 In the previous lecture, we discussed about the mechanism of different types of nuclear reactions like elastic scattering, inelastic scattering, direct reactions and most importantly the compound nuclear reactions. Today, we will discuss another type of reaction that is nuclear fissures which also undergoes through nuclear compound nuclear formation only, but nuclear fission and nuclear fusion, particularly the fusion reactions utilized for production of energy, that itself is a subject. So, with I thought I will discuss them in more details. So, today I will talk about nuclear fission and nuclear fusion reactions. So, nuclear fission and fusion can be explained using the binding energy curve. What I have here is the binding energy per nucleon, that is called the average binding energy as a function of mass number of the nuclei and so, you are familiar with this graph the binding energy per nucleon is in the range of 7 to 8 MeV per nucleon and if you see the fine structure, the binding energy per nucleon increases then up to mass 60 it increases and goes up to almost 8.8 MeV per nucleon and subsequently for higher masses the binding energy per nucleon decreases. Now, if you recall the relationship between binding energy and masses, so binding energy was equal to ZMH plus NMN minus mass of the nucleus. So, higher the binding energy lower is the mass. So, that we can tell from here that nuclei which are around heavier side of where I can at tonight's, their binding energies are low but their masses are low. In terms of we can see in terms of the mass numbers, you must have seen the mass defect can be positive or negative. If mass defect is positive that means the masses are higher binding energies are low. If mass defect is negative that means the binding energies are higher. So, now in nuclear fission what is happening, you split a heavy nucleus to lighter fragments also in the process the binding energy per nucleon is increasing that means masses are decreasing. So, there will be energy released. So, this process will be exoergic when you split a heavy nucleus of lower binding, average binding energy to two heavy nuclei of heavier binding, higher binding energy per nucleon then energy is released that is what is nuclear fission. And the nuclear fission, nuclear fusion reaction, you are using the lighter nuclei like deuterium, tritium and forming heavier nuclei. Again, you are going from reactants of lower binding energy per nucleon to the products of higher binding energy per nucleon. So, any process in which you go from low binding energy per nucleon to high binding energy per nucleon will be exoergic and such reactions, nuclear fission and inclusion can be explained on the basis of the average binding energy curve. So, what happens in nuclear fusion like nuclei like deuterium, deuterium or deuterium, tritium and so on use together to form a heavier nucleus, relatively heavier nucleus like EM plus a neutron is emitted and they have very high Q value. So, this is around 17.6 MeV energy is released which is primarily going to the neutrons. So, neutron will in fact have 14 MeV deuterium energy and the rest will go to helium. So, this is a there are different types of reactions where isotope of hydrogen used together to form where elements like helium and so on and in the process lot of energy is released. Then nuclear fission, nuclear fission the heavy nucleus captures a neutron. So, 235 uranium captures a neutron, become 236 uranium and which then splits into two fragments and there are many such pairs. It is not it is just a one of the examples of a pair of fission fragments, but there are many, many such many hundreds of such fragments are found binary fragments and in the process again sometimes 2, sometimes 3 neutrons are emitted and a large amount of energy is emitted as the kinetic energy of fission fragments and other particles that are emitted in the fission process. So, both these reactions, large amount of energy is released and we will discuss shortly how to compare energy production from these two processes. So, comparison of nuclear fission and fusion particularly with regard to that means this energy to produce power. So, nuclear fission and nuclear fusion if you see in terms of the energy released per nucleon into nuclear fission let us say assume 235 plus neutron. So, you have 236 uranium, there are 236 nucleons and 200 MeV is energy released. So, per nucleon 200 by 236 around 0.8 MeV per nucleon or per atomic mass unit energy is released. Compared to that in nuclear fusion reaction take the case of DT fusion. In DT fusion 17.6 is the Q value of the reaction and 5 nucleons are involved 2 and 3. So, per nucleon 3.5 MeV is released per atomic mass unit 3.5 MeV is released. So, you can see compared to nuclear fission fusion has much more energy per gram or per nucleon of the target material. So, it is having a positive point with regard to energy released per unit mass. Now, so that is the plus point of fusion, but in the case of fission the fission can be induced by neutrons, neutral particles or in low energy particles, but in the case of fusion as we are using the charged particles the it requires there to cross the volume barrier and if you recollect that 1 electron more than 4 kelvin for 10 keV almost 100 million degree kelvin temperature is required. So, that is the disadvantage. Nuclear fission gives rise to a large amount of radioactive fission products some of which are very very long lived and nuclear fusion also produces tritium and neutrons, but the we do not have a long lived radioactive acid produced in nuclear fusion. In the case of nuclear fission the nuclear electricity had been already being utilized it is being produced for a long long time. So, it is a reality whereas the power or the fusion reactor is yet to be become a reality and so efforts are on to in fact tap the fusion power to produce electricity. So, we will discuss both these aspects sitting in the subsequent presentation, but before that let us be try to go down the memory lane wherein how the historically the fission process came into being. See you know in 1932 