This video is regarding binding energy. It's the missing energy that keeps a nucleus together. Let's have a quick recap of jewels and electron volts. We already know that one electron volt equals to energy and electron gains when it is accelerated by a voltage of 1 volt. The value of 1 electron volt is equals to 1.602 62 * 10 ^ -19 JW. For example, if you want to convert 5 electron volt into jewles, you have to multiply it by the value 1.6 * 10 ^ -19. On the other hand, if you want to convert jewles into electron volt, you need to divide the number provided in jewles by 1.6 * 10 ^ -19 to find the answer in electron volts. Energy is measured in jewles. But when we talk about a very small value of energy, then we talk in electron volt. Introduction to atomic mass unit also known as amu. In nuclear physics, we use amu as a standard unit of mass rather than kilogram. 1 amu is equals to 1.6654 6654 * 10 ^ -27 kilg. So we can see what a small unit is atomic mass unit because we are talking about subatomic particles. Amu is also written sometimes just as U. So for example mass of hydrogen atom can be written as just 1 0078 u rather than full amu. All right mass energy equivalence if mass equals to 1 U then energy needs to be calculated in a smaller unit such as electron volts. Okay, let's have a quick look at this video which will explain us in detail about mass energy equivalents to help us better explain the concept and I want to introduce the concept of atomic mass and how we measure it. We need a unit that is actually a little bit more helpful rather than using kilogram. So we have a unit called the amu or the atomic mass unit which is simply a standard unit in mass in nuclear physics is based on carbon 12. And if carbon 12 made up of six protons and six neutrons, if its atomic mass is set exactly 12 amu, since carbon 12 is 1.99x 10 ^ of -26, we now have an atomic mass unit that is 1 U is equivalent to 1.6605 by 10 ^ of -27 kg. We're going to use numbers that are a little bit more friendly to us. So, as a result, the mass of a proton in atomic mass units or a amu is 1.00728. A neutron is slightly heavier at 1.867. And if we wanted to know the atomic mass unit of an electron, it's 0.55. Energy can be converted into mass and vice versa. And that of course is due to E= MC^ 2. If we have our 1 AMU and we convert that to energy, how much energy is that? Well, the energy of course can be calculated using standard SI units in MC^ squ. Mass of course is the mass in kilog and energy is in jewels. But with the reminder that we can convert energy into a smaller unit called the electron volt. Our one electron volt is equivalent to 1.602 by 10 ^ of -19 juw. We end up getting a conversion that 1 U or 1 amu has the conversion of energy of 9.315 by 10 to the power of 8 electron volts or what we can say 931.5 mega electron volts. So that's our conversion between mass and energy and that's a value we're going to be referring to. So now let's have a look at a larger atom with a number of nucleons. And this is where I'm going to tie in my analogy that I did earlier. Let's have a look at a chlorine. Chlorine is made up of 35 nucleons. It's made up of 17 protons, 18 neutrons, and of course it's got 17 electrons. What are their respective masses? And this is like a Lego pieces with 17 protons. I end up getting 17 by the amu in terms of protons. I get this value 17.12376. Similarly, I get the mass of neutrons equaling 18.15606. And then of course, I have my mass of electrons as well. So, this is the combined mass of my chlorine atom. If I add all those up. Okay. So, and if I do the mathematics, I get 35.28917. [Music] That seems fine. All your building blocks should equal the sum total of the parts. But we do know the mass of a chlorine atom. It is equal to 34.980175. And that includes the electrons. You'll notice that this is now less than our initial mass. We have lost mass by putting our nucleons together. So what happened? Well, we clearly have a difference in mass. We have a difference of 0309 U in mass units. If I now convert that into its energy, then all I need to do is multiply this 0309 by the total amount of energy conversion, which is 931.5 mega electron volts. I get 287.83 mega electron volts of energy. that somehow has been converted. Where has that gone? Well, that is the energy that is binding my nucleons together. What is the binding energy? It is the energy required to hold the nucleus together. This energy is gained due to the conversion of the mass defect by Einstein's E= MC² relationship. Now clearly larger atoms having more nucleons and therefore more binding energy gained will have larger binding energies. Does that mean larger atoms are having stronger binding energy overall and therefore more stable? No, that isn't the case. So really that's not a good measurement of how stable the atom is. If you want a really stable atom, you need a very large binding energy, but you need to also take in account how many nucleons we have. And so what we're interested in is in the binding energy per nucleon. So we divide the total binding energy by the number of nucleons. And that gives us a good measure of how stable an atom is. So what we do now is we graph all our elements on a periodic table with respect to the binding energy per nucleon. Yaxis we put the binding engine and it can be as up to a value of eight. On the x-axis we put the mass number which is simply the total number of nucleons. And when we graph that you can see we get a very characteristic graph. It's a very famous graph in terms of nuclear physics. This hydrogen's down here, okay? And then helium over here. This is helium right here. And this is hydrogen. And hydrogen has to be there because it actually only has one nucleon. But as you go from left to right, we start to see an increasing binding energy per nucleon. In other words, the atoms become more stable in this direction. But on the other side, what we find is we get more stable if we go from large to small. And so therefore, we go more stable from right to left. Now the question is is what is this pinnacle right here? What is our most stable atom? Well, that happens to be iron. And iron is the most stable element on the periodic table. It is the largest binding energy per nucleon. Now this has significance later on particularly when we want to look at fusion and ad fish and nuclear decay. They'll be subjects of future videos but in essence we've now discussed why certain atoms are stable or unstable when we look at binding energy and specifically binding energy per nucleon. So this this YouTube video has helped us to understand the concept