 okay so I assume you guys are able to solve questions your own those two chapters preceding two chapters yes or no yes and yeah and tomorrow you have a test right yes any of you have joined my tendons is going down less going lesser and lesser now you have any uts coming up is it yes start tomorrow's test hard well how does it matter whether test is hard or difficult it's all relative if it is hard it'll be hard for everyone rank will be accordingly so never look at your marks look at your rank relative standing where you are okay so don't worry about the hardness of test hardness of the test will soon increase to very hard I don't want it to I want it to represent like J mains right now okay because it is J mains paper the advanced level paper was slightly easier than how it was so probably yes next time onwards I'll intentionally made it difficult okay so let's start this chapter nuclei okay nuclei is the plural form of nucleus so obviously we are going to discuss about the nucleus in this particular chapter okay and this chapter has a special focus towards the nuclei and the even though the previous chapter name was atoms we never discussed about the nucleus part of the atom the reason was that we when we started studying about the atom we found out that the electron is electron behaves completely different the way the nucleus behave fine so that's the reason why these two things electrons and the nuclei their behavior cannot be in the same chapter okay so that's the reason why they are two different chapters so that exclusive focus can be given to the nucleus and that's how the chapter name is there exclusively nuclei and since we have to give exclusive focus towards nuclei and you will soon realize that it behaves in a very different manner the way electrons behave you might have a little bit of idea also so because of that we will study it as if it is completely new to us okay then how do we study something which is completely new to us we will try to find out how does it look like what is its dimension what is its mass okay so we first try to find out what is the basic nature or the basic features of all that and then we get into how we can know how it is useful to us what are the other properties so first and foremost we'll be discussing few things which are you can say physical attributes of the nucleus okay so write down in the Rutherford experiment it was very clear that the nucleus is at the center and it is considered to be very dense as if an entire mass of the atom is concentrated inside the nucleus itself in fact when we talk about atomic mass write down by the way what is going on in school we are about to start magnetism magnetism matter no sir electro matter moving charges yeah oh so I am little bit ahead or very far ahead quite far ahead but the room is back how are you through you've told others through all right so atomic mass is so through came out from covid congratulations roof anyways so atomic mass when we find out we found out that entire mass is as if that entire mass of the atom is concentrated at the nucleus okay it behaves as if so that means that's very very dense okay so electrons mass is negligible compared to the protons and you know during those times when the study of nucleus had started already people did not have much idea about existence of neutron but since we know it I can write here that electron mass is negligible not only compared to proton but neutron also okay so first thing is studying the mass of the nucleus and if I already know that entire atoms mass is the mass of the nucleus only approximately then why will I separately find out the mass of the nucleus I will just find out the mass of the atom and I'll say that mass of the atom is mass of nucleus only in a way okay but at the same time since I am talking about the one atom or let's say couple of atoms at a time I need to deal with very very small unit of mass I'm not talking about let's say 5 kg mass 10 kg mass like that I'm talking about a very very small mass that is mass of the atom okay so just like in the previous chapter we came to know about the smaller unit of energy what was it electron volt okay similarly in this chapter we will be talking about smaller unit of mass do you know it already atomic mass unit smaller unit of mass people tried to define the smallest possible mass that exists so that they can say that even mass is quantized okay but then of course it is like people thought that atom is indivisible then they thought proton is indivisible then proton and neutron they can further be divided so still people are finding smaller and smaller particle but anyways we can talk about the smallest unit of mass practically you know naturally existing we can say naturally existing smallest unit of mass is what we are trying to define which is atomic mass unit okay so the full form right on is atomic mass unit we wrote previous chapter everything in terms of electron volt because we were dealing with very very small amount of energy I don't want to write 10 is for minus 19 joules every time so atomic mass unit since it is so fundamental okay it is the basic unit of the mass you can also call it one unit if I just say one unit of mass it doesn't mean 1 kg 2 kg like that it means one atomic mass unit okay and the way it is defined one unit the way it is defined is mass of mass of carbon 12 carbon 12 has mass number of 12 okay 6 protons 6 neutrons the mass of C 12 divided by 12 this is the definition of one unit why they have taken carbon as a reference why not some other element there are multiple reasons to it and we are not getting into that but they have taken it like this okay mass of the carbon 12 atom is 1.992647 into 10 is for minus 26 so we at times start to wonder that how can we be so accurate about measurement of mass there is one technique mass spectrograph which enables us to find out mass very accurately so those are those techniques but again not in our syllabus curriculum we don't have to worry about it just that this is how it is so this is the one atomic mass unit one unit is this much suppose I talk about 10 units will be how much 10 times of that five units will be five times of it okay now it was assumed during those days that the neutron proton whatever exists inside the nucleus okay they are the fundamental units so fundamental unit means that they cannot be divided further okay so according to the definition of one unit wherein I know 12 particles are inside the nucleus 12 fundamental particles I've divided by 12 mass of proton is similar to mass of neutron so every every atoms mass should be what should be near integer multiple of AMU or you are able to understand what I've written here if protons and neutrons cannot be divided further then every nucleus will have some integer times proton and integer time neutron this is effectively what this is effectively mass of a proton or mass of a neutron very close to that I'm dividing by 12 so every atoms mass should be near integer times the mass of one atomic one AMU is this clear are you able to understand what I'm saying here yes everybody right yes so but then in nature when they have found out the masses of the atoms they were surprised they as in the people who were studying it okay so they were surprised that masses of the some naturally existing elements for example chlorine if they you know for example if I have to measure the mass of chlorine I don't take only one atom of chlorine and put it on the wing balance and measure its mass isn't it I take let's say 510 moles of chlorine measure the mass and divide by whatever number of atoms it could have I could never isolate only one atom of chlorine and even if I isolate I cannot directly you know put it in a weighing pan and measure it so that's how we measure it it