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Binding energy graph

Let's explore the graph of binding energy per nucleon vs Mass number, and make predictions of the nature of nuclear force, and nuclear reactions (fission & fusion). Created by Mahesh Shenoy.

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Video transcript

let's explore binding energy graph and use that to understand nuclei and nuclear forces a little better but before we start a quick recap what's binding energy well binding energy can be thought of as the energy needed to break the nucleus apart break the nucleus for example if you take oxygen 16 16 is the mass number meaning total number of protons and neutrons inside of it then its binding energy happens to be if i just looked it up happens to be close to 128 mega electron volt electron volt is a very tiny unit of energy and mega just means 10 to the power 6. so this is the binding energy and what does that mean it means if i were to separate all those 16 protons and neutrons apart i would have to supply 128 mega electron volts of energy this much energy to break this nucleus another example if i were to take say uranium-235 a very famous isotope used in bombs and nuclear reactors then its binding energy happens to be a 1786 mega electron volts so what does that mean this means that if i have to break separate all the 235 protons and neutrons of the uranium break this new uranium it takes this much energy so that's the meaning of binding energy energy to break the nucleus okay a very quick question to you do you think we can use this to say that uranium is more stable compared to oxygen because it it takes more energy to break uranium compared to oxygen can i say that what do you think can you pause the video and think a little bit about this well it sounds reasonable but if you do that auxin is going to be very angry at you it's going to say hey i only have 16 particles with me so obviously it's easier to break me whereas in uranium there are 235 particles all pulling on each other and keeping each other together so obviously it's a bigger family it takes more energy to break it so that's an unfair com comparison so yeah we can't just use this number to compare their stabilities to compare them we'll have to use same numbers but how do we do that well one of the ways to do that is asking the question how much energy it takes to separate one proton or one neutron from the oxygen and from the uranium that would be a fair comparison because we're taking equal number one so let's calculate for oxygen to separate 16 it takes 128 mega electron volts so if i want to separate one neutron or one proton how much energy does it take well i just divide this by 16. if i do that i've already calculated it happens to be turns out about eight mega electron volt and these are rough numbers so this means to separate one proton on neutron it takes eight mega electron volts of energy for oxygen how much for uranium well for 235 it is this much so for 1 i would divide this by 235 and this is why i chose these number these these examples if you do this calculation it happens to be 7.6 mega electron volt what does that mean that means to separate one proton or neutron from a uranium it takes less energy compared to that of oxygen and so who is more stable it's the oxygen that's more stable compared to uranium and so you see if you want to talk about stability you take the binding energy and divide by the mass number to calculate the binding energy per nucleon energy required to remove one part one you know proton or neutron and that's what we're doing here we're looking at binding energy per nucleon of all the different elements and comparing all of them so what does the graph look like well here it is tada so what is the graph trying to tell us well it's saying that for if you look at lighter nuclei then as the number of protons and neutrons increases as the mass number increases notice the binding energy per nucleon their stability basically starts increasing it becomes more and more stable then it reaches a maximum value and then slowly starts decreasing but pretty much stays a constant and if you're wondering at this point which is that element which has the maximum stability then that element turns out to be iron 56 and that means iron 56 is the most stable element in the universe because it has the maximum binding energy per nucleon and its value happens to be somewhere close to these are all rough numbers okay not exact close to about 8.5 8.6 mega electron volt so the most stable element in the universe is iron 56 but now let's think a little bit more about why is it that the binding energy per nucleus the stability increases very quickly initially but then pretty much stays a constant in fact it starts decreasing but it pretty much stays a constant why is it doing that but it's got to do with the fact that nuclear forces are short ranged okay what does that mean well let me take an example let me just show you a few nuclei over here in each case let's think about how hard it is to remove this green particle harder it is more stability okay now over here in the first case this green particle is only pulled by two but over here the green particle is being pulled by four other particles and as a result we can say that it's harder to pull this one so more stability so this one has a higher binding energy per nucleon more stability compared to the previous and the same thing happens over here because there are more