Quantum Tunneling Explains Radioactive Decay and the 2025 Nobel Prize

[00:00:00]this video is sponsored by brilliant.org I never understood why radioactive elements even exist today hear me out okay if you take the most common isotope of radium radium 226 it turns out that it has too many protons and neutrons making it too unstable and so it spits out an alpha particle reducing the total number converting itself into radon turns out radon is more stable compared to radium now here's my question if radium can become more stable by converting into radon by giving you an alpha DK why doesn't all all the radium Isotopes dek into radon the moment they are formed what are they waiting for shouldn't all the radium isotop instantly Decay and that should be the case for all the radioactive elements the moment they are formed they should instantly Decay and become more stable right so why do they even exist that's the whole question but they don't do that they don't instantly DEC instead if you have for example a bunch of radium with you which you shouldn't have by the way because it's super radioactive but if you did radium 226 then it turns out that if you wait for about 16,000 years only half of it would have decayed and if you wait for another 16,000 years half of the remaining would have decayed that's how the DK goes it doesn't happen instantly this by the way is called the halflife of radium 226 all the radioactive elements have some halflife like this but the question is why does the DK happen so slowly now don't get me wrong I'm glad that radioactivity doesn't happen instantly it goes as the way it goes because it's the reason why the core of the earth it's one of the reasons why the earth's core is still hot so without it you and I wouldn't have existed but still the question is why does that happen that way the most common explanation I got for this silly sounding question to my teachers was that hey radioactivity is a Quantum process Quantum is inherently probabilistic so it's kind of like rolling a die and waiting for a six for example the chances of that happening is very small and so you have to wait a long time for that but that is a very handm kind of an explanation it was very analogous and I didn't get a deep intuition behind what's really going on during a dek what causes where does the halflife even come from and why are certain elements stable while other Isotopes unstable in the first place like none of that made any sense to me until I came across George gamma's work and then my mind was blown so if I do this video right not only will we gain a deep intuition behind Alpha DK which we'll focus on in this video but we will also ReDiscover a profound quantum mechanics principle which has far-reaching consequences so if you're ready for this let's begin so gamma what's going on why doesn't radium just throw out the alpha particle instantly and just get done with all the DK well gamma says because there's a barrier over here see the alpha particle inside the radium is attracted by the strong nuclear force that is the dominating force over there so if you want to pull that out then you need to push it against the strong nuclear force until you get out of the nuclear range so that requires energy you need to put energy to get it outside the nuclear range once it's out over there then nuclear force no longer exists then the kum's repulsion will take over and then the alpha particle will come out so it's kind of like a ball being stuck inside a well if you want a ball to go from here to here it has to First overcome this barrier and to do that you need to put in energy to overcome that barrier in the same way over here you need put in energy to overcome that barrier but once you overcome it then it's a downhill from there and I'm like okay that kind of makes sense so the alpha particles require a minimum energy to overcome the nuclear force of attraction makes sense so the my next question is how do the alpha particles get that energy to overcome the barrier and Gamma says they don't I'm like what what do you mean they don't radium radium nuclei do emit alpha particles once in a while so clearly they must be overcoming the barrier what do you mean they don't GMA says well we have experimentally seen that they don't overcome the barrier I'm like what do you mean how H how do you even say that what kind of experiments do you people do to to come to the conclusions like this and Gamma says that's a good question mahes let's let's take some numbers over here and this is the interesting part folks okay so if you take some numbers over here for example let's consider the potential energy over here to be zero okay then the potential energy of the ball when it comes over here well we can calculate that if we know the mass of the ball we know the value of gravity and we know this height mg we can calculate the potential energy of the ball when it comes here let's just for the sake of simple numbers call that to be 10 units okay now gamma asks Mahesh under these circumstances how much minimum energy does this ball need so that it can overcome the barrier and I'm like well it needs a minimum of 10 units of energy right so that if it has 10 units of energy all of that can be converted into potential energy if it has less than that it will not even reach over here if it has more than that then it will reach over here okay and then once it reaches over here it goes downhill what happens to all that potential energy I'm like all that potential energy gets converted to kinetic energy so when it comes over here all that 10 units would have gotten converted into kinetic energy so the kinetic energy over here must be at least 10 units it can be more if you had pushed with more energy it would have had some kinetic energy here as well but it should at least have 10 units of kinetic energy when it comes over here long story short if the ball makes through you should detect