is like you are putting let's say you know that you are putting 10 apples on a weighing pan weighing balance and then whatever mass comes out of it you're dividing by 10 like that is how people were measuring the mass of naturally existing elements and they found out that the mass of chlorine to the surprise was nowhere near to an integer it was 35.46 units okay this puzzled them now and anybody knows why it is like this anyone so it's because chlorine has many isotopes so definitely there should be this there should be this thing that chlorine exist in many forms in exist in multiple forms now does this prove the discovery of neutron so it doesn't as in as I tell me number of electrons in the chlorine atom for in all the forms has to be equal or not yes sir has to be equal the existence but it doesn't give you anything else like how do I not know that the new why are you speaking in between what I was saying was that does it give an indication that neutron exist there has to be something else definitely the all the chlorine forms have to have the same number of electron because the chemical properties exactly same okay item is completely neutral so number of protons should also be equal to number of electron so then why masses are different these multiple forms will have different masses are not yes okay they will have different masses so from where the different masses could come there has to be some neutral particle it cannot be charged because then the atom no longer can remain neutral okay so this gives an you can say an indication that something neutral exist okay but then discovery this is not the discovery this is like you can say an indication that inside the nucleus there has to be something else other than proton understood nothing nothing so then like all like elements which have isotope shouldn't like all of them have a non integer mass which is you will see how mathematically it comes out okay so it is not necessary that mathematically everything should fit like that so let's see for example chlorine how it is 35.46 let's see that first if you see naturally existing chlorine it exists in two forms form number one a pure form of that has atomic mass of 34.98 units this is near integer this is chlorine 35 okay naturally it is 75.4% okay then you will have chlorine 37 also which is 36.98 units and this exists 24.6% in nature okay so if you talk about the pure form of chlorine definitely it is near integer times okay but naturally existing chlorine mass how you find out with this data the chlorine mass will be what 34.98 into 75.4 plus 36.98 into 24.6 divided by 100 it's a weighted average it is like it's like you know it's like saying that okay five people have an age of 20 years 10 people have an age of 18 years so the average age will be what 5 into 20 plus 10 into 18 divided by 15 so same way okay 34.98 will be there 75.4% of time and this much mass 24.6% so that's why this is the average mass of the chlorine which comes out experimentally to be this tell me any doubts till now Paramp others okay so you can see this is a hint here that the calculations will be there in this chapter okay just like any other chapter in modern physics even here the calculations are there okay you as a student have to understand in physics two types of chapters are there one conceptually very involved questions will be tricky other one questions won't be tricky but calculations will be hard you have to be master of at least one type of chapter you can't leave both okay do this and if you master both nothing like it will score both ways so lithium exist in two form lithium 3 6 7.4% lithium exist in this form which has this mass okay another form of lithium is 7 lithium 3 92.5% of the time and unit is the mass unit is 7.016 00 units you have to tell me what will be the experimental mass when you measure the naturally existing lithium how much it will be don't use calculators but did I say you have used calculator okay so I can see many of you already answered everyone should participate your answer should be sign do you think your answer will be more than this can it happen is it possible it in a way taking the average isn't it okay so it will be 7.5 into 6.01512 it is at times becomes irritating to calculate such things that's how it is if you start liking the calculations nothing like it because those guys who are good with the numbers they are the ones who are highly paid okay this will be equal to 6.941 units okay got it all right so this is the this is the about the mass of the atom and which is also the mass of the nucleus as well because electrons mass we are ignoring okay so this gives a hint of some neutral particle inside the nucleus and this led to the discovery of the neutron in fact if you formally go with the process which has led to the discovery of the neutron is something like this right on discovery of neutron the best part was that hydrogen has three isotopes hydrogen deuterium and tritium okay and another good thing was that their mass ratios was found to be one is to two is to three okay so it was well known that hydrogen had one proton so deuterium must have one proton the definitely it will have plus one neutral particle it should have tritium should have one proton and two neutral particle so that sort of put a thought in everybody's mind that there has to be something which now they have to discover and find out okay so it was the Chadwick Chadwick who was you know bombarding the alpha particle on beryllium okay when he bombarded alpha particle in the beryllium beryllium okay he noticed noticed some strange radiations coming out these radiations were undeviated by magnetic and electric field okay this proves that they are neutral so everybody thought that it is photon because photon is also neutral okay so can be photon okay but then they have conservation of energy and momentum which in detail we are not discussing conservation of energy momentum and all those things when they did they identified that this particle which is coming out cannot be photon it need to have some mass and that sort of indicated that the waves that are coming out the waves that are coming out particle particle waves they're not em waves just like alpha particle beta particle like that okay and it is neutral so then they found out the mass is similar to mass of proton so definitely it is not because of the orbiting any particle it has to come from the nucleus only so this sort of you know led to the discovery of the neutrons okay this is how the discovery of neutron happens fine and it was established that mass of neutron was 1.00866 units in terms of a mu I'm writing and write it in terms of kgs also 1.67 into 10 is a power minus 27 kgs okay now this is all story which is practically it is useless just I told you so that you understand the full story but numerical wise it is not that useful okay so now neutron exists okay so there has to be you know and these are the fundamental particles so we need to assign some name to it because every like every physical quantity we assign name and for fundamental things we must have some symbol some name so that's a reason why everybody thought of coming out with some symbol which can be utilized so it was accepted that Z will be used to represent the atomic number okay definitely there would be some story why Z is used why not ABCT is used but I'm not getting into that so Z is the atomic number which is nothing but number of proton which tells you more or less about the chemical properties because chemical properties are driven by how electrons interact and number of electrons are equal to number of protons so definitely the chemical if you just look at the chemical property number of proton matters okay but when you talk about the nuclear property it is the number