 Right down next topic size of the nucleus see when it was discovered that there is something like nucleus that exists in an atom which is extremely small and almost entire mass of the atom is residing inside the nucleus itself then you know the curiosity was there to find out the dimensions of the nucleus and try to understand the physical aspects of the nucleus so right now we are only talking about the physical aspects of the nucleus okay once we have an understanding of the physical property of the physical aspect of nucleus we will also talk about the the reaction part of it how nucleus takes part in reaction so that will be coming under the nuclear reactions part of it but right now let us first let us first discuss about the size of the nucleus okay so when Rutherford conducted this experiment you know Rutherford and his you know students Geiger and Martson they have conducted this experiment so what they have done is they have experimentally found out that the distance of closest approach for 5.5 mega electron volt alpha particle is about 4 into 10 ratio power minus 14 meters okay this was a distance of closest approach assuming that the only force that is there is electrostatic in nature are you guys understanding what I am talking about last class we have found out distance of closest approach in the Rutherford experiment is it yes or no yes so this is what is found out of course you cannot directly view at the nucleus and try to measure the size of the nucleus directly so you have to find the size of the nucleus by doing some indirect way of the measurement so this is one of the way in which you fire the alpha particle you know that whatever its kinetic energy is and try to see what is the distance of the closest approach okay so that will give you a rough indication of what is the size of the nucleus so if you increase the kinetic energy beyond 5.5 mega electron volt what is observed is something which cannot be explained just by assuming you know electrostatic forces alone so there will be something called nuclear forces also that will come in the picture all right so that will also start influencing the behavior of alpha particle when it get reflected off from the nucleus okay so several experiments were conducted and empirically it was found out that the radius of the nucleus can be written as r is equal to r naught a to the power 1 by 3 okay where a is the atomic right down a is the atomic mass and r naught is given as 1.2 into 10 ratio power minus 15 meters okay now r naught is the radius of which nucleus whose atomic mass is 1 so r naught is the radius of the nucleus of hydrogen atom fine so the you can see that the radius of the nucleus is of the order of 10 is power minus 15 whereas the radius of atom is of the order of 10 is power minus 12 so that is why we can say that radius of nucleus is thousand times less in size compared to the size of the atom okay so this is what the relation is with respect to radius of any nucleus of atomic number a now can you find out can you find out the density of the nucleus okay find out density of the nucleus of an atom whose atomic number right down whose atomic sorry atomic mass number is a okay do you know what is atom mass number anyone what is mass number number of neutrons plus protons okay and we know that one proton mass of that is close to one units and one neutrons mass is also close to one unit so the mass of the entire nucleus is like you know mass number multiplied by one units so like that you can assume roughly so using that can you find out the density of the nucleus for atomic number a and also treat the nucleus as a sphere yeah you need to get exact value just give me one minute you guys this time all right did you get the answer to make sure you are using SI units okay so density is nothing but mass divided by volume only so how will you calculate the mass will get mass as the mass number multiplied by the mass of one units yes or no which is 1.67 into 10 raised to power minus 27 this is the mass of a nucleus mass number multiplied by mass of one unit divided by volume which is nothing but 4 by 3 pi r cube what is r cube it will be from here r naught cube into a isn't it so a get cancelled off so something amazing has happened here is that the density doesn't depend on the mass number so density of the nucleus is independent of what mass number it is so it doesn't depend what atom you are talking about the density of the nucleus is fixed this will be equal to none of you have simplified it 0.14 into r naught cube so that is 1.2 cube into 10 raised to power yes you are close the actual answer is this 2.29 into 10 raised to power 17 kg per meter cube it's a huge density okay it's tremendous amount of tremendous value it is now in order to just understand how big this density of the nucleus is can you find density of this dot let's say the radius of this dot is 0.01 mm okay it's very very small can you find out quickly what will the mass of this dot as you need to be a sphere of radius 0.01 mm just get a rough number quickly volume into density are you guys not able to calculate approximately 900 kgs so can you get a feel of it now how large this density is it's tremendous value okay so just because the size of nucleus is so small even though the density of nucleus is so high the mass of the nucleus comes out to be very less otherwise it has tremendous density okay so size of the nucleus is so small that you know if you can just expand the size of the atom to the size of the classroom which you have in your NPSS school the size of the nucleus proportionately will become size of the you know one pin tip a pin tip it will be the size of the nucleus will become so it's very very small so this is about the size of the nucleus now we have discussed some of the physical aspects of the nucleus now we are getting into the the