that ball to have more than 10 units of kinetic energy does that make sense and I'm like yeah that makes sense and in fact this also works the other way around if you want to push that ball into the well it should again need a minimum of 10 units of kinetic energy so that it can overcome this barrier makes sense right okay now guess what just like the ball this alpha particle inside the radium nucleus can be modeled to be you know being stuck in a well well not a physical well but a potential well that is created by not gravity but strong nuclear forces and kums forces okay so just like before there is a barrier it needs to overcome in order to escape that makes sense right but what's cool is that just like how we we calculated using MGH the barrier potential energy the minimum energy needed to overcome the barrier even here we can calculate what that minimum energy is and all you need to do that is kum's Law and that I found is pretty awesome just by using kum's law you can even calculate how much is the minimum energy you you know the alpha particle requires to overcome which is pretty amazing you know if you ask me but anyways we not go through the calculation if you do that calculation then it turns out that the barrier potential is about 25 Mega electron WS okay so gamma asks Mahesh this means how much minimum energy does this nucleus need alpha particle need to escape and I'm like well just like before it needs a minimum of 25 Mega electron WS of energy if it has that then all of that energy will get converted into potential energy when it is just over here it just escape the nuclear clutches and then finally when it goes downhill when it you know gets repelled all of that potential energy gets converted into kinetic energy so how how much kinetic energy should it have when over here well since all of this got convered to kinetic energy it should have at least 25 Mega electron WS of kinetic energy right it can have more because you know it could have had more energy to begin with but it could at least have 25 Mega electron WTS of energy so long story short alpha particles should come out of radium nuclei at at least a kinetic energy of 25 Mega electron WS right that makes sense because it has overcome the barrier but guess what we can measure this experimentally and we when we did we found that they don't come out with 25 Mega electron volts of energy in fact what we find is that they come out experimentally when we measure with the energies of close to 4.9 Mega electron WS which is significantly smaller than the barrier potential and Gamma says look Mahesh if they had overcome the barrier how can they have such low energies there's no energy loss anywhere in between so how can they have such low energies and I'm like yeah that's a that's a interesting question how are they going through the barrier with such little energies maybe something's something's weird with radium and it turns out this is not just the case with radium every single Alpha DK if you look you'll find that the kinetic energies usually come out at the range of 4 to 8 Mega electron ws and the barrier potential is close to 25 to 26 Mega electron Vols so something is going on over here these alpha particles should not be able to escape over here they should just keep going bouncing back and forth with that little energy they shouldn't be able to overcome the barrier so gamma how can these Alpha particles even with such little energy overcome that massive barrier well GMA say it's kind of like how even with such little time you can overcome your massive learning barrier using brilliant the sponsor of this video first of all I've been recommending brilliant to my students way before they started sponsoring me mainly because you can start learning for free by interacting with it you learn by doing so even if you spend a little bit of time every day you start becoming a better Problem Solver and they have courses in various subjects like physics math or data programming and even a AI for example check out their updated calculus course 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escape the barrier well gamma says first of all let's convert this into an energy level diagram where the vertical represents energy levels it's slightly more intuitive to think of it this way so again we're saying the same thing if you want to escape the barrier then the alpha particle needs to have an energy Above This level only then it can easily Escape it if it has energy level below this barrier like like what we have over here then it should just be bouncing back and forth it shouldn't be able to escape it so how does it do that well gamma reminds us mahes alpha particles are not tiny balls bouncing back and forth they are quantum objects and all of the cool properties of of the quantum objects is the uncertainty principle their positions are not very well defined there is a minimum uncertainty in that and so rather than thinking of our alpha particle as tiny balls bouncing back and forth like this it's slightly better to think of it somewhat this way where their position is not very well defined this is also not completely accurate but it's slightly better than thinking of them as a ball now because particles don't have a well defined location it's possible that when the alpha particle is very close to the barrier due to its uncertainty it can be found outside the barrier purely from the uncertainty the chances of that is very low but if you just wait long enough let's just do that let's just keep waiting waiting there you see that just purely by chance it found itself outside and once it goes outside then the kum's force takes over and then it just gets released this is how purely from the fact that particles have uncertainty they could be overcoming the barrier without actually having the energy to do that now classically there is no way this could happen if a ball had less than the energy necessary