of electrons electron don't take part it is a proton and neutron who take part so then mass number becomes more important than atomic number but anyways so Z is the atomic number and is the neutron number number of neutron and a is the mass number I think all of this you have studied in chemistry you know better than me sometimes mass number this is Z plus N okay so mass number is basically a number okay it is not mass I'm getting it mass number has to be an integer it is some of the neutron and the proton okay and when you write the symbol for any atom we write it like this Z a the atomic number is written below like this and mass number on top like that for example for gold the atomic number is 79 and the mass number is 197 okay so once we are clear about these things that they are the fundamental particles and we see naturally existing elements so we tend to put some relation among them like if same same number of the protons are there but the neutrons are different we call them isotopes so like that you know it helps to categorize things in one place you know it helps us to study the isotopes together because there are many similarities that's the reason why separate names are given so isotope is the first one isotope implies same atomic number but different mass number isobar what is isobar anyone different atomic number same mass number same mass number different atomic number then you have isotone cabbie isotone same same neutron same same number of neutrons a minus Z okay so now we have slightly better understanding of nucleus first we discuss about its mass then rather for experiment only prove the existence of the protons now we know inside the nucleus apart from proton there are these neutrons that also exist now it's about the size we talked about the size we talked about the mass we talked about the particles inside it now let's talk about the size of the nucleus right down which we already know very very small isn't it we already know size of the nucleus is extremely small from the Rutherford experiment in fact Rutherford experiment gave us a rough indication about the size of the nucleus how does it give by if let's say you are putting an alpha particle of kinetic energy of 5.5 mev okay then you don't need to do you need you don't need to conduct the experiment also you can calculate it mathematically for alpha particle of this much mev distance of closest approach distance of closest approach is roughly 4 into 10 is power minus 14 meter closest approach from the center of the nucleus so what I can say about the radius of the nucleus will be less than this or more than this everyone less than right so of course the alpha particle is not touching the nucleus it comes very near and then goes back okay so this is how it is now there is a formula also in terms of the mass number so empirically it was found out that the radius of the nucleus can be written in terms of number of particles it has inside it okay because nucleus is so densely packed because you know see the radius of nucleus is of the order of 10 is power minus 14 let's say and the atomic size is how much of the order of anyone knows it then this minus 10 10 is a minus 10 meters okay so nucleus is at least nucleus is 10 so minus 15 so size of the atom is one lakh time more than the size of the nucleus so the nucleus is densely packed and it is so densely packed that if number of particle has to increase the size has to increase okay so it makes sense to have this type of empirical relation r is equal to r0 a to the power 1 by 3 is the mass number where the value of r0 is 1.2 into 10 is to power minus 15 meters now this is of course the radius of the gold nucleus we're talking about when we did the Rutherford gold foil experiment what is this radius this one are not over here whose radius it is formula take a look at the formula what is a hydrogen when r is equal to r0 when a is 1 so this is the nucleus radius of the hydrogen of hydrogen atom okay so this is how it is related now I want you to find out the density of the nucleus and our density of the nucleus for for an atom having mass number a yes this mass divided by volume density in kg per meter cube you have to find you have to tell me the value okay no one got it at we got something at wick that's not correct density has to be very large masses how much a divided is this correct volume is 4 by 3 pi r0 cube into a is this correct so we have to multiply by you in the numerator you so 1.67 into 10 is for minus 27 multiply with that a is gone so r0 is this substitute and tell me what is the answer why we multiply with you because the mass of the atom is hot in terms of kg if mass number is a yes nobody got it density of the nucleus matter 2.29 into 10 raise to power 17 I work close to that approximations but I got 2.4 okay now that you know so the density of the nucleus doesn't depend on mass number it is independent independent of which atom we are talking about any atom has the same density in the nucleus cutting so this density is extremely large okay this density is so large I mean it is difficult to realize it just by looking at the number so let's do one thing here assume you have a sphere of radius let's say 0.1 mm which is like the tip of a pin this much radius of sphere you have it is made up of the nuclear density material density of that is density of the nucleus so find out the mass of that sphere how much it will be okay it is 9.6 into 10 raise to power 5 kg all right you have to multiply density with 4 by 3 pi r cube like that and you will get 1 million kgs which is extremely large okay so you can understand the kind of density we are talking about inside the nucleus just because it is very very small the overall mass of the nucleus is lesser compared to what we see things around but if same nucleus density if I used to build a bigger object it would be tremendous the mass of it okay all right so this is about the mass of the nucleus and we realize that mass is very very densely packed because the density is so big all right so now let us proceed further these are the physical attributes okay now we'll be talking about something related to just give me a moment somebody's calling me multiple okay sorry about that right so I was talking about the physical attributes of the nucleus now we have studied about the mass of the nucleus size of the nucleus particles inside the nucleus we can get into something more meaningful which relates to the usage of how we can utilize something inside the nucleus so let's start that discussion with a very very important concept which is mass energy equivalence have you heard of mass energy equivalence anyone yes so till now everybody was talking about the conservation of energy and conservation of mass Einstein came up with a famous equation which relates mass energy and with disrupted everything Einstein told everyone that energy need not be conserved mass need not be conserved energy plus mass will be conserved as in mass can be converted into energy energy can be converted into mass okay both can be interchanged each other where C is the speed of light in air which is 3 into 10 raised to power 8 meters per second and you can see the amount of energy in joules you will get tremendous amount of energy can be generated if you convert let's say 1 kg of the mass into energy you'll get 3 into 10 is power 8 square joules of energy okay so mass has a very very concentrated form of energy so if we somehow utilize this okay to generate the energy it will be very useful to to mankind okay and that is this aspect only is utilized when we talk when we talk about the nuclear energy okay in fact soon you will understand something more interesting discuss that but first what you do is that you find out how much one gram of one gram of