 Hello everyone, welcome to the lecture on nuclear reactions. So far we have discussed the properties of nuclei as well as radiations and now we will switch over to another aspect of nuclear energy chemistry that is nuclear reactions. In nuclear reactions we will discuss the energetics, the cross sections, the mechanism of nuclear reactions and also production of isotopes that are useful in many applications. In the first part I will talk about the energetics of nuclear reactions but before starting before discussing the energetics of nuclear reactions I should be good idea to go through little bit of history of the nuclear reactions and some of the laws that govern the nuclear reactions like the what are the things that are conserved in nuclear reactions. So it will be suppose you want to set up a nuclear reaction or you want to complete a nuclear reaction to know the conservation laws then you can easily complete the reaction. So that also we will discuss in today's lecture and little bit about the energies that are involved in the nuclear reaction. So first let us see the historical aspects of the nuclear reactions. Maybe already you know that the first nuclear reaction was carried out by Ernest Rutherford in 1919 and that is the reaction which ultimately did to the discovery of proton. Rutherford in fact bombarded the nitrogen 14 target using the alpha particles that were available from the naturally occurring radioisotopes of radium and polonium and so when he bombarded the nitrogen target with helium atoms helium from the natural electric radioisotopes like polonium to 10 then the oxygen 17 and a positively charged hydrogen atom were produced and this caused fluorescence scintillations at the screen. And so he in fact based on the charge and so on he concluded that this positively charged particles are nothing but the protons and that is how the this was the first nuclear reaction where the atom was transmuted but this reaction gave rise to stable products. In this particular reaction oxygen 17 and hydrogen proton both are stable products. So this reaction though being the first in the nuclear reaction produced stable isotopes and so Rutherford in fact named this positively charged hydrogen atoms as protons in 1920. Then subsequently the neutrons were discovered by James Chattowick the student of Rutherford in 1932 and in this reaction again the alpha particles the projectiles that were used were from the naturally occurring radioisotopes of polonium to 10. So again polonium alpha particle bombarding barely of 9 even you also bombarded other isotopes like aluminium 27 and lead to the discovery of neutron. So so far till the 1920s the projectiles that were being used were charged particles mainly alpha particles available from the naturally occurring radioisotopes of radium polonium and the energy of these alpha particles as you know was in the range of 5 mg. But when you want to bombard the heavier elements isotopes of heavier elements then the columbic barrier creates a hindrance infusion and therefore there was a need to develop accelerators which will produce high energy charged particles. So that is where a big jump took place in the development of accelerators and the need arose to increase the energy of charged particles. The 5 mg alpha particles available from radium polonium could not cause reactions in heavier elements and that is the time in 1920s and 1930s you will find lot of discoveries took place developments took place of different types of accelerators I will just briefly go through some of them. In 1932 Cockroft and Walton at Cavendish laboratory Cambridge in fact they developed a voltage multiplier which will which will by which you can generate the high energy particles. So basically you have a cascade of accelerators and which you can charge to higher and higher goods like in a photomultiplier tube the photomultiplier tube you have the cathode and then you have the diodes of having higher and higher voltages in this cascade generator you have the electrodes having higher and higher voltage. So you can multiply the voltage to higher and higher voltage and then you can accelerate the charged particles. So in fact though it was developed in 1929 but they caused they split the atom using these protons in 1932 and so the first time demonstrated that using the accelerated charged particles you can cause a reaction in a nucleus and for this they got Nobel Prize in 1951 Cockroft and Walton. So that was a landmark development in the early 1930s concurrently with that Van de Graaff at Princeton University USA developed an electrostatic accelerator. Electrostatic accelerator is very simple. Suppose you have a potential V and you have a charge 2. So if you have a negative charge minus 2 and you have a positive potential then the energy that will the charge particle will acquire will be QV. Like in electron accelerated potential of V volts will be called an electron volt. So you can actually accelerate in an electrostatic manner any charge particle accelerating to the potential, opposite potential you will acquire the energy electron the charge into the potential. So that is the straight away electrostatically you can accelerate particles and Van de Graaff in fact generated few MEP particles using electrostatic accelerators. In fact there has been a course in NPTEL on accelerator physics and so those