 Hi, I'm Zor. Welcome to Unizor Education. Today we will talk about something which is related obviously to electricity, but it has practically no importance in everyday life, but it's very, very important from an educational standpoint. So today's lecture is educational, more than practical. Besides, I know that many universities or some kind of schools, whatever, they are actually asking students to solve this particular problem, which I'm going to present to you again just as a test of how well educated they are. Because this problem, though the final formula might be a little bit more complex, it's really in a simple form encompassing your knowledge about electricity. So let's just talk about this particular problem. We are talking about the speed of electrons, the speed of electrons as they are moving, carrying the charge with themselves. And basically we would like to know how fast they are moving. Now, this problem, the solution to this problem I'm going to present right now, it's actually part of the whole course called Physics for Teens, presented on the website Unizor.com. I do recommend you to watch this lecture from the website because it has detailed notes for each lecture. All lectures are obviously organized in some systematic way. And there are some things which I put into the notes and they do not really present on the board, for instance, in this particular case I will present the general formula, but I will not use this formula in practical calculations for some specific case which I put into the notes. So it's very important to use the website. And the website is completely free, there are no ads. Okay, so how can we calculate the speed of electrons as they are moving along the wire? Well, we all know that if we will switch on the electric switch, the lamp will be lit immediately, or practically immediately, but with the speed of light. Now, does it mean that the electrons are actually moving? Okay, here is our thing. Let's say this is the source of electricity and this is the switch, which we will flip into the closed position. Now, probably this is some kind of a lamp and this is some kind of a source of information, not information, source of energy, electric energy, generator, battery, whatever. And as soon as we flip the switch, the electrons from the negative side will start going, going, going, going back to the positive. Now, if this battery is powerful enough, or if it's a generator which generates all the time, then the electric current will circulate here and the lamp will be lit all the time. So, how fast electrons are moving? Not, definitely not with the speed of light, which is actually the speed of electric field, as it is propagating through the, through the electric wire. So, we are talking about electric current, specific electric current, and we would like to find out what's the speed of electrons which carry this particular current. So, let's just assume that the current we have, so we have something which is called amperage. So, it's given, the amperage, the current, this is the number of coulombs per second, number of coulombs per second. Now, we have to find out what's the speed of electrons which are moving there. Okay, so how can we find this out? Well, first of all, our first interest is how the electric current actually is happening inside the wire. I mean, there are atoms, let's just for simplicity consider it's copper. So, there are some atoms of copper inside the wire. This is the wire and these are atoms of copper, right? Now, each atom has electrons around it. As soon as we apply the electric field, so this is electric field, so we have some negative charge on one end of this wire and positive charge on another end. As soon as we apply, the electrons will start their movement because they will be pushed away from the negative, right? This is the axis of electrons, this is the efficiency of electrons. So, the electrons which are circulating each atom will experience the force which will push them into that direction. So, if we know the current, we know the number of coulombs per second which are traveling from negative end to the positive end, we can very easily find out how many electrons are needed to carry this current, right? Every electron has certain amount of charge in it, which is, well, it's negative, it's something like minus 1.6 times 10 to, I don't remember, I think it's minus 19 of coulombs, right? So, if we know the number of coulombs per seconds and each electron carries that many coulombs of electricity, we can divide I divided by E and what do we have as a result? Well, as a result we have the number of electrons, right? So, this number of electrons, each second are traveling from left to right, from negative to positive in this particular case. This many electrons are traveling and they carry all the electricity which we need, they carry the current. So, this is an amperage divided by the charge of one particular electron. Okay, so we have the number of electrons, somehow we have to convert it into their speed. Well, let's just consider these electrons are contained in, let's say, certain segment of the wire. If we know this length of this segment and we know that each segment, all electrons which we are talking about are moving from left to right, that is the speed of, this length is actually a speed of electrons because they cover this particular distance per second, right? So, this is the number of electrons per second which are carrying all our electricity. So, all we have to know right now is where exactly is this segment of the wire where all these electrons are located. And this is related to inner structure of the atoms, obviously. So, we know the number of electrons, we have to convert it into basically the length of this segment. Obviously, we consider that we do have the area of this wire. So, if we know the volume which is the place where all these electrons are located, we'll divide it by area and we will get the length of this segment. So, what's happening inside the wire with