substance if you somehow convert it into energy completely how many joules of energy will be generated find out okay others quickly calculate and these are the simple calculations right bigger calculation are waiting for you hold on m into c square 10 is a minus 3 kgs into 3 into 10 raised to power 8 whole square this is 9 into 10 raised to power 13 joules okay do you know the Bangalore city on an average consume 6000 megawatt power so in in one day Bangalore consumes how much energy Bangalore consumes around 6000 megawatt is 6 into 10 is for 9 into 24 hours 60 minutes 60 seconds okay this is roughly 7.7 into 10 is a power 14 joules so just by converting one gram of mass into energy one gram of substance can run the Bangalore for almost 24 hours entire Bangalore if you somehow convert one gram of mass into energy that much how concentrated energy the mass has okay and now coming to the most important aspect of the energy mass equivalence is about exothermic reactions you have heard about exothermic reactions in chemistry yes exothermic reactions so exothermic reaction let's say x plus y are the two reactants which will give you a product z plus heat okay heat is most basic form of energy heat now from where it is coming from these two have interacted and heat is generated why chemistry you've learned right why heat is generated what is bond what is bond chemical bond like between two what it is so the electrons go into like a more stable state because they like they get shared between the atoms in a way you're talking about the energy what is this energy required to keep them okay yes so bonds are basically nothing but electrostatic force plain and simple right forces are stronger leads to lesser potential energy forces are weaker leads to higher potential energy so basically potential energy of z is lesser than the potential energy of x plus potential energy of y that is why extra energy is released now that is one way of understanding it okay that is one way of understanding it potential energy is you can say it's a hypothetical concept we have derived potential energy to be negative of the work done to bring something from one place to other okay if you try to understand in a more basic manner as in on the basic level what is happening it's like you know I'm arguing with you for example why are you able to sit in a chair you'll say because of the chair chair is stronger somebody will say no it is because the plastic or the wood in the chair is strong enough to hold you somebody will say no it is the atoms inside the chair which are tightly held on each other that is the reason why chair is not breaking when you sit on it somebody will say okay no it is about the vendor all four some way it is never ending you can keep on discuss and somebody will start claiming that when you sit on a chair you never even touch the chair it is electrostatic force or repulsion between you and chair so same kind of thing can have multiple explanation to it okay and the most basic explanation without any bias in this exothermic reaction is this that by some mass some mass of reactant got converted into energy this is what at the very very core level is happening so if mass of X is MX mass of Y is M Y this mass is slightly more than mass of Z so this difference in mass is getting converted into energy and this is what the heat energy that is coming out but in chemistry when chemical reaction happens the heat energy that comes out is very very small in chemical reaction so mass difference is not seen it is not substantial in fact you will not be able to measure any mass differences so there has to be some other way of determining the amount of energy that will be released so so you can introduce concept of bonds concept of hybridization and all those things to understand about it okay but then this is what is happening in fact in chemistry there is conservation of mass also there is a law Dalton's law I guess okay but then in reality some mass is getting converted into heat and same thing when happens in nuclear reaction right now the electrons of X are reacting with electrons of Y Z is getting formed when nucleus react nucleus of X when it reacts with nucleus of Y and if it is an exothermic reaction the amount of energy release will be so high it is almost 1 billion times more than the energy release in a typical chemical reaction so if energy release is so high you cannot ignore the mass difference between the nucleus of Z and nucleus of X and Y there is substantial mass difference so why will I introduce unnecessary concept of you can say the bonds you know if I have to explain the same thing in terms of bonds I can as well introduce something like nuclear bonds inside the nucleus one proton and other proton will have a nuclear bond because of the nuclear forces there will be hybridization inside it okay but I don't I don't need it because I could directly visualize the mass difference so amount of energy that will be released I can directly get it by finding the difference in the masses and just multiplying with C square that is the power of the Einstein's equation it caters to very very fundamental aspects of everything okay anyone has any doubt of course there is a assumption here product is more stable when whenever exothermic reaction happens product is more stable you have released some amount of energy so lesser energy is remaining with Z so how much energy is left with Z how do you calculate how much energy is there with Z whatever is a mass of Z into C square that is the energy with Z that is a maximum amount of energy it can give now it can give the energy in the form of making bonds or whatever you may think of it can have chemical reaction nuclear reaction whatever it does it cannot give more energy than mass of itself into C square okay anyone has any doubts anyone so but like further on did they like sort of ensure that conservation of mass was observed absorbed as in observed like like over here we're not exactly obeying conservation of mass right mass conservation is a hypothetical it doesn't exist okay if if very less amount of mass is getting converted into energy you can use that approximate just like the lens formula the mirror formula was an approximate formula right young's double-seed experiment is an approximate formula and in chemistry you might have learned about the binding energy when for example hydrogen plus hydrogen when it creates hydrogen bond energy is released okay so this energy you can say bond energy yes or no bond energy or you can say binding energy between two hydrogen yes or no okay so similar kind of concept is there with respect to the nucleus also okay we are talking about here you know when when you see the nucleus I mean I don't know how to put it you know very clear manner but when for example you're dealing with the previous reaction what was it hydrogen plus hydrogen gives H2 okay you are treating as if the hydrogen is the fundamental particle here you are not worried about inside the hydrogen what it is one hydrogen atom reacts with another hydrogen atom creates hydrogen molecule and you don't have to worry about the nucleus at all but when we talk about the nucleus we have to worry about what is inside the nucleus there might be multiple protons multiple neutrons we have to see the interaction among them okay so this is the fact here that inside every nucleus you can say inside the every nucleus you can say that you can say there are some bonds getting formed proton proton proton and neutron two neutrons are getting formed getting forming a bond so I can talk about a nuclear binding energy here okay you'll be more clear about it when you listen to it with more and a nuclear binding energy alright so for example two protons and two neutrons okay when it creates a helium