 Hi, I'm Zor. Welcome to a new Zor education. We continue talking about what's inside the atom, more precisely what's inside the nucleus. So the previous lecture was talking about protons and neutrons. And we continue this particular topic. And today we will talk about isotopes. Now isotopes are basically different atoms, which are the same in something and different in something else. Now what's the same? The same is electrical characteristics of the atom, which means number of electrons and number of protons. So two different isotopes of the same element have exactly the same number of protons and electrons. But the number of neutrons inside the nucleus might be different. And that's what actually differentiates one isotope from another. Different number of neutrons. Protons and electrons are the same numbers. Now this lecture is part of the course called Physics 14 on Unisor.com. It's presented. There is absolutely no financial strings attached. The site is totally free. No advertisement. You don't even have to sign in if you don't want to. I do suggest you to watch this lecture from the website because it's a course. It has menus. It has certain dependency between the lectures. And there is some logical sequence of lectures because I'm using in a subsequent lecture whatever I was talking about before, obviously. The website contains a prerequisite course called Maths for Teens. So whether you took that course or you just know all the material, it's necessary to know your math before you study physics. Also, many exams are there. You can take them as many times as you want. Also, every lecture has a textual supplement which basically looks like a textbook. So you can watch the lecture or you can read the text for that particular lecture with some pictures or whatever whenever it's required. I do suggest you to watch the lecture from the website and use the functionality of the website which obviously includes menus and exams. Back to isotopes. Different isotopes of the same element have the same number of protons which is Z. It's atomic number. Remember, number of protons which is equal to number of electrons is called atomic number of the element. Atomic number of hydrogen is 1. Atomic number of helium is 2, etc. Now, so Z is atomic number and it's the same, it's number of protons in different isotopes. N is number of neutrons in the nucleus and that is different in different isotopes. So the same element, let's say hydrogen, it might have one proton and no neutrons. It's a regular hydrogen which occurs everywhere. Now, the isotope can have one, still one proton and one neutron. That's called deuterium. And the third isotope known to physics is again the same one proton and two neutrons. That's called tritium. These are different isotopes of hydrogen. One is the regular one and two others are isotopes, so both. Now, the chemical characteristics of elements are based on electrical kind of qualities, right? Number of electrons because it's electrons which are actually involved in chemical compositions to create a molecule, let's say. So if you remember we were talking about sodium plus chlorine, it gives you sodium chlorine which is regular table salt, right? So these are reactions among upper layers of electrons. The shells and top shells which are on the outer, outskirts of the atom. So number of neutrons, in theory, should not really affect the chemical composition, or at least almost. We can say right now, at least on the level which we are trying to understand what this is all about, we can say that the number of neutrons is not really affecting the chemical bonding between different elements. However, the physical characteristics might be quite different. That's very important. Now, how do we identify isotopes in the books or when we are talking about? Well, we are identifying them by atomic mass. So number of electrons or protons plus number of neutrons is called atomic mass. So atomic mass of regular hydrogen is one, atomic mass of deuterium which has one neutron and one proton is two, and atomic mass of tritium is three because it has one proton and two neutrons. So how do we do it? Well, again, by specifying atomic mass. And here are examples. Carbon, in most cases, most frequently occurring kind of carbon, has six protons and six neutrons which makes its symbol C6 and 12. So six protons and 12 is atomic mass because it has six neutrons, six plus six equals 12. Now, we usually put it as carbon 12, specifying mass here. So in the textual description that we are saying, carbon 12, carbon means it has six protons and 12 means that the atomic mass is 12 which means it has six neutrons. Now, we do have carbon 13 and carbon 14. So this would be C613 and would be C614. So this one has, so in all cases, Z is equal to six, N is equal to six, Z is equal to six, N is equal to seven, and Z is equal to six, N is equal to eight. We get to 14 mass, right? So that's how we identify different isotopes if we think it's important for the context of something. Similarly, we have uranium 235 and we have uranium 238, two major isotopes of uranium. So this would be U92238 and this would be U92235. So 92 protons are in uranium no matter what because it's uranium and the number of neutrons in this case is what? 143 N is equal to 143 and in this case N is equal to 146, different number of neutrons. Okay, so this is all about how we identify the different isotopes. Okay, fine. Next, as you're saying, while chemical properties might be the same in different isotopes, physical might be different. And one of the most important physical characteristics which is different in different isotopes is that some isotopes are stable like this one. This is the stable carbon. That's what we see everywhere. Now, this carbon which has eight neutrons, this atom is not stable. It decays and sometimes the decaying is very slow. Like, for example, in this particular case, certain mass of this particular isotopes of carbon decays in half, which means it actually diminishes in 57-30 years. Now, there are some isotopes which have half-life, which means they're diminishing in half, basically, in millions of years. And there are some which are dissipating in milliseconds. So it all depends. But in any case, this is one of the very important difference between different isotopes. So the number of neutrons affects the decaying of the atom. But probably every atom is decaying in some way or another. I don't know. But those which