of atomic mass unit and binding energy per nucleon. Just to reinforce the concept, I have another video for you. It's a short one just for the concept of binding energy. This video is to talk about binding energy for a nucleus. Let's say I have four Lego pieces. All right. out of which two are green and two are red. Let's say the green ones are 1 g each their mass and for red ones for each red piece the mass is 2 g. Now I'm going to form a shape any shape out of these four pieces of Legos. If I ask you what is the total mass for this figure I have made of Lego, you will say 1 g + 1 g 2 g plus 2 g 4 g plus 2 g 6 g. Mathematically you are absolutely right. This whole shape of Lego should be 6 g. But what if I weigh it and I say it's just 5.5 g in total. Where is that.5 gone in binding these pieces together? Now let's have a look at this concept at a nuclear level or subatomic level. Let's say I have a hydrogen atom. We know that hydrogen atom consists of one proton and one electron. A dutarium atom that is an isotope of hydrogen. It contains one proton, one neutron and an electron. So technically if I add mass of one neutron to mass of hydrogen atom, I should get mass of dutarium. Let's see mass of hydrogen atom is 1.78 U where U is the atomic mass unit. Mass of neutron is 1.87 87 atomic mass unit. When I combine these, I get 2.0165 U. This should match with the mass of dutarium. However, mass of dutarium is 2.0141 U which is this much atomic mass unit less than this. So why it happens that when two smaller nuclei are combined together then the product that is formed the mass of that product is less than the mass of its individual constituents. This is called mass defect. The mass defect in nuclei can be converted into energy using the famous energy equation E= to MC². Binding energy of a nucleus is the energy required to keep any nucleus binded. All right? Or in other form it can be said that the binding energy of a nucleus is the energy needed to break it apart. I'm sure this video must have helped you to understand the concept of binding energy. Let's have a look at a very very famous graph in nuclear physics. Uh this shows us the binding energy per nucleon. It's in mega electron volts and this is the mass number. All right. Uh as you have seen in the YouTube video as well that um as the binding energy increases it shows that the stability of that nucleus increases. All right. But as the mass number increases, the stability decreases because we know that as the nucleus size increases, the nucleus becomes less and less stable because there are too many neutrons and too many protons. Okay, just a quick reminder that mass number is number of nucleons that is number of protons plus number of neutrons. Okay, iron is the most stable one. Here below iron, whatever nuclei we have, they combine to fuse and on the right hand side of the ion, the nuclei, they try to fen I mean they break apart. All right. So there are some basic uh important points about uh binding energy. Let's have a look at those. The mass defect in nuclei can be converted into energy using equals to mc². This is known as the binding energy of the nucleus. The binding energy of the nucleus indicates how much energy is needed to separate the nucleus into individual protons and neutrons. Both of these points have been covered in both the videos. Higher value of binding energy indicates a more stable nucleus. Why? because it means that more energy is required to break apart that nucleus. It means they are they they are um together in in a very solid shape and it is difficult to break them apart. Binding energy per nucleon for a given nucleus is found by dividing its total binding energy by the number of nucleons. binding energy per nucleon. Whatever is the value of binding energy, divide it by the total number of nucleons to find binding energy per nucleon. Elements with mass number between 40 and 80 need more energy to break. Thus, they are more stable. Iron has the most stable nucleus. Its mass number is 56. Nuclei smaller than iron undergo fusion. Nuclei larger than iron undergo fision. We have seen that through the graph. Joining two lighter nuclei together to give a single nucleus of medium size also means more binding energy per nucleon because from the graph we have seen that the smaller nuclei they have less binding energy and the medium-sized nuclei they have more binding energy. More binding energy means mass defect is more right. So energy created is more. This process is called nuclear fusion. This is the main source of energy for sun and other stars. So when two smaller nuclei they combine together there is a mass defect using Einstein's equation equals to MC² whatever energy we get from that mass defect that is released in the process of fusion. All right we will also look at nuclear fusion and fusion in detail in the next lesson. Nuclear fision. When a heavy nucleus splits into two medium-sized ones. Now again remember that larger the nucleus. All right lower it is its binding energy and when it splits into two mediumsiz nucleus their binding energy is more and therefore mass defect is more and therefore more energy is created. Okay. So when a heavy nucleus splits into two medium-sized ones, each of the new nuclei will have more binding energy per nuclei than the original nucleus did. And this all can be traced back to the graph. This extra energy will be given off and it can be a lot. Splitting a heavy nucleus is called nuclear fision. All right. Before going into it, there are some more couple of things that the binding energy per nucleons increases dramatically for the very small nuclei. As they fuse together, the binding energy per nucleon increases. This is the energy released during fusion. Okay, I will upload my scanned notes along with this PowerPoint presentation so that you guys can go through it. All right. Now if you have let's say 1 kilg of uranium 235 that had undergone fision completely at the end you have a block of radioactive fision fragments with a mass around.999 kilogram all right because of course the product the product nuclei will have a lesser mass right than the in independent individual nuclei which were giving the fision process Okay, less than 1% of mass is converted into energy. How do we find that percentage of mass mass defect that means this? Here the mass defect will be 1 kilg minus.999 kg divided by initial mass that is 1 kilg* 100. Remember this formula we will be doing numericals based on this formula. All right, I hope this presentation will give you an idea about binding energy and in our next class we will do numericals based on it.