James Chadwick discovered neutron and it was soon realized that neutron can be captured by nuclei and when the neutron is captured by a nucleus you get by n gamma a higher isotope of that element which is invariably beta minus 80 and beta minus essentially gives you the next higher element. So, Enrico Fermi at Rome very soon realized the importance of this particular concept of producing higher element using n gamma area and she had in his mind how to extend the periodic table at that time the highest element known was uranium element atomic number 92 and so if uranium 238 captures a neutron then we get 239 uranium which may undergo beta minus to give you element 93. So, with that objective he in fact started experiments to irradiate uranium 238 with neutrons and look for the radioactivity of the products that are formed. But Enrico Fermi was a physicist and he did have one or two chemistry people in his group. So, what they found that this particular reaction instead of a particular one isotope having one half life they found several isotopes having. So, there will be a lot of half lives and at that time they did not have the nama's property setup which you can distribute between different isotopes. They used to the one has to do the chemistry to separate different isotopes and count for the beta activity. So, they were not in the position to solve this puzzle what is the reason for or which are the isotopes that are produced when you bombard with 38 uranium with neutrons. But they had an idea that if you if element 93 is produced it might decay by alpha. So, that will become 91 that is protetinium and again it can go further decay to by alpha to get elements radium. Radium is 18, 86, 88 and this is 89. So, these elements would be produced by the alpha decay of the element 93 and other elements. But they were not in a position to do any meaningful radical separation to identify this radioisotopes. So, then the established chemistry groups in Europe, in France, Irene Curie, Patrick Julian and Paul Savage started the experiments on bombardment of thorium and uranium neutrons and they were experts in doing radical separation. So, they were trying to separate actinium for which they used the lanthanum as a carrier it was chemically they are similar lanthanum will like to homologous actinium. And so, when they did the radio chemistry they found some of the activities got concentrated with the lanthanum pattern. And so, they actually they have seen lanthanum as a fission product, but they did not do an unambiguous chemistry to establish this lanthanum. They were thinking it is actinium. That is at that time, Fautahan in same time period at Berlin was studying again the same reaction, weird name bombardment of my neutrons. And again, they were focusing on radium, the radium could be one of the alpha decay products of higher elements and that time they were using radium as a carrier to precipitate out radium. So, they got the activity of radium with radium, but they wanted to make sure whether it is radium or berium. So, what they did? They used radium 226 as a tracer to follow the path of radium and then get the chemistry. And what they so, they found what they did to separate berium and radium is a very very tough task. So, they did fractional crystallization of the berium and radium fractions and they found that whatever they were calling as radium actually was berium. So, they they could unambiguously confirm because there the bombardment of radium by neutron gives berium isotopes not radium because they have used radium as a tracer putridium as a tracer. And activity got separated with the berium fraction not with the 226 radium. So, this was a landmark discovery in December 1938 by Otto Hahn and Straszmann. In fact, there is an excellent story behind this where well old colleagues like Lisa Mitner, Lisa Mitner was working with Otto Hahn and she had to leave Europe because of this Nazi movement and later on in United States she actually in fact gave the theory of nuclear fission. So, anyway the Nobel Prize for the discovery of nuclear fission went to Otto Hahn in 1944 and the theory behind nuclear fission then was given by Niels Bohr in 1939 very nice paper in physical view published by Niels Bohr. So, the nuclear fission the the reaction it can be even the spontaneous fission which we will discuss shortly or a capture of a neutron by a heavy nucleus like in 1935 given rise to two fission fragments plus neutron and larger amount of energy. If you recall my discussion during the liquid drop model from the energetics point of view, the liquid drop model can explain occurrence of fission by competition between surface energy and coulomb energy of a nucleus which is deforming. So, this is the diagram to explain nuclear fission we have a nucleus as a liquid drop. So, the liquid drop model will predict that the nucleus remains spherical in its ground state because the surface energy, the surface energy will try to be minimized and the surface energy of a sphere is minimum compared to form nuclei. So, the surface energy term tries to see minimum energy in the form of a spherical nucleus. Now, you know that fission is taking place. So, the nucleus has to deform. This is the x axis in the deformation the degree of deformation this is very symmetrical deformation alpha 2. So, when the nucleus is deforming the surface energy is going to increase E s and the coulomb energy is going to decrease because now the protons are little bit apart from each other. So, they are going to get to E square by D. So, further apart the protons more is the less is the coulomb repulsion. And so, depending upon the nuclei the delta E s and delta E c the change in the surface energy and coulomb energy then it will decide whether it can go fission or not. So, the deformation energy surface energy of a deforming nucleus in terms of the deformation parameter this is the surface energy of a sphere that is your know A s A raise to two-third and this is the coulomb energy of a sphere z square upon A s z square upon A raise to one-third. So, the two the change in surface energy coulomb energy will