we kind of consider as non-decaying are very, very stable, like this one, like this one. And those which we definitely know, we can measure actually that in certain amount of time the amount of that particular element which we're dealing with decreases by 50%. Now, what's important is that the neutrons are actually acting as stabilizing factor for the nucleus of the atom. Why? Well, look, electrons are surrounding the nucleus relatively to the atom size, the nucleus size in a relatively long distance. And the nucleus is keeping electrons on their orbit while using the electrostatic forces. Protons are positive. Electrons are negative. And there is an attraction. So electrons are flying, you can say, at least right now, around the atom on certain orbits. And they are kept on the orbit by attraction of the protons and not flying away. Well, in metals, for instance, upper electrons can actually go away. But that's OK. I mean, we're not talking about particularities. We're talking about principle. Now, so unlike charges, plus and minus, positive and negative, attract, like charges repel each other. That's why on the same orbit we cannot have too many electrons. They will repel each other and push outside. But at the same time, we're talking about nucleus where the protons, which are all positively charged, are together. So what keeps them from actually flying apart and destroying the whole matter? Well, there are some other forces in nature, not only electrostatic, not only magnetic forces. There are other forces, not only gravitational forces. So the forces which are keeping the nucleus together are called nuclear or strong forces. Now, the strong forces exist between two protons, between protons and neutrons, and between neutrons and neutrons. So all the combinations of particles inside the nucleus are attracted to each other by these strong nuclear forces. They are acting only in a very short distance. They are not really affecting electrons or anything else. But on a short distance, they are strong enough to overcome repelling force of protons among themselves. It's also important that the number of neutrons is usually greater or equal to the number of protons. Why? Because if you have a proton and proton and proton and proton, it's nice to have a neutron in between to basically separate protons from each other. So in a three-dimensional world where you have protons and neutrons somewhere near each other, this particular inequality assures that protons are not too close to each other. So there are some neutrons in between protons. And that's what kind of helps to keep the nucleus together. Because electrostatic forces still exist, so we do not have to put protons near each other. So it was really very smartly designed. This world was designed by somebody, a very smart guy. So that's very kind of a natural consequence. But it doesn't mean that it's always better to have more neutrons than protons. Because in this particular case, this is not stable as much as this one. We have two more neutrons. But that seems to be like extra. These extra neutrons are not really necessary to keep. Six neutrons is sufficient to keep the carbon nucleus together. So eight is too much, and that's why we have this kind of decaying. And we will talk about decaying. So that's, again, that's kind of an inequality between protons and neutrons. Okay, and now I would like to really talk about one particular application of our knowledge about isotopes. Now this particular application relates to something which is called radioactive dating. Now dating in terms of determining the date or age, rather. It's not like meeting men and women. Okay, so I'm sure many of you heard about carbon methods of identifying or determining the age of something like a bone some kind of animal who lived millions of years ago, right? Well, not that far, but something like 60,000 years ago, yes, it can be actually determined using this particular method. So it's based on carbon, not just regular carbon, but the carbon which is this one, which has a known decaying property and known measured decaying property, like half-life is, as I was saying, 57, 30 years. 57, 30 years. Half-life. Okay, so how this particular thing is done? Well, let's consider in the environment you have certain amount of this particular kind of isotopes, isotope of carbon. Let's just put aside how it's occurring in this environment. So most of our carbon is normal, which is this one, six protons, six neutrons, but there is some percentage. Let's consider its permanent percentage of carbon with atomic mass 14, carbon 14, in the nature. Now, chemically, this carbon is exactly the same as this one. So we are consuming, I mean we living beings, which means animals, people, trees, all plants, etc. They're all consuming carbon because carbon is part of the inner structure of the blocks from which we are all made. Now, so we are consuming this from the surrounding environment, which means it's kind of coming into our inner construction, inner atoms, which we consist of, molecules, whatever. Now, the problem is in the case, but since we live, we are breathing, we are acting, or tree has whatever the manifestation of the life in trees, it grows, etc. So we are always consuming from the surrounding environment carbon, which includes certain percentage of carbon 14, which probably means that inside of our bodies, inside of animals, inside of trees, etc., the amount of carbon 14s, like a percentage to other kind of carbon, is more or less the same as in the surrounding nature because we're living, we're constantly consuming something, so even if it's really decaying, we are compensating. Okay, now, as soon as something stops living, like animal dies or tree dies or something like this, it stops consuming this carbon from the outside. The regular carbon stays as it was because it's not really decaying, at least not noticeably, but this one is noticeably decaying. And by examining by how much percentage of this carbon relative to this is in the dead tree, for example, which we have found, we can really measure how much time went by since this particular tree has died because the carbon 14 is not replenished and in the case. So this is the whole story. Now let's talk about the details of this. First of all, where the carbon 14 comes from. Okay, here is the story. You have basically cosmic radiation which bombards the Earth's atmosphere all the time. And it's relatively high-energy, ultra-short