particles surrounding this green one more pull it becomes even harder now to pull out this green particle from the nucleus so stability increases and so this initial part of the graph makes sense now as you increase as you add more particles more pull and as a result it becomes harder to separate them and therefore the stability increases but what happens after a particular point what happens over here shouldn't the same thing continue well no you see it turns out that nuclear forces are short-ranged meaning that particles can only influence or pull on their immediate neighbors so let's see what happens from here to here when i add those extra blue particles they are no longer the neighbors of green particle right and so these blue neighbors are just too far away from the green particles and turns out that these blue particles these extra blue particles are no longer going to pull on the green particles and so the only particles that are pulling on the green one are its immediate neighbors pretty much the same amount as these ones and so notice over here it's the amount of energy required to pull this green particle apart or outside the nucleus is pretty much the same as over here because no extra pulling force does that make sense that's the meaning of short range and that's why from here to here the binding energy pretty much stays the same and this the same story continues from here to here even though i've added more blue particles they're just too far away they're not going to influence this green particle and so you see as i go heavier and heavier after a point even though i'm adding more particles the number of neighbors for each particle stays the same and as a result the energy required to remove any one particle after a point stays the same and so because nuclear forces are short ranged after a point we will find that the stability pretty much stays the same now if you're really curious you might ask but wait it's not a constant the stability is decreasing why is that happening well i don't want to get into too much complexity but remember there is another repulsive force at play as well protons and protons repel each other and because of this repulsion it becomes easier to pull particles apart now initially over here since the nuclear force is much stronger than the proton proton repulsion force the nuclear force wins out and we can completely ignore the proton proton repulsion but from but from here onwards the nuclear force stays the same on each particle right but the proton proton repulsion starts increasing because electrostatic force has no short range it is a long range force and so because the repulsion starts increasing although the attraction stays the same the repulsion starts increasing that's the reason why it actually makes it a little easier to start pulling your green particle apart as you go down but you don't have to worry too much about that but that's basically the proton proton repulsion is the reason why the binding energy per nucleon actually decreases but that's not worry too much about it let's for our sake it pretty much stays a constant okay finally we can use this graph to even predict what kind of nuclear reactions we can predict over here one of the nuclear reactions is where you have a very heavy nucleus breaking into smaller nuclei we call that nuclear fission and this is the reaction used in nuclear bombs now why does that happen well let's see let's look at the binding energy graph if you take a very heavy nucleus and let's say it were to split into smaller nuclei then these react these products would be towards the left side and we know we can see from the binding energy graph that these end up having a higher stability compared to the reactant and therefore such reaction is favored remember in any reaction whether it's chemical or whether it's nuclear reaction stability nature wants to go more towards stability and that's where spontaneous reactions happen and since in this reaction the reactant products are more stable compared to the reactant this reaction is favored and enormous amount of energy is released and that's was used in atomic bombs so this is called nuclear fission now can you can you predict why we can't have nuclear fission for lighter elements so if i take an element over here which is say i don't know maybe carbon or nitrogen why can't we have fission over there can you look at the graph and think about it pause the video and think about this all right if you take a very light element like nitrogen or carbon and now if you if that undergoes fission if it splits then notice the react the products would be even lighter and notice they will be less stable compared to the reactant and so this is not favored and so this is not a spontaneous reaction and so you don't expect lighter elements to undergo fission reaction does that make sense so what happens to lighter elements well lighter elements undergo fusion reaction these elements they tend to fuse together to form heavier elements because now notice the heavier element is more stable compared to these lighter elements and so you expect light elements to undergo fusion and that's what's powering up our sun or any other star for that matter nuclear fusion hydrogen is combined to form helium and later helium can get combined to form even more heavier elements and so on and now i'm pretty sure you can look at the graph and explain why heavier elements don't undergo fusion reaction i'm pretty sure you can try and do that yourself