dictate that the nucleus cannot go fission or not. So, if you will see the ratio of delta E s delta E c upon delta E s at this point when the nucleus becomes committed to fission that can be written as in terms of E c 0 upon two E s 0. So, basically you take 2 by 5 alpha 2 square E s 0 and 1 by 5 alpha 2 square E c 0 and take the ratio you will find E c 0 by 2 E s 0 is the delta E c by delta E s and that becomes equal to A c z square by A over the one-third upon 2 A s raise to two-third and which you can write in terms of z square upon A upon a constant term 50.13. This is called the fissility parameter fissionability of the nucleus is dictated by this term. So, higher the value of this fissility parameter higher is the fissionability of this nucleus. So, the nucleus is undergoing deformation. So, the shapes of the nucleus like this is called the saddle point like a transition state in chemical reaction and once a nucleus is able to reach the saddle point then it becomes committed to fission and when the two fragments are about to separate that is point that point is called the fission point above the fission to separate the two fragments. So, ground state saddle point and fission point these are the three stages of the this new nucleus. So, the the facility of the nuclei if you see that like for example for 238 uranium or 236 uranium it will be 0.71 z square by A upon 50.13. So, that nucleus if you see the spontaneous fission half life it will be very very high and power 14 15 years. You go to telephonium 252 252 californium x is 0.76 or 236 uranium x will be 0.71. So, side increase in the fissility parameter point from 71 to 0.76 the half life is 2.6 years for total half life but fission half life is 85 years t half or fission of total p2 californium. So, slight increase in the fissility parameter leads to a drastic reduction in the spontaneous fission half life. So, this is the schematic of the phenomena that occur during the fission and the post fission phenomena. A neutron is captured by the target nucleus and you have 236 uranium which is excited it can undergo beta minus decay to become the higher element or it can undergo fission. So, in the fission the compound nucleus will undergo hydration deformation. So, these are the like 7 point or close position point and then because of the colombic repulsion between two fragments you will have one two fragment a heavy fragment and then the latter fragment and then this. So, I am showing here binary fission because two fragments are formed there could also be ternary fission also three fragments are formed. Then these fission fragments are highly neutron which they have very high n by z. So, this because of the high n by z they have excess neutrons they emit neutrons the binary energy of neutron is very small. So, first they emit neutrons, tron neutrons or go to three fission neutrons per fission. Then if a neutron is not possible then you have the gamma rays the neutrons gamma rays and then once the by gamma prong to gamma ray emission they become fission products the fission fragments by emission of neutrons and gamma rays become fission products and the fission products will undergo then beta minus decay and the process they have to be gamma ray emission also to end up with the stable input. So, this is the journey of the fission process from neutron capture by the two third heavier nucleus to fission products to and ultimately a lot of energy is imitated in the form of its fragment kinetic energy, the energy of neutron from the gamma rays, energy of beta minus and neutrinos and the gamma decay after beta decay there will be gamma decay from the so, this is how the energy is distributed in different forms a total of 200 or maybe energy or little bit more than that you will find it is spent distributed in different forms here. Now, let us go little bit much deeper into the different aspects of nuclear fission. I will explain two processes, two observations one is the mass distribution second is the candidate distribution. So, mass distribution that means what as a function of mass how the yield is varying. If you see from the liquid drop model point of view the liquid drop model will predict a nucleus splitting into two equal halves that is having the highest energy to be released. But what happens in this particular case of 235 linear you will find that we have a double hump barrier that means the asymmetric fission is more favorable. 117 is here, 117 mass is equal to the splitting of the nucleus into two equal halves, but that has got a very low yield. Yield means you know out of 100 fission how many times the particular pair is formed. So, this is a fission yield curve where total area will be 200 percent because 100 fission are taking place you will have 200 fission products. And the cross section for this reaction for 235 uranium Newton in fission thermal neutron is 583 bonds which is very very high and the average mass of lighter and heavier fission products are 95 and 138 for 235 uranium and the atomic numbers will be varying for 30 to 65 to 72 160 for lighter and the heavier mass peak yields are varying from maximum yield about 7 percent minimum 0.001 percent. Very interesting thing I will tell you here that if you see the 239 plutonium fission then the heavier mass peak remains the constant and to conserve the mass the lighter mass is shifted to heavier mass, lighter mass fission product masses shifted to higher and it tells about the mechanism of the fission process that means that the heavier side has got some fission products which have a very stable configuration and so their yields are higher and to compensate for the total mass lighter mass peak shifts. So, now for each mass this success is a mass number for each mass number there is a chain of isobars like if you take this pair is formed z1 plus z2 92 here iodine and strontium you will find that this there will be a chain of isobars so 138 iodine will undergo beta minus decay to xenon to cesium to barium so until it becomes stable similarly strontium 95 undergo beta minus decay to yttrium zirconium niobium and finally stable. So, whatever