students who want to know more about accelerators and the physics behind them they can attend that course which is currently going on. In about the same time Lawrence at Lawrence in fact later on became Lawrence Berkeley that time to University of California Berkeley developed acyclic accelerators. So that was called pachylotron which can accelerate the charge particles between the D of a magnet and then accelerate to very high energy. So in fact the diameter of the magnet actually will decide the energy to which you can accelerate the charge particle. So concurrently you will see electrostatic accelerators, cyclic accelerators were developed in when their need arose accelerate the charge particles to higher energy than the that are available from the naturally occurring radio acid. In fact later on in 1950s other variants of accelerators became available this curve like one of them are called tandem accelerators. So tandem essentially means two stage. So you start with a negative ion accelerate to a positive potential and then so you have the potential and at this you put a stripper coil and then you will see two plus. So it is a two-stage acceleration one is from the negative ion to positive potential and then the positive potential will repel the positively charged ions to ground steps. So this is the two-stage acceleration called tandem accelerators and one of the accelerators of this type are called peltron accelerators that the pelt charging how you charge the accelerator is called by pelt charging methods but it is called peltron accelerator and by tandem now since it is a two-stage acceleration you can go to much higher energies than what you get from the electrostatic accelerators. So over the background there is a big jump energy when it came to tandem accelerators and later on linear accelerators became also very popular wherein you can accelerate in steps so small small steps by an alternative potential. So you have a ion let us say positive ion you have a negative potential and then again you change the the potential for to negative and so subsequent steps of increasing length of the accelerating tube you can accelerate the particles to much much higher energy and the linear accelerators are in fact the the length of some of the accelerators are in few kilometers in fact the latest the highest energy accelerator in the world today is at San Geneva that is called the large head round collider let us see and which gives rise gives 6500 giga electron volt protons it is a linear accelerator having subcomponents of 27 kilometers. So the subject of accelerators in fact have advanced so much that you can now in the particularly in the high energy physics domain there has been a need to develop high energy accelerators so that you can create different particles. So when you in fact it is called a proton-proton collider so when the two protons collide you can generate a lot of energy and from that energy so many other particles like you know with the different particles the baryons the quarks and leptons they can be produced and so it is like a factory to produce different types of particles so that is how the high energy subject of high energy physics have advanced because of the development in the accelerators. At the same time the developments in accelerators had led to other aspects like the discovery of transuranic elements. The transuranic elements you know that the elements up to uranium were known in the 1930s and then and the discovery of nuclear fission took place in 1938. In fact the attempt by Enrico Fermi was to synthesize elements beyond uranium and in the process Arne and Stasman developed discovered nuclear fission but the experiments at Berkeley continued to synthesize heavy elements beyond uranium and in 1940 Clarity, Siborgh and Macmillan in fact used the cyclotron developed by Lawrence wherein they used the deuteron beam to bombard uranium to 38 to get to the neptronium to 38 plus 2 neutrons this 238 neptronium is 2 days half life and by beta minus decay generates 238 plutonium which has a half life of 24,000 years. So this was the discovery of a new element plutonium element atomic number 94 prior to this element 93 neptronium was discovered by neutron induced reactions on uranium that was 238 uranium and gamma 239 uranium undergoing beta minus 2 to 239 neptronium by 3 days this is 23 minutes. So the transuranic elements discovery was also contributed by the development of the accelerators and now I had many of who be knowing that the accelerators have contributed in the synthesis of heavy elements now the elements up to 118 have been discovered all of them are possible elements beyond 103 now beyond the trans beyond the actinides in fact now are possible only by means of accelerators. So by accelerators you increase the atomic number of the nuclei by adding that atomic numbers and so this is a subject in itself where you can synthesize heavy elements you can study the chemistry of heavy elements all using the accelerators. So accelerators have impact not only in the fundamental research extension of periodic table or high energy physics now as we will see along in this particular lectures now accelerators have also provided the means to produce radio isotopes which are useful for applications in healthcare industry agriculture and so. Okay now let us come to the nuclear reactions fundamentals