nucleus helium has two protons and two neutrons right yes here are helium nucleus okay two protons and two neutrons inside it is like reaction between two protons and two neutrons and by the way does this reaction exist does this reaction happens in the nature this reaction doesn't happen right but hypothetically if it exists then whatever energy is released is the bond energy similarly here if this reaction exists if this reaction exists whatever energy is released you can say this energy is the nuclear binding energy or you can say the energy that this nucleus releases when it gets formed all of you able to understand multiple bonds are getting formed proton proton proton neutron two neutrons when they are getting formed energy is released everyone type it have you understood this concept that two protons and two neutrons in isolation they are lesser stable but when they form a nucleus when two protons and two neutrons create a nucleus they become more stable and if they become more stable they will release energy okay so this is the this energy that released is the binding energy of the nucleus first you write down energy released in the formation formation of nucleus is its binding energy okay now why it is called binding energy by which one is more stable nucleus or two protons and two neutrons in isolation are they more stable of course nucleus is more stable right and if nucleus is more stable nucleus won't break just like that because by energy of the nucleus is lesser so how much energy is required by the nucleus to break into its constituents what do you think same energy that was released same energy that was released it is a very similar concept the way it was there in chemistry the energy released here is the same energy that is required to break the hydrogen bond okay same thing here you will require this much energy to break the nucleus that is why it is called binding energy okay because same energy is needed to break the nucleus okay now tell me which whose mass is more two times mass of proton plus two times mass of neutron this mass should be more or mass of the helium nucleus which one should be more whose mass will be more this mass of that mass everyone reactants reactants why because only energy is released small negligible mass gets converted to some mass of these two reactants got converted to energy even though inside the nucleus you have still two protons and two neutrons but the mass of the nucleus is lesser than these two which is strange okay this energy is released because mass is getting converted into energy now when you supply the energy to break the nucleus then energy will be converted into mass and then two protons and two neutrons will come out from the nucleus okay now if I if I tell you the mass number of an atom is a and atomic number is z atomic number is z can you find out what will be the binding energy of this nucleus nevan first write down the reaction how does the reaction look like so we need to know the mass of the actual thing also read that's also given mass of the actual thing yes sorry about it mass of the nucleus is capital M anyone others what are you doing okay reaction is what how many protons are required z proton z into p plus how many neutrons a minus z a minus z neutrons they should react to create a nucleus plus whatever binding energy is released so how much the binding energy will be released binding energy released will be equal to z into mass of proton plus a minus z into mass of neutron minus the mass of the atom that into c square isn't it yes yes so just the reactants mass minus the product mass into c square that is how the binding energy is on in fact this thing m into c square this is valid not just only to find out the binding energy but it can be it can be utilized for any reaction okay this is the most basic way of finding how much energy will be released any reaction okay so at least in nuclear reaction you should feel free to use this chemistry will be dealt differently so binding energy can be written as delta m into c square okay delta m is also referred as mass defect referred as mass defect why does referred as mass defect because you are expecting the mass should be same as mass of the neutron plus proton but it is not it is lesser than that fine so we know that mass defect usually it will not be in of the order of kgs or grams like that usually it will be very less mass defect okay it will be in terms of amu like 5 amu 0.2 amu like that very very less or just you so it makes sense to find out for one unit of mass defect how much energy is released if I know one unit of mass effect how much energy is released for x unit of mass effect I just multiply by x okay so find out for one unit of delta mass energy released is how much and you should find in terms of electron volts not in joules anyone got the answer okay no one but you've got something who Vikas Richard okay alright looks like many of you tried energy is basically mass defect delta m into c square so mass defect one unit is 1.67 10 raise to power minus 27 that is one unit into c square that is 3 into 10 raise to power 8 is square alright and then you to find it in electron volt this you have to divide by the charge of an electron to get it in electron volts so you will get 9.315 into 10 raise to power 8 electron volt okay and you can get it like you can write like this 931.5 mega electron volt this is the first time you will get a glimpse of the kind of energy we are talking about here when we discussed about the electron our energy never went beyond few electron volt it was like maximum we have seen 13.13 what was it 13.6 13.6 z square energy okay so how much it'll go max to max it'll go for 100 electron volt okay a 200 electron volt but here we are talking about billion electron volt okay which is extremely large so we are dealing with something which can give rise to high amount of energy and energy is most important thing in day to day life we are converting all sorts of energy into different different types like electricity is converted to light energy and electricity generated by converting mechanical energy of the water into the kinetic energy of the turbine then it converts to electrical energy which comes to us then again it is used by various appliances so it is all about energy you run your vehicle by converting chemical energy into mechanical energy so here is the kind of energy which is very very concentrated form of energy okay so that is why the study of nucleus is all the way more important because it gives a glimpse of something very important for mankind wearing you can generate the energy very easily but the same time even the bomb is energy only so if it is controlled you will call it nuclear reactor if nuclear reaction is uncontrolled you call it nuclear bomb okay so the mechanism is same alright so can you tell me if if binding energy is higher binding energy we can calculate depending on the mass defect okay if binding energy is higher can I say nucleus is more stable nucleus is more stable can I say that yes others see if binding energy is more it means more energy is released so the remaining thing the product will have lesser energy so does it mean that the nucleus is more more energy is released more stable it is many of you will say yes in fact almost everyone okay but that is not true because when we talked about the let's say bond in chemistry when we discuss about that the product being more stable we discuss about let's say a bond only when that bond is broken even you know that carbon carbon plus carbon if it creates single bond energy released is lesser carbon plus carbon if it creates double bond energy is released slightly more triple bond it is even more so you will say that this is more stable sorry triple bond is most