to overcome the barrier it wouldn't be able to or you know go there at all unless it dug a tunnel through it then and only then it would be able to go through and that's why what whatever is happening over here is we give a name to it we call it tunneling we call it quantum tunneling but of course you and I understand it's it's not like the alpha particle is creating some kind of a mystery tunnel no no no this is at the end of the day coming from the quantum principle that we know the uncertainty principle or to be more precise we should actually think in terms of wave functions turns out that the wave function does not go to zero it dies out but it has a very tiny amplitude outside so it has a very tiny probability uh you know of finding the particle outside but like I like to think more in terms of of the uncertainty principle even though it's less accurate it's slightly more intuitive and the uncertainty principle also comes from the wave function so I like it this way so long story short alpha particles tunnel through the barrier even though they don't have enough energy and they do that purely from the fact that their locations are uncertain so this was the model that gamma proposed okay so this is pretty profound so can you now answer original question why don't all the radium nuclei instantly Decay well the answer is because the alpha particles are stuck inside a potential well they don't have the energy to overcome the barrier but there is a small chance there's a small probability that they can you know be just due to uner principle be found outside now that probability is insanely small however if you wait more time that probability increases isn't it that probability adds up right if the longer I wait the more attempts it gets and the probability keeps adding up so as I wait wait wait the probability keeps adding up becomes more and more and more and eventually for radium it turns out that if I wait about 16,000 years the probability of it tunneling through adds up all to be 50% this is the reason why if I have a bunch of radium which you shouldn't have by the way because super radioactive but if you do and if you wait for 16,000 years half of it would have decayed because the tunning probability adds up to 50% so what's mind blow you know what's mind-blowing is we now have a deeper Insight of where halflife even comes from halflife is actually the amount of time you have to wait until the tunneling probability all adds up to give you 50% that's where it all comes from that's beautiful isn't it and this also means now we have a theoretical way to model halflife we just have to compute the time we have to wait for the tuning probability to add up to become 50% it's very hard to do it and there are a lot of complic but in certain cases we have found theoretically the half lifee values to be very close to the values that we find experimentally which is amazing that's an amazing success for gamma's theory that is incredible model gamma but wait I promised you complete intuition right so here's a final counter question if radioactive elements give you Alpha DK Y at tunneling and become stable why don't all Heavy Isotopes do the same thing we know that ion is one of the most stable elements in the universe so all the heavy elements after ion if they you know gave you an alpha decay then they would be lighter and they would be more stable so shouldn't all Isotopes after ionb radioactive why do we even have stable isotopes in the first place I love the way my questioning is changing right the more I learn the more fundamental our question is becoming which is awesome but what's your answer for that gamma and Gamma say that's a great question so first let's look at the alpha decay of a few other radioactive isotopes so for example if you consider uranium 238 then it also is a radioactive isotope it gives you alpha particles and there the alpha particles comes with the energy of about 4.3 Mega electron volts so you see it's slightly less energetic than that of radium so what would you expect to happen for its tunneling probability I'm like see if the energy is lower you can you can see that hey the barrier width is larger so tunneling is harder which means I would expect the tunneling probably to be slightly smaller and Gamma says no mahes if you actually solve the ringers equations which we're not going to do but if you do you find that a small change in the barrier width gives you orders of magnitude changes in the probability so you're right tuning is going to be harder but the probability would not be slightly smaller it would be ERS of magnitude smaller which means the amount of time now we have to wait for the tuning probability to add up to be 50% would be orders of magnitude higher so the half life of uranium 238 would be not just a little bit more than 16,000 years it would be orders of magnitude more than 16,000 years and that's exactly what we find the half life of unit 238 is 4 and a half billion years and gamma's Theory can now explain why such a astronomical difference in their Half Lives even though there's a small difference in their you know energies of the alpha particle it's all because of the tning probability there is small changes in the barrier with gives you astronomical changes in the tning probabilities okay let's look at one more just for fun if you now consider ionium 212 which is also an alpha DK Source the alpha particle here comes at 8.9 Mega electron Wes oohoo what do you expect to happen for the halflife here mahes I'm like oh my God the barrier width is now much smaller than before and so the probability must be astronomically larger it must be that much easier to Tunnel through and so the amount of time I have to wait for the probability to add 50% must be astronomically smaller so the halflife should be I don't know extremely small and that's exact what we find the half life of penium 22 is3 microc this is all starting