pair of fission products are formed in one fission process they will start undergoing beta minus decay and you can see the half-lives are increasing which is the ones which are very much away from stability and short half-lives and they buy the chain of beta minus decay all of them will come to stability. So, that takes time the half-lives are increasing some of the fission products have very very long half-life almost billions of years half-life. So, another property of this fission process is the kinetic energy distribution so I mentioned that kinetic energy of fission fragment is 168 MeV so the total energy about 200 MeV the dominant row is taken care by this and so what happens when the two fragments are separating this is the what I have shown at the fission point if it is equal fragment both fragments are equal therefore symmetric fission that is the mass numbers are same. So, when they separate out there 1, there 2 e square by T the kinetic energy is related release this much much. Similarly, it could be a arithmetic pair one light and one heavy and then it could be slightly different. So, normally you know from the if you see the spherical fragments you would find the symmetric splitting will give you higher kinetic energy if you see from Z 1 Z with Z 1 equal to Z 2 this kinetic energy is maximum. But if you see the actual observation as a function of mass number of heavier mass product this is the symmetric splitting 180 to 36 by 2. So, what they found experimentally that the total kinetic energy is lower for a symmetric splitting compared to the asymmetric splitting where it is 200. So, for mass number 132 the total kinetic energy is higher again it cannot be explained on the basis of liquid torque model and so the higher kinetic energy at 132 was explained due to the shell effects if you recall the shell effects I said that those with the magic number of nuclei they are having spherical shape and so if this heavier mass is around 132 this is spherical and once the nucleus is spherical the kinetic energy will increase. Another observation that in the previous slide I found I will I showed you that the mass number 138 is constant for different piston nuclei 1 to 35 or to 39 and that again 138 mass having highest yield was attributed to a different magnetic number before the shell neutron 808. So, these are the kind of explanations experimental observations of double mass distribution and total kinetic energy can be explained in terms of the nuclear shell effects. Okay, so ultimately when fission takes place a neutron is captured by the heavy nucleus and in the process you have two fission fragments and there could be two or three neutrons produced. Now this fission reaction if it left uncontrolled it leads to a device nuclear device at a bomb which you can call because this neutrons can subsequently induce fission in many more to 35 unit nuclei and therefore it becomes a chain reaction if you do not control means you do not suppress the neutrons this in multiplying neutrons will lead to a explosive device and the whole thing will explode in a very short span of time that is the concept behind the nuclear device. But the same thing if you control the reaction in such a way that every for every neutron that is absorbed by a nucleus at least one neutron is left to propagate the chain then it becomes a controlled chain reaction. So, in the controlled chain reaction normally now when neutrons are produced they will be captured by structural materials they may escape from the device. So, you may not have even one neutron left to sustain the reaction. So, you have to have the reactor designed in such a way that at least one neutron is there available to sustain the chain reaction that is the concept behind a nuclear reactor. A nuclear reactor you have if the fuel the fuel is in the form of pellets like uranium oxide and which is now so this is the you have a fuel the tube and which inside you put the fuel pellets. So, this is the you have a fuel the tube inside the pellets are filled and you can have it. So, this lines are like this and then you have the outside the fuel there is a pressure tube the pullant is flowing to take away the energy of the mission. So, that mission the heat the pullant will be flowing this pullant is flowing through this reactor the pressure tubes and then this heat little form steam there is a heat exchanger heat exchanger will then take the steam to turbine and you can run the turbine with the steam. So, the whole process of fission ultimately leading to generation of steam and then that steam running a turbine is the concept behind a nuclear reactor. So, you require the cloud and the twist to keep the fuels intact you know you have a cladding material in casing of the fuel then there is a pullant this flowing through the pullant channels. So, outside the cladded fuel you have the another annular pipe through which the fuel liquid will flow the pullant could be heavy water or light water or state will be sodium also. And then you have the moderator also to formalize the neutron because common neutrons are more reactive than ask neutrons. So, you need to reduce the energy of neutron make them thermal so that you have more fission reaction. And again to control the reaction so that you don't the reactor doesn't go out of hand there are the control rods. So, the control rod will not contain the neutron economy in such a way that there is no an advertent highs in the neutron number at any point of time. In fact, as a function of time also you will find the neutron economy will change and the control rods are adjusted so that the reactor remains as critical. So, all this the entire thing basically becomes the concept behind a nuclear reactor. So, fission has been tapped to produce electricity whereas and the nuclear device based on fission also as a reality as all of you know. So, this is the nuclear fission has been tapped for nuclear power production. In the next lecture I will discuss about nuclear fission how it can be used for power but in the status behind the technique of fission energy or electricity. Thank you very much.