stable double bond is slightly lesser stable and then single bond is least stable between carbon and it is only about bond between the two carbon okay so you can easily talk about the stability of it but when we discuss about the nucleus okay so inside the nucleus you'll have multiple protons and neutrons okay hypothetically let's say they are interacting and creating bond among each other let's say you have my no sorry neutron protons like that okay so you can say that there is this kind of interaction this nitrogen at the edge is interacting with these three the proton however at the center is interacting with six nucleons nucleons basically is nucleons are referred as proton plus neutron because they are inside the nucleus we call it nucleons just a nickname so you'll realize here that this proton this one sorry not proton neutron this is lesser stable less stable because it is not interacting with majority of them whereas the proton is more stable this one is more stable okay so binding tells you binding energy gives you an indication of overall stability overall stability of the nucleus suppose you have to break the entire nucleus into its constituent entire nucleus okay I want every proton every neutron to be separate from each other then you can say okay fine if you mean that when you talk about the stability of nucleus then yes you are correct but when I talk about the stability of the nucleus my my this thing is that stability write down stability of nucleus implies all neutron and protons are intact even if even if one neutron or one proton is gone I would consider nucleus to be broken nucleus has lost its integrity okay this is the way I want to compare the stability because you know nitrogen can become phosphorus by just accepting or releasing one proton so it is very easy to lose the identity itself once nitrogen become phosphorus or phosphorus becomes oxygen by putting protons here and there then I can't say it is the same nitrogen nucleus once it become phosphorus isn't it so that's why when I talk about the stability of the nucleus I don't mean that I am trying to break the entire nucleus I am trying to just know of the nucleons proton or neutron away from it so overall stability has no meaning here I have to see on an average how stable every neutron or every proton is I should not compare overall stability I should compare on an average how much stable every particle inside the nucleus is everybody understood this view whatever I just said have you understood yes so but when we are comparing the stability between the two nucleus when we compare stability into nucleus we need to compare binding energy divided by mass number that is binding energy per nucleon how much every particle inside the nucleus on an average is stable that is what we need to compare okay and we write it as this ebn means binding energy per nucleon eb means binding energy okay but doesn't this have the same problem that no no no it doesn't have the same problem it is a better indicator because if number of particles are more if you divide with that number even though binding energy is higher it will come out to be lesser stability you are assuming binding energy will increase proportionately to number of particles isn't it no sir like to compare the stability shouldn't we take the lowest like take the thing which can get removed the most easily and I know I know what you're saying but that is not possible to find out so the next best thing is on an average that's what I keep repeating that I am finding the average stability of every nucleon understand yes that is I am repeating that and do you think that neutron at the edge remain there only it keeps on moving in fact I don't know whether you may not know anyway if you study quantum physics little bit neutron and proton they are having dynamic equilibrium neutron become proton proton will become neutron and that's how they are fluctuating it's very very messy once you get into it so you know on an average when we compare everything behaves like that only because the neutron which is at the edge right now immediately you will see that it is at the center so don't feel that it is something static we are comparing on the y-axis write down binding energy per nucleon it is and on the x-axis you have mass number so you can see that in this chapter mass number is more important than atomic number okay nobody cares about what electron is doing because the effect of the electron is negligible negligible guy it is not even noticed when the nucleus becomes active so it makes sense to plot this graph and see the stability order or binding energy per nucleon for the elements when we compare it and the graph looks something like this everyone plot this graph something like that so which element how will you use this graph to find out the most stable nucleus or do you think so it's that maxima that last sharp edge everyone agree to it yes this maxima suppose this point this represents the most stable nucleus okay and it turns out it turns out that the mass number of this is 56 do you know whose mass number is 56 iron iron so iron nucleus is most stable nucleus okay that is what out of all elements it is observed fine but then iron reacts with water and it loses its integrity and how can it be more stable so that's just a chemical reaction so over there the nucleus is not like change nucleus doesn't care even chemical reaction happens nucleus is not doing anything here we are talking about the stability of the nucleus okay the physical property of course will be driven by the electron only because physically the most amount of the space is occupied by the electron so it will drive the physical property okay physical and chemical property also okay anyways so this here which element will be here do you think the first one hydrogen hydrogen and over here the very famous you might have heard of uranium 238 uranium okay so now what every nucleus will try to do what it will try to do natural tendency will try and go towards iron try and go towards the iron okay so the lighter nucleus will try to go in this direction the heavier ones try to go there okay so what is happening is by the way how the lighter will become towards how the lighter one will go towards the iron by combining okay when they combine this process called fission when fission is happening not fission sorry sorry fusion when the nucleus are getting fused inside each other the mass number increases number of protons neutrons are becoming more so it is going towards the iron nobody cares here again about the electron once protons are increasing the it will accept the electrons from other places here it has to be fission the nucleus has to break okay nucleus has to break and you can see that if let's say uranium 238 reaches the iron this much energy per nucleus it will release this much energy if the uranium reaches here okay and it is found out that the binding energy per nucleon for the iron binding energy per nucleon for iron is 8.75 mev okay and this is the maxima okay every element if you consider if you compare every elements binding energy irons is the highest so if you're finding binding energy more than 878.75 you are wrong okay this is the maximum possible binding energy anyone has any doubt in this diagram so why does this happen like why why why does it have such a shape huh that will discuss that we are going to discuss but till now whatever we have discussed any doubt see I will not be able to explain this exact thing okay this is you can say sort of noise but we will definitely talk about the pattern of it why it is like this the pattern so let's first discuss about the observation of the graph after we clearly write down what is the observation from the graph then we will discuss the conclusion of the