all the atoms of whatever the metal or whatever the material is used for the wire? Now, the atoms, as we know, contain nucleus which has inside protons and neutrons. And there is a certain number of electrons which are circulating around this nucleus. Well, the interesting thing is that they are circulating on different orbits. And every orbit has a certain number of electrons it can actually contain. The smaller orbits, the closer to the nucleus, can carry less electrons on their orbit. The further from nucleus we go, the more room we have for electrons to be on those orbits. Now, don't ask me why we have certain distinct orbits. There are certain theories, very involved theories related to quantum mechanics, etc., which explain it. So, right now we're not going into this, we're just giving the fact. So, the inner orbits have a certain number of electrons and there is a maximum. And every other orbit which is further off the nucleus has its own maximum number of electrons it can carry. Now, how many electrons are all together? Well, as many as many protons are inside, right? Because they should be neutral. Now, just for example, if we will consider copper for instance, this is the chemical cuprum. It has 29 electrons, 29 protons and 34 to 36 neutrons. So, these are in the nucleus and these 29 electrons are circulating around. Now, the nature is built in such a way, I will use this particular statement, that the inner orbit has two electrons. The next one has eight electrons and the next one has 18 electrons. Now, I told you that the further we are from the nucleus, the more electrons can be circulating on that orbit. So, these are maximums. So, what's my sum? 1028, we have 29. So, we have one more. So, there is one electron here on the outermost on the fourth from the nucleus orbit. And so, this is one. So, this orbit is not completely filled up. And the interesting property is that only the electrons from this outermost orbit participate in the normal transfer of electric current. I mean, obviously we can establish certain conditions when we will just, you know, swoop up all the electrons from the atom. That's probably possible too, but it's not happening in the normal circumstances, okay? So, if we're talking about regular lamp and regular electricity, then the forces are not that great. So, it's only the outermost electrons are actually participating. So, what's interesting is, in this particular case, if we know the number of electrons based on whatever the material our wire is made of, we have to find out how many electrons are on the outermost orbit. And let's consider this number is N e. So, this is number of electrons at the outermost orbit of the material the wire is made of. So, in the case of copper N e is equal to one because it's only one. We have 28 out of 29 are fully completing the orbits and then the outer orbit we have only one. So, in case of copper N e is equal to one, in case of other metals like aluminum, for instance, or silver, that's a different number. But we don't remember which one. It doesn't really matter. So, N e is number of electrons of this particular material at the outer orbit of their atoms. Now, because of that, from the number of electrons and knowing the number of electrons in each atom that participate in the electric current, we can find out the number of atoms. So, the number of atoms is equal to N e, total number of electrons, divided by N e, number of electrons, let's call it active electrons. This is number of active electrons per each atom. In case of a copper, it's one. So, that would be equal to I divided by N e times E. Now, we have the number of atoms, right? So, remember our picture? These are atoms. So, we know the number of atoms which contain all those active electrons which are needed to transfer per second this particular amount of coulons. All right? This particular amperage. It's per second. Now, what's the volume of this? How can we find out if we know the number of atoms, how can we find out how much they weigh? Or what's their mass actually? Because if we know the mass, we can divide it by density and that would give us the volume. Now, density, again, is known characteristic. So, we will use it, obviously. But now, we have to find out what's the mass of all these atoms. So, we have the number of atoms, we have to convert it into their mass. And then, divided by density, we will get the volume. And divided by area of the wire, we will get the length. All right. So, how can we find out? Well, we do know something about mass of substance. There is an Avogadro number. So, what is Avogadro number? Avogadro number is the weight in grams of one mole of substance. And one mole of substance is amount of grams, number of grams, number of grams equal to atomic mass. So, Avogadro number is number of atoms in one mole and one mole of the substance is number of grams which is equal to atomic mass. Now, why is this? Well, let's just think about this again. Now, these are atoms, right? Atoms have nucleus and electrons. Atomic mass is basically the number of protons and neutrons inside the nucleus. Now, in case of copper, for instance, it's 29 protons and 34 or 36 neutrons. So, there are different, obviously, atomic masses in these particular cases. And it's an approximate value. But if you will add them together, you will have, what, 63 or 65. So, basically, the atomic mass of copper is something like in between. It's like 64 point something. I don't remember what exactly. Now, why is this? Well, it's because atomic mass of carbon, which contains 12 particles in the nucleus, is exactly 12. So, whenever we are going to some other material, some other element and protons and neutrons are probably the same as those which are inside the nucleus of carbon. But the protons and neutrons are slightly different. So, basically, the number is not exactly the even number. That's why we have 64 point something. Now, if we are actually okay with some approximation, then considering nucleus of the carbon has 12 particles, protons