 6. So this is how the electrons of carbon are positioned. There are 2 shells. The first shell has only one sub-shell and it has 2 electrons. The second shell has 2 sub-shells. The first one has 2. And whatever is left of electrons, 2 of them, goes to the second sub-shell. Now, this is not the limit. The limit is 6 for the second sub-shell, right? Okay. Now, let's skip a few more. Let's go to silicon. Silicon has atomic number 14. So we have 14 electrons to spread around. Well, let's just continue this thing. I think it's an interesting kind of exercise. So the first sub-shell can have only one sub-shell and 2 goes there. Great. Let's talk about the second sub-shell. 2 goes to the first sub-shell and the second shell. Now, the second sub-shell has the second. The second shell has the second sub-shell, which can hold up to 6. Now, we need 14. So these 6 will be definitely taking. Now, the second shell has only 2 sub-shells. So we cannot go into the second shell anymore. So we need to start the third shell. Okay. The third shell has the first sub-shell, which can hold 2 of them. Now, what do I have right now? I have 10, 12. We need 14. So we need 2 more electrons. Well, we have the second shell of the third shell and the remaining 12 electrons will go there. That's silicon. Okay. Now, it's actually getting much more interesting as we go down the table of elements. The next one I would go with argon. Argon is the noble gas, actually. Now, it has 18, number 18. Now, in many cases, or what people do, instead of repeating all this, I will repeat all this, but they're kind of abbreviating. So instead of this, for example, they can call something like this pot, for instance. This pot is equal to 3 liters or something like that. I mean, they do abbreviate. So they take the pot, and instead of putting all these shells and sub-shell, they put something which they already have written about and then attach a couple of more. But I will go all the way through. All right, so argon has 18. Well, let's think about this guy, 14. We still have some capacity here, right? The sub-shell P has 6 maximum, right? So we can put 4 more, and 4 more will be exactly this. So what I will do is I will basically repeat the whole thing. 1 is 2, 2 is 2, 2P6, 3S2, and 3P6, that's the maximum, and that will be 18. 2 and 2, 4, 10, 12, 18. So we have 18. And as you see, we have completely exhausted the second sub-shell of the third shell with argon. I specifically decided to finish up filling completely this second sub-shell because the next example will be extremely important. And here is why. Let's take exactly the next element after argon, which is potassium. Potassium is K-calium. Atomic number is 19, one greater than this. Now, let's just think about it. If you have one more electron, now obviously the last sub-shell, the second sub-shell of the third shell is completely exhausted. So what do we do? I mean, it's natural, and let me tell you, from the mathematician's standpoint, it's absolutely natural. So whenever we have exhausted the second sub-shell of the third shell, I know that the third shell has three sub-shells, right? The third has SP and D. So my natural instinct would tell me that I have to just put one more electron into the next sub-shell, which is sub-shell D. So I would put that this is equal to argon 18 plus 3D1. So I repeat all this. These are first two sub-shells completely, and the third shell with two sub-shells. And they know there is a third sub-shell in the third shell. So I can put this electron. But this is not exactly what happens. Well, people did experiments. What happened was instead they have the same thing as argon, so which means all these sequence, and the next one was 4S1. So instead of using the third sub-shell of the third shell, it goes to the fourth shell, first sub-shell. I'll just question why. And here we go to the subject of this lecture, which is energy levels. Here is the problem. You remember that again in previous lectures, we were talking about energy of the electron as it rotates around the nucleus. It's a Coulomb constant, square of its charge, divided by two radiuses, radius of the orbit. Now, we did actually derive this formula. This is full energy, potential and kinetic. Kinetic energy is positive, and potential energy is negative, and the total result is negative. Now, why is it negative? Well, because it's not we who are supposed to spend some work putting electron on the orbit, because electron is attracting to nucleus. It's whenever we want to take it away, we have to spend energy. That's why potential energy is negative. And by absolute value, potential energy is greater than kinetic, and that's why the whole result is negative. However, it is negative. However, as r increasing, the absolute value of the total energy is decreasing. So, basically it's negative, but it goes to zero, as r increasing. As r increasing, the