reaction part or some let us say the the properties which relates to energy part of the nucleus okay so the first concept with respect to that is mass energy equivalence okay now what is observed is whenever you have a nucleus sorry I'm talking about just nucleus okay whenever you have nucleus suppose it has four protons and four neutrons okay if you find out the mass of this nucleus so let us say this is mass of the nucleus and you find out the mass of proton separately four times mass of a proton and four times the mass of neutron okay suppose this sum is m not n okay it is always found out that the mass of the proton and the mass of neutron together okay their total mass is greater than the mass of the nucleus where once they are inside the nucleus somehow the mass of this total thing is decreasing okay so there is something weird going on here all right in fact if you just take one proton okay a single proton is unstable a single proton is unstable it cannot stay like this and single neutron is also unstable what the single neutron will do it will convert into proton and it will give one electron with you know neutrino or anti-neutrino with it so it just decay down these particles are not stable but then amazingly when they go inside the nucleus they become stable okay so there is something special that is happening inside the nucleus that is making it more stable all right I think in chemistry you might have learned many things about no forming bonds so when two nucleus when two atoms they come close to each other the electron from one atom get attracted towards the nucleus of the other atom so some sort of bonding happens and we say that now there is a chemical bond between the two atoms okay and when the bond is more stable some energy is released isn't it like two atoms when the react and the product is more stable than reactants energy will be released okay similarly here also when the proton and neutron when they create a nucleus which is more stable some sort of energy should be released okay now when a bond gets formed we say that it is bond energy okay we say that it is enthalpy of the bond okay and when nucleus gets formed the energy that get released is called binding energy the energy because of which the proton and neutron they are bounded inside the nucleus okay so you can say that some sort of nuclear bonding is happening between proton-proton neutron-neutron or neutron-proton okay but then we just like in chemistry we went into much greater detail when we talk about the chemical bonds right types of bonds are there what are the hybridization and all that but when we talk about the nuclear inside the nucleus we are not getting into too much of detail as in the hybridization what kind of bond they have and things like that we'll keep it very very simple at a high level that when a nucleus gets formed there is some sort of attraction let's say nuclear force is there that is making sure that when they are together it is more stable okay so keeping that in mind this mass energy equivalence is conceptualized okay so what happens is when these protons and neutrons when they come close to each other okay when protons and neutrons they come close to each other they form the nucleus let us say four protons and four neutrons okay they come close to each other and they form a nucleus which has four protons and four neutrons okay part of the mass gets converted into energy that is why the energy of this sorry but that is why the mass of this nucleus is less than the collective mass of these constituents are you getting it now why it is just here only why not in chemistry also some part of the mass gets converted into energy in every exothermic reaction it happens there also there also whenever exothermic reaction happens part of the mass only gets converted into energy okay although you can look at it in a different way also you can say that you know the products are more stable or the stronger bonds are getting formed but end of the day bonds are nothing but electrostatic force of attraction okay so the basic thing is that whenever some sort of you know reaction happens where energy gets released part of the mass gets converted into energy into energy energy cannot be created just like anything I mean it can't be created out of nothing okay so something has to get converted so that is what is happening here mass is getting converted into energy okay and the famous Einstein relation which is there which creates the equivalence between mass and the energy so if mass m is converted into energy e then e will be equal to m into speed of light square okay so remember this this is the mass energy equivalence okay now when I say that this nucleus let us say has mass m n and these four proton and fro neutron have mass of collectively mass m and not whose mass will be more m and not or m and not right so the difference in mass is called a mass defect okay this is called mass defect we can also call it as delta m so this is mass defect more the mass defect more is the energy that get released and more is the mass defect more stable the product is because more the energy released it means that the products are more stable are you getting it so it is directly proportional to how much mass defect the reaction has so greater mass defect automatically means that products are more stable okay so although this reaction doesn't happen in nature therefore proton comes and reacts with for neutron and nucleus gets formed but we can imagine such reaction like in chemistry also we imagine you know different kinds of reaction like bond energy whenever we are trying to find we just imagine a reaction and you know like that we deal with the enthalpies of the reactants and product similarly here also we can imagine such kind of reaction and come out with how much energy will get released given what is the mass defect