and neutrons, and its atomic mass is by definition exactly 12, then atomic mass of one particular particle is about one. So, that's why the number of these particles gives you the atomic mass of any other nucleus. But in any case, considering protons and neutrons are slightly different, very slightly, but still different. And there are maybe some other things involved which we are not talking about. The atomic mass is approximately the number of particles inside the nucleus. Now, obviously, since nucleus is the most massive part of the atom, electrons are relative to nucleus, it's just one minuscule part. Electrons are very light. It's nucleus which constitutes the mass of the atom. That's why the bigger the nucleus, the bigger the mass of each atom. And if we do it proportionally, we have a number of grams equal to atomic mass. So, in this case, we are talking about 64, for instance, grams of copper, or 12 grams of carbon, or whatever, one gram of hydrogen. It corresponds to the number of elementary particles inside the nucleus. All of these should contain very, very similar number of particles, right? Bigger particles and bigger mole of this particular substance. But the number of particles is the same, and this is the Avogadro number. So, we know that considering the atomic mass is MA, so MA is atomic mass of our material which we have our wire is made of. So, in case of copper, MA is 64. So, if this is atomic mass, so we know that MA gram of our substance, of our material, have MA atoms. This is Avogadro number. But we know our mass is different. Our number of atoms is MA, so what's their mass? Well, it's a primitive proportion, right? So, how to determine MA? MA is equal to, this is the mass of these atoms. It's equal to MA times N atoms divided by the Avogadro number, which is MA times N atom is I divided by NE and Avogadro number NA. So, this is the mass of all the atoms which contain all the active electrons which deliver the amount of electric charge we need per second. So, all these electrons inside of these, all active electrons inside of this particular piece of the wire, each second moving forward. So, the length is actually the speed of these electrons, right? So, how to calculate this length? Since we know the mass, we can find out the volume of this, which is basically mass divided by rho, which is density. We know the density of material, like in case of copper is something like 8 point something gram per cubic centimeter, or we can convert it into millimeters or cubic meters, whatever. So, this is the volume and if we have a volume and this is considered to be probably a cylinder, right? We have to divide lengths, would be equal to MA divided by rho and divided by area, if this is the area of the wire. So, we have to know the area of the volume of the wire, obviously, which gives us the relatively large but understandable formula, understandable because I just did it one step after another, divided by NE, E and A, rho and A. So, this is the formula. So, this is the length of this piece of the wire which contains all the active electrons which deliver the charge every second. So, which means this is a speed, actually. This length is how long is the movement, the distance, how long is the distance covered by active electrons per second, right? Now, what is what? Let me just explain again. What is MA? MA is the atomic mass of the material. So, it's basically how many protons and neutrons are in the nucleus, like in case of copper it's about 64, a little bit more than 64 point something, because neutrons and protons weight slightly differently. I is supposed to be given as an input to this problem, it's the current. It's how much electricity in coulons are transferred through the wire per second. This is the current. Now, what's NE? NE is number of active electrons on the outermost orbit of the atom of the material this wire is made of. In case of copper it's one. In case of aluminum, I don't remember how many, etc. E is charge amount of electricity of each individual electrons. That's why I divided by lower case E is the number of active electrons we need, right? And then we divided by NE to get the number of atoms which carry these electrons. And then multiplied by NA in the denominator and MA in the numerator we basically transfer it into mass. And then mass divided by rho will give me my volume, because this is the density. And A is cross section of the wire, that gives me the length. Now, in the notes for this lecture I have calculated this thing for copper of certain diameter or certain cross section area and certain current, certain amperage. And again, the purpose of this E is basically to give you a lot of different things from different other areas around the electricity. So, it's a structure of atomic structure, it's even geometry when we are divided volume by area of the cross section to get the length of the cylinder. I mean, there are many different aspects of this which I think is very educational. It has, again, no practical purpose at all. People don't really need this information, how fast electrons are moving inside the wire. But it's an interesting problem, and obviously people were thinking about this. And you know what, quite surprisingly for me, by the way, that the real movement, it's really in millimeters, even in fractions of millimeters per second. So, it's really slow. I mean, if you will calculate it for a few different cases millimeters really per second, even fractions of millimeters. So, that's interesting. And that completes my lecture today. I do suggest you to read the notes, because the notes are also, they contain exact calculations for some specific case, which is, again, very interesting I would say. And again, don't forget that this is something which, in many cases, students are asked to solve this problem to demonstrate how knowledgeable they are. So, that's why I have decided to include this particular problem for purely educational purposes. Okay, that's it. Thank you very much, and good luck.