potential, the total energy is increasing, but still remains at zero. Now, what does it mean? It means that as we are approaching greater and greater radiuses, the difference between energy levels becomes less and less and less. Now, we know that every orbit has some kind of an energy, right? So, we need something like a few different sub-shells, which means few different orbits on each shell level, right? So, unfortunately, unfortunately, I don't know, it looks like the shells overlap from the energy standpoint. So, if I will go like a model of the atom, so this is one shell and this is another shell. Now, this shell has sub-shells. And this shell has sub-shells. And whenever you increase the sub-shell number, the third sub-shell of this shell is energetically, if the distance is the energy level, energetically it would be greater than the first shell of the next. The first sub-shell of the next shell. So, that's why shells are... This is one shell and this is another shell. So, these are sub-shells. My fingers are sub-shells. So, they are overlapping. And that's why the energy level of lower shell, lower shell, but higher sub-shell, may be greater than the lower sub-shell of higher shell. So, that's basically how it is. And now we get a principle. How electrons are distributed among shells and sub-shells. And it's attributed to a few names. I don't remember them, obviously. Aufbau principle. And then there are Medlang and Klitschkovsky. People who were kind of explaining the whole mechanism of this, that electrons are not going like sequentially into shells and sub-shells within the shells. No, they are going sequentially according to the energy level. Now, in the beginning, let me go back to my graph. In the beginning, when the radiuses are small, which means the shells are in the first shells, like the first shell, the second shell, the difference between energy level is significant between the shells. And that's why there is a room for sub-shells here and sub-shells here, and they are not overlapping. But the farther we go from the nucleus, so the shells was numbered like 3, 4, 5, etc., they are so close to each other that the sub-shells of this one overlap with the sub-shells of the next shell. And that's why, since the principle says that electrons take the orbit in the order of increasing energy, not in the order of increasing shell number or sub-shell number, increasing energy, that's why we have this situation. Instead of going into the third sub-shell of the third shell, electron goes to the fourth shell, but the first sub-shell. So again, third shell, third sub-shell has greater energy level than the fourth shell, first sub-shell. That's how it is. And as a result of this, all shells and sub-shells are ordered basically in the level of energy they carry. In this order, I put in writing in the textual part of this lecture, it's basically like 1s is less than 2s is less than 2p is less than 3s less than 3p. And here instead of less than 3d, which is the third sub-shell of the third shell, it's actually 4s and then 3d. Because, as I was saying, the first sub-shell of the fourth shell has less energy than the third shell, sub-shell of the third shell. That's what it is. Now, why this is this way? There are really very neat theories about this and they're completely beyond the level of this particular course. But there are certain very, very logical explanations because it's related to how exactly these shells are organized and sub-shells, etc. So basically, that's all I wanted to talk about. I think the most important thing for you to understand this kind of notation, that's number one. And the second is that shells overlap with their shells as far as energy is concerned. But when you see something like this, you should not be surprised. This is very easy to decipher. The shell number, the sub-shell letter, which basically corresponds to number, and the number of electrons this particular sub-shell carries. This is an electronic structure of every element. If you go to some textbook, whatever, and you were basically studying this electronic structure, you will always see notation like this. So I would like you to understand it. There is nothing outlandish or very, very difficult to understand about this. It's very, very easy. Shells, sub-shells, and number of electrons per sub-shell. With this particular twist that electrons are filling orbits, not in the order of shell, sub-shell, but in the order of energy levels from lower to the higher, which happened to correspond in the beginning, the shell-sub-shell number. But as we go further with greater atomic numbers, with greater number of electrons, then this particular order might be distorted in some way or another. And potassium is a perfect example. Okay, that's it. I do suggest you to read the notes for these lectures. And this is it for today. Thank you very much and good luck.