so any nuclear reaction we will follow certain nomenclature and certain notation to develop a nuclear reaction suppose we want to complete a nuclear reaction. So we can write simply capital A is the target small a is the projectile small b and capital b are products so they we call them small a is the projectile capital a is the target is an ejectile means a smaller particle product and heavy residue is a heavier of the two products that are formed so this whole thing can be written in terms of a comma bracket a comma b into capital b that means capital A and capital b are little bit heavier nuclei and small a and small b are smaller nuclei projectile or ejectile. Just to give you an example when helium is bombarded now aluminum 27 the famous reaction for discovery of neutron and also the discovery of artificial activity you get a neutron and phosphorus 30 so alpha is the projectile aluminum 27 is the target neutron is the ejectile and phosphorus 30 is the heavy residue so the same reaction can also be written in terms of 27 aluminum bracket alpha n 30 phosphorus or a bracket a comma b so you can set you can write the notation for a nuclear reaction in this way. So the projectile for a nuclear reaction could be neutron proton alpha particle it will be heavy ion like carbon lithium oxygen or you can even induce nuclear reaction using a gamma photon so if projectile could be any particle similarly the target mostly the target will be mostly a nucleus a heavier nucleus on which the projectile is bombarded then the ejectile means the particle that is emitted the smaller particle that is emitted will be called ejectile it could be gamma ray neutron proton alpha or heavy ions they can be emitted in the nuclear reaction and then you will be left with a heavy residue that mostly will be a nucleus so you when you are setting up an equation if you are have to fill in the blanks you can use these notations and certain conservation laws that I will be discussing shortly. So now let us discuss what are the conservation laws when we write a nuclear reaction and I will be using this as an example to illustrate the points the conservation laws. So 27 aluminum alpha n phosphorus 30 is the like a reaction which we will use to illustrate the points so in any nuclear reaction the charge is always conserved so that will help you in writing the nuclear reaction and for example aluminum 27 30 means the atomic number so it is 15 2 and 0 so 13 plus 2 is 15 and it is 15 here so atomic number is conserved so number of protons essentially the number of protons in any nuclear reaction is conserved similarly the mass number in any nuclear reaction is always conserved you can see here 27 plus 4 31 and 30 plus 1 31 is always conserved and since the atomic number and the mass number are always conserved in nuclear reaction so neutron number is also conserved any nuclear reaction you will find the neutron number is also conserved so delta you can also write delta z to 0 delta a equal to 0 delta n equal to 0 so that will help you in setting up a nuclear reaction. Now when it comes to mass and energy as you know that mass and energy are inter convertible so when you in fact when the nucleons combine to form a nucleus energy is released or if you want to break a nucleus into constituent nucleons you require energy so mass and energy are inter convertible so that is why when it comes to conservation of mass and energy it is the sum total of mass and energy that is conserved not mass alone mass alone is not conserved energy alone is not conserved it is the mass plus energy together they are conserved so when I am putting e these are the kinetic energy of the nuclei so mass of the reactant for a projectile plus kinetic energy of the projectile plus mass of the target plus kinetic energy of the target so this is an initial mass and energy equal to mass of ejectile plus its kinetic energy plus mass of heavy residue plus its kinetic energy so on the left hand side and right hand side mass and energy together have to be conserved. Now you can rearrange this equation now so take the masses on the one side mass of reactant plus mass of target minus now this two quantities will come on the left hand side minus mb minus mb so in the bracket we can put a plus equal to kinetic energy of products eb plus eb minus kinetic energy of reactants because the reactant will from here become negative sign and so this quantity the difference in the masses of reactant minus product is called the q value and q value can also be defined in terms of difference in the kinetic energy of products minus that of the reactants this q value is called the energy of a nuclear reaction so energy of a nuclear reaction is an important quantity it could be positive it could be negative if q value is positive that means energy is released in nuclear reaction these are called exoergic reaction if q value is negative that means energy is required to cause a nuclear reaction they are called endoergic reaction like in chemistry you have exothermic and endothermic in nuclear chemistry we will call exoergic and endoergic. We will discuss more on the q value subsequently another quantity that is conserved in nuclear reactions is the linear momentum the linear momentum is nothing but mass into velocity and so the linear momentum is also conserved and the corollaries of this linear momentum conservation