electromagnetic waves. We can call them gamma rays, something like this. Now these are electromagnetic oscillations of a very, very high frequency, and that's why very, very high energy. Remember, the quantum of energy is H, Planck constant times frequency. We did talk about this. Now, what these high-energy electromagnetic oscillations do? Well, they bombard the atoms, and in this particular case, there is an atom of nitrogen. It has seven protons and seven neutrons, which makes its atomic mass 14. Now, what happens with this? Well, the cosmic radiation bombards the atoms which are in our upper layers of atmosphere, and they basically destroy these atoms. They break them apart. So, whenever the atom is broken apart by cosmic radiation, well, there are some protons and neutrons, and electrons are flying around. So, some neutrons attack or hit the atom of nitrogen. Now, the neutron has atomic mass 1 and no electric charge, right? So, it's zero, one. Okay, so what happens here? Well, what happens is, whenever the neutron hits the atom of nitrogen, which has seven protons and 14 and seven neutrons, what happens is it kicks off a proton and electron. Proton has charge 1 and mass 1. And what happens? And places itself instead of this proton. So, what happens? Now, instead of seven protons, we have replaced a proton with a neutron. So, it's six. But the atomic mass is exactly the same, because we are replacing proton with a neutron, the atomic mass is the same. And that's why what we have here is 6, 14. And this thing combines together into H11, which is hydrogen molecule, one proton and one electron, combined together, and that's what happens. So, whenever a neutron hits nitrogen, we have created the hydrogen molecule, an atom and an atom of carbon-14. That's the source of carbon-14 in our atmosphere. So, it's all from all these cosmic radiation, which break the atoms of the upper atmosphere, producing a lot of particles, among them neutrons, free neutrons, which hitting the nitrogen, produce hydrogen and carbon-14. That's the source of carbon-14. And again, carbon-14 is decaying. Carbon-14 is created by this bombarding from the gamma rays from the cosmic radiation. So, it exists in our environment. And let's just assume that we know how much, what's the percentage of this carbon-14 relative to the more common, regular carbon-15. Okay, fine. That's how carbon-14 is created. Now, it's consumed by living organisms, and inside these organisms, approximately its concentration is the same as in our nature, more or less. Okay, then the organism dies. We can't really replenish carbon-14 from the environment, and carbon-14 decaying. So, what happens next? What is decaying, basically? Decaying means the following. We have this carbon-14, and what happens is, one of these extra neutrons of the nucleus, which it has, is basically converted. It's not really needed to keep the nucleus together. So, it goes through transformation, and it's difficult to explain right now about the details of this transformation, but it can be transformed into proton and electron and something else, because neutron is neutral, and it has the atomic mass 1. Proton has atomic mass 1, but it's partitively, but then if there is an electron, it neutralizes the electric charge, and proton plus electron becomes neutral again. So, basically what happens is, one of the neutrons is converted into proton and electron. So, when it's converted into proton, it becomes nitrogen, because if neutron is converted into proton, it increases the atomic number, but atomic mass remains the same. From neutron to proton, it's the same, one. Electron goes out, and there are some other things which happen in here. Well, I can tell you that it's called electron-antimutrina, and some energy is released. I mean, these are really a complicated byproducts of this decaying. But my point is that this particular carbon-14 is converted into nitrogen, back into a regular nitrogen, and that's what decaying is all about. And then there is something released as well, as I was saying. So, this is the decaying process. So, this is how carbon-14 is created, and this is how it disappears. And it disappears with certain speed. Now, let's talk about speed. Now, what does it mean that half-life is 57-30 years? It means that if you have certain amount of carbon-14, let's call it one, one of something, it doesn't matter whether. In 57-30 years, it will be only one-half-life. That's what half-life means. So, in one, in two terms of 57-30, it will be half-of-half, which is one-quarter. In three, one more 57-30 years, it will be one-eighths. Right? You see the idea? y is equal to x times 57-30 years. Go by. It will be one divided to two, the power of x. Three to the power of three, two to the power of two, x to the power of x. So, if you have determined that you have that many concentration, that much concentration of carbon-14 in the dead tree, it means it was x times 57-30 years past since it died. So, let's just do it slightly differently. If you determine that your concentration is n times less than normal, then n is equal to two to the power of x. x is equal to log n to the base of two, and y, which is the period, is equal to 57-30 times log n base two. So, this is the formula. As soon as you know that, okay, the concentration is one-hundreds of original concentration. Assuming you know the original concentration. Then you put one-hundred here to this formula, two to the power, whatever it's like, what, seven approximately. So, it would be seven times, whatever, about 40,000 years. So, one-hundreds concentration of carbon-14 in the dead tree means it died about 40,000 years ago. So, this is the basis for radioactive dating of certain things. And there are obviously limitations, approximations, etc., etc. We're not talking about the details of this methodology. My point is to talk about nucleus and transformation of nucleus when carbon-14 is created and then decaying. As an example of the inner structure of the nucleus and how protons and neutrons and electrons are interacting with each other. Okay. So, I suggest you to read the textual part of this lecture. It's on physics-14 course of Unisor.com. You go to part called atoms. In the atoms you have sub-menu called, how is it called? I think it's called nucleus and electrons. And then you have this part which is called, this lecture which is called isotopes. That's it for today. Thank you very much and good luck.