graph as in in what we can conclude based on whatever we have observed okay write down observation this chapter is also becoming theoretical but soon it will become mathematical okay just hold on just maybe half an hour and then the chapter become completely mathematical hmm so binding energy per nucleon is practically constant for the mass number between 30 and 170 and maximum binding energy is 8.75 mev this is the max so you can see here like I'm talking about this zone it is more or less constant here okay there's a plateau there then it is observed that binding energy per nucleon is lower lower for both mass number less than 30 or mass number less sorry greater than 170 okay so these are the observations so based on these observation we need to come out with some explanation what is exactly happening okay binding energy binding energy high means stability is more okay if stability is more what I can say about the forces and bonds attractive forces are hmm if it is more stable attractive forces what I can say you're asking me back stronger everybody understand it something is more stable then it is having a more the attractive forces are stronger okay for example neutron proton proton and neutron if they have to remain inside the nucleus there has to be attractive forces among them otherwise how can they be so close to each other the stability will come only when they're attracting each other are you getting it so more is the attraction among them more stable it is so energy and force concept you can correlate like that okay keeping that in mind can you guess what is happening here so could it be that the more number of proton neutrons here more attraction will happen level like there's so much that repulsion starts happening no no no say it again the last sentence again so after like 170 there are so many neutrons and protons that some repulsion also happens that's why again there's no reason why repulsion will suddenly start but then the first statement was correct if number of nucleons are lesser then the amount of attractive forces will be lesser because it needs numbers right if let's say five neutrons are near to a proton then it can have five kinds of attractions if only one neutron is near to proton only one bond will be getting formed okay what is happening when atomic number goes beyond 170 why it is lesser stable okay clearly this thing everybody agrees right this thing everybody agrees that that an attractive very strong force exist inside nucleus but it has to overcome the coulomb force of repulsion between the two protons isn't it it has to overcome because two protons are having same charges so they will repel each other so this attractive force should be so strong that it should overcome all that okay this has to be present now what happens is because of this attractive forces only because of the nuclear force you can call it nuclear force okay because of this nuclear force only everything is happening here when like what Dorchir said when atomic number is less than 30 number of nucleons number of nucleons are lesser and hence attractive forces are not many you can say bonds okay what is the chemical bond new the electrostatic force only you can say here nuclear bond a nuclear force creates bond okay and between 30 and 170 what happens is it becomes saturated okay you'll have we have enough number of nucleons for every neutron and proton it's like at max if close packing happens at max let's say one proton can be surrounded by six nucleons let's say hypothetically then no matter how many you can put it further it can surround only six only okay so it saturates after 30 it kind of saturates and number of the attractive bonds remains that many only so that's why binding energy per nucleon remains more or less same now the fourth point is very critical wherein when the mass number goes 170 okay then then the attractive force clearly attractive force magnitude goes down goes down see number of nucleons should be saturated if it is saturated here it should get saturated there also but over here the attractive forces magnitude goes down what is the reason it was identified that the size of nucleus grows this leads to lesser amount of attractive forces and this also proves that nuclear force is a short range force so immediately after beyond a distance nuclear force magnitude will go down suddenly okay so this is what should be happening here which everybody has accepted and that is the nature of the nuclear force also it tells us the nature of nuclear force that if the size goes beyond a particular level then the nuclear force magnitude should go down okay okay anyone has any doubt till now sir can you go back to the previous slide why I have to write the last question I'll switch on the fan think of any doubt yes sir no one has any doubt so I have a question sir we said that irons binding energy was 8.75 and that's maximum right so but then like a few minutes back we said the 931.5 is for one u so that means the mass defect should always be less than that 8 by 931 then yeah if you're talking about the formation of nucleus but then there can be other nuclear reactions where in energy release is lot higher you're talking about only the formation of the nucleus isn't it yes sir the reaction in which the nucleus gets formed if that is the only reaction then yes that's correct okay sir if it is here is saying even if a is greater than 170 it will have enough number it will still be able to attract nearby nucleons like it did yes here it can do that but what happens to the nucleons which are at the edge of the sphere okay they will become more distant more and more they become distant from the others and also the nuclear force is kind of compensating for the coulomb or the charge repulsion which is happening between two protons so if the nuclear force becomes negligible between let's say one edge of the proton and the other edges proton then these protons rather than attracting will start rippling each other so it is a notorious kind of force actually which should compensate for the coulomb's repulsion between two protons but as soon as its value goes down little bit coulomb force of repulsion will take over okay and that creates the instability and of course whatever i'm telling you is not the full detail people spend their entire lifetime studying about the nuclear force okay so i'm just telling you so that you get a basic idea of it okay so i hope you understand right so it is always a fine balance between the coulomb repulsion and this strong force the strong force will remain strong till the distance between two neutrons and two protons very very less the moment it becomes slightly larger coulomb force can take over because coulomb forces large range it'll not become suddenly zero so since we have introduced something very important here let us study it in a greater detail greater detail as in still we'll be talking about it theoretically only the numericals related to nuclear forces are not there in our curriculum it is not there even in your engineering curriculum it'll be there if you take let's say bsc msc physics like that if you take then they will talk about it okay so a graph is plotted between the two nucleons you can say between the two neutrons you have taken two neutrons and you've plotted a graph okay and what is observed is this on the y-axis you have potential energy in mega electron volt and on the x-axis you have distance between the two neutrons okay it is observed a graph like this is seen so you can say this line represents zero potential energy when the distance between two neutrons is extremely large the potential energy becomes zero or you can say between the two protons also same thing r is a distance between them in terms of femtometer if it is the order of