will be clear very soon when we will have the subsequent lecture. Angular momentum is another quantity which is conserved in a nuclear reaction angular momentum is the sum of the spin angular momentum and the orbital angular momentum l plus s so you can say i equal to l plus s orbital plus spin angular momentum so this i is again conserved before reaction and after reaction and in addition to that the parity and statistics the parity if you recall the parity of a function is like minus 1 to the power l where l is the orbital angular momentum or you can say if any function also has got a parity depending upon whether it will change the sign upon change of coordinates or not. The statistics we have either Fermi derived statistics called fermions or bosons so the again the statistics also is conserved before and after the reaction so they are more into the details of nuclear reactions but for the moment the important quantity that we need to know about conservation is charge mass number and hence the neutron number mass energy linear momentum and angular momentum. Now, let us just go into the q values of nuclear reaction how to calculate the q value of nuclear reactions. So, simply again I can write the reaction as capital A bracket small a comma small b to capital B so this is the projectile the target ejectile and the heavy residue and let me just discuss the q value can be given in terms of the mass of the reactant minus mass of the products into c square. If you write in terms of the atomic mass units then you would say c square and this q value can be positive or negative. So, let us work out some examples to demonstrate this point how what kind of masses we need to put into the nuclear reactions to calculate the q value of nuclear reaction. I give you some examples neutron plus cobalt 59 gives rise to cobalt 60. So, this is called a n gamma type of reaction capture reaction that means actually this cobalt 60 will be excited and it will limit a gamma ray to come to ground state and that cobalt 60 in ground state is radioactive having half life of 5.27 years. But this cobalt 60 when it is excited it will emit gamma ray within 30 seconds. So, that is why it is called 59 cobalt and gamma 60 cobalt. This gamma is not the gamma ray emitted after beta decay of cobalt 60 but it is called a prompt gamma ray. So, this reaction the q value will be mass of the neutron here you see here what I have shown here the masses are the mass defects mass minus a is called delta n mass defect. So, this you can write my square. So, if you write the mass in atomic mass units minus the mass number and into 931 you will get the mass defect in delta m in MeV that is what is written in terms of mass of a neutron 8.071 plus the mass defect of cobalt 59. So, it is minus 62.224 now minus the mass defect of cobalt 60 minus 61.644. So, that is equal to 7.488 MeV. See one thing you must note here that since the though I am writing here mass defects the delta a value for a nuclear reaction is 0 because the mass number is conserved. So, here it is possible to write the masses in terms of m minus a because the a will negate get cancelled. So, that the difference in the mass defect means nothing but difference in the masses because the a will get cancelled. So, the masses are given as mass defect in m minus a when you want to calculate the q value. There are certain cases which you will discuss you cannot substitute the mass by the mass defect when you are calculating the energy requires energy or central mass energy which will become very clear very soon. Now this in neutron capture reactions you will find are always exoergic reaction because you are combining a neutron to a nucleus. So, whenever a nucleus combines with the neutron energy equivalent to the binding energy is released. So, this energy is nothing but the binding energy of neutron in cobalt 60. So, such reactions neutron capture reactions are always exoergic that means energy is released and the energy released is equivalent to the binding energy of neutron in the product nucleus. Another example is helium 4 plus beryllium 9 carbon 12 plus neutron. So, again the masses are written in terms of the mass defect. So, for alpha particle the mass delta m 2.425 MeV beryllium 9 11.348 MeV to carbon 12 the delta m is 0 because this is the carbon 12 scale and so for carbon 12 the mass is 12.000 and so on. Neutron 8.0 so on. So, this is the q value for the reaction is 5.702 that is positive and hence it is exoergic reaction. There are some reactions like helium 27 helium 4 comma n phosphorus 30 here you can see helium 27 minus 17.197 MeV alpha particle 2.425 neutron 8.071 and phosphorus 30 minus 20.201 and this reaction has a negative q value of minus 2.642 MeV. So, this reaction having negative q value is called exo, end to x reaction because energy is required to induce this reaction whereas for exoergic reaction the energy is released in the nuclear reaction. So, nuclear reactions particularly the q values will be in the range of q MeV and it could be positive or negative. So, the nuclear reactions the energetics are the important property of nuclear reactions and as you will see subsequently you can in fact use the energetics to calculate the threshold of the nuclear how much energy is required to induce a nuclear reaction that we will discuss in the subsequent lecture. Thank you very much.