to make sense isn't it okay now to answer your question Mahesh let's consider one of the stable isotopes like gold 197 you are right if it were to give you an alpha DK it would be lighter and it would be more stable and you can now hypothetically calculate with what energy the alpha particle would come out all you have to do is figure out the energy before the DK and figure out the energy after the DK which you can do calculations and again encourage you to do that yourself and if you do it you would find the alpha particle would come out with the energy of A9 Mega electron W mahes what's the tunneling probability of that oh my God such a small decrease gave you such astronomical decrease in the halflife now look at this this is so small the Turning probability would be so low I don't know the halflife could be I don't know trillions to the power trillions to the power trillions of years or something like that so technically technically gold would DEC if you wait long enough time in fact every single element after iron would DEC give you Alpha DC if you waited long enough time but the time scales we're talking about are so ridiculously large that for all practical purposes we say they are stable this makes sense right so the reason why stable isotopes heavy stable isotopes are stable is because the energies of the alpha particles are so low that the time we have to wait the Turning probability becomes almost you know negligibly small that we can call them stable in the time scale we imagine this is profound like isn't this making sense like I love how much explanatory power gamma's model has amazing isn't it but guess what I told you turning has far-reaching consequences and another consequence of tunneling is that it keeps the Sun Alive GMA asks what powers of the Sun and I'm like that's easy Fusion protons are fusing together but remember protons also are repelling each other so there's a kums barrier so just like like before if they have to fuse they have to overcome they need to have enough energy to overcome that barrier and come within the nuclear range and only then they can fuse and just like before we can calculate what that barrier potential is just by using kum's law and then by using a little bit of thermodynamics you can figure out at what temperature would these protons have enough energy to overcome that barrier and that temperature happens to be somewhere close to 10 billion Kelvin and the sun's core temperature is about 15 million Kelvin which is way lower than the necessary temperature so as it as crazy as this may sound the sun is actually too cold for Fusion to happen classically speaking that doesn't have enough energy then how does sun fuse the protons together tunneling that's the only way they can cross through the barrier and fuse together so tunneling is literally what's keeping the sun alive it's what allows sun to fuse protons at a much lower temperature than classically needed amazing isn't it now at this point you may be like mahes this is all great and mind-blowing and stuff but it's still a theory isn't it well think again because we have actually harness the power of tunneling and one of my favorite examples is the scanning tunneling microscope which can be used to map out the surface features at the atomic level and the way it works is if this is the surface that we need to map we just bring a needle very close to it and put a voltage then even though there is no conducting Gap there's a barrier over here electrons can tunnel through if the barrier is is small enough to give you a tunneling current and we can measure that current using computers and so we now start mapping them and keep moving the needle forward and if we encounter a hill the barrier has become smaller the T tunneling current becomes larger substantially and that's how the computer will detect and say aha there must be a hill because I detect a very high current and therefore to get back the same current I need to pull the needle back and that's how we can figure out how the you know where the tip of that Hill is and similarly if we encounter a valley the potential barrier has increased the tunneling current will decrease substantially and again the computer will say aha the tunneling current has decreased therefore there must be a value over here and so I need to push down the needle forward to get back the same current and this way by trying to keep the current same we can map out the entire surface and we can do that at the atomic level in fact here's a picture what you're seeing is the surface reconstruction of a you know a clean gold you can literally see the reconstructions of the atoms over here that is incredible isn't it but finally finally Quantum tunneling is also a huge challenge for our Electronics because see so far our technology has been growing substantially our computing power and memory you know storage capacity has been growing all because we were able to shrink the size of a transistor transistor is a basic building block of a computer right but after a particular size if you make it too small then the electrons will tunnel through the insulating barrier which they're not supposed to and then your transistors will stop working which means there is a theoretical limit to how small you can make these transistors giving you a theoretical limit on how much computing power or how much memory you can have in a given area we have not yet reached that limit today but we will at someday leech that and therefore there is active research going on in figuring out new technology that can somehow overcome tunneling and for that quantum mechanics is the key tunneling is a huge reminder of how successful the quantum theory really is and learning this way where you ReDiscover things is really the most awesome way the most fun way to deepen your insights so you can click on this video to ReDiscover something else and get your mind blown again I'll see you