tennis for minus 15 okay so we are plotting the potential energy between them this is minus 100 you can say this is plus 100 this is zero okay this distance is three femtometer this is around one and this is two okay so this is an experimental finding here you can see that the potential energy between the two neutrons becomes suddenly zero if the distance between them is of the order of three femtometer isn't it so we also know that the force is equal to minus of daba u by daba r so in a way the force is force is basically the slope of potential energy versus distance okay of course you can't go beyond one femtometer because it's like you're physically touching the two neutrons okay that of course there will be normal reactions and other forces will then come under play that will never happen naturally so we'll be talking about the situations of distance between the two neutrons where beyond one femtometer so we can see beyond one femtometer there is an increase in the potential energy if I go from one to two potentiality increases and that will create a backward push so that I go back to the lesser potential energy level and what is the amount of force that will be generated slope of the curve here d by dr will be the force which will push me back to this position okay so I'll not be able to go beyond one or I you know there is a very strong force which is pushing me back towards this distance I'm not able to increase the distance between the two neutrons okay but suppose the distance between the two neutrons become three then what is the slope here everyone what is the slope between u and r zero zero slope is zero so force will also be zero okay so nuclear force suddenly becomes zero but before it becomes zero between one and two or two point five femtometer the slope is very large you may tend to think that slope is not that much over here we are talking about distance in femtometers okay so it is a large distance sorry this is a small distance fine so if I if I look at this graph what all things I can conclude is this nuclear force first of all same thing we are repeating nuclear force is much more stronger than coulomb force second like what again this although we have discussed nuclear force falls rapidly to zero if distance goes beyond few femtometers and then the nuclear force between neutron neutron proton proton and neutron proton is approximately same it does not depend on the charge it is an attractive force fourth one which is a good news for you that nuclear force does not have simplistic expression for the force like the gravitational law universal gravitational law and the coulomb law you don't have the simple expression for it and probably that is the reason why it is not in the syllabus also but theoretically this much is there in our curriculum so there could be some theoretical questions on it based on whatever we have discussed anyone has any doubt so can you write the expression just for fun I don't remember actually let me just see just for fun huh there was fun we don't have time to finish the curriculum itself and anyone else has any other doubt so before one of femtometer will force be repulsive see like I said this is the potential energy between two neutrons so it it can lead to repulsion because of the physical you know there will be touch between them right contact yes any doubt see I'm not going to write the expression here even I'm not able to find it itself okay if somebody finds it can post it on the group later on after the class right now though I'm not able to find it and yes that point somebody said the least potential energy is the you can say it is the equilibrium position okay it is kind of equilibrium position and it denotes the least potential energy here so if you little bit push this way there might be oscillation about this equilibrium position okay so now coming back to something related to the binding energy here I will just write down a reaction here between two nucleus and you tell me how much energy will be released one nucleus then the other nucleus creates this one and let's say this is c okay atomic number is a1 atomic number is a2 atomic number for c is a3 okay binding energy per nucleon for a is b1 for b it is b2 for c it is b3 you need to tell me how much energy will be released so I was seeing I found some of nuclear force that's all right I don't care about it okay leave it we are not going to discuss nonsense in the class completely out of your curriculum answer it here anyone got it okay you might have learned about the enthalpy of formation if you know enthalpy of formation of reactant enthalpy enthalpy formation of reactant and enthalpy of formation of the product how you get the heat released in that reaction do you remember products minus reactant product enthalpy minus reactant enthalpy same thing here binding energy per nucleon is b3 so total binding energy is b3 into a3 this is the this is you can say enthalpy of formation of the nucleus c that minus b1 a1 minus b2 a2 okay this is the energy released no doubts so these kind of questions they do exist and it looks like a chemistry question but it is asked in physics sometimes okay let's take a question before the break and then we can take a break there is a coin whose mass is 3 gram okay you need to find out energy that is required energy required to separate all neutrons and protons from each other okay you can assume that the coin is made of copper 6329 the atomic mass unit is 62.92 960 units and these things are given mass of hydrogen atom can I say mass of hydrogen atom is mass of proton everyone yes is this and mass of the neutron is 1.008665 units find out will there be a small difference proton and hydrogen mass yes here that is fine we are ignoring the electrons mass 10,000 times smaller than the mass of everyone I'm sir I did I will criticize not dead today sorry sorry I meant to the bathroom so okay so how will you do this everyone should I find out the binding energy of one copper nucleus and then multiply with number of copper nucleus will that work what do you think yes it should work so binding energy of one copper nucleus and n these two things I have to find out the binding energy of one copper nucleus how will you get it 29 protons so 29 into 1.007825 plus number of neutrons how many 63 minus 29 into 1.008665 minus 62.9296 yeah this is the mass defect that into what 931.5 Mev this is the binding energy everybody agree to this yes sir this is how much mass defect is how much 0.591935 you as far as I know so this much Mev so this is the binding energy of let's say one nuclear sorry one nucleus I'll just write it as 0.59 into 931.5 approximate answers are fine no problem with it but at least your first two digits should be proper so number of nucleus how many number of nucleus will be equal to number of atom every atom has a nucleus just like every galaxy has one a massive black hole at the center so 6 divide 3 divided by 62.92 this is the number of moles isn't it that into Avogadro number 6.023 into 10 raise to power 23 these many numbers that you have to multiply with this to find out the amount of energy required in terms of electron volt it is 1.584 into 10 raise to power 25 Mev okay and in terms of joules it is 2.5 into 10 raise to power 12 joules so you can see again how concentrated the energy is just one copper coin can give you so much energy all of it done anyone has any doubt done yes or no is it clear yes there's you'll get a break if you say that yes yes so but Mehul you already taken a break you went midway for a break right Mehul like I think he has again taken a break okay we will meet after 15 minutes come in time okay now 15 minutes 628 right okay come on time chapter is till now very theoretical after the break you'll see the mathematical part of it