Understanding QFT - Episode 1: How spin was discovered

why don't electrons spiral down towards the nucleus that's it that's the question we will answer in this video and in doing so we will discover spin the most important property of nature but this is just the first in a series of videos in which we will discover that nature is made of symmetries this is the beautiful realization at the core of a theory called Quantum field Theory although among friends it goes by qfd if learning Quantum field Theory sounds intimidating and why wouldn't it just keep in mind that the people who discovered that didn't know anything about it they just learned one thing at a time and that's why today's goal is just to learn why electrons don't spiral down towards the nucleus now could we learn this in a much shorter video sure or if that was our only goal but our goal today is also to set the foundations for qft and those foundations are not made only of mathematics they are made of observations about nature for this reason each episode is gonna tell the story of one question scientists had about nature and how they found the answer to that question only then we will build the mathematics to understand the solution for example in this episode we will see the story of how people discovered the nature of light and the structure of the atom ending with a discovery of Spin and then in the next episode we will build the mathematics to understand spin from scratch using only what we learned in this video and wouldn't you know it what a coincidence those are the simplest version of the mathematics of quantum field Theory and that's it this will be a journey and I hope you enjoy it let's first meet the protagonist of our story Niels Bohr I like him let me tell you one story about him when Borg was a starting University there was a contest in Denmark to measure the surface tension of water and Borg wanted to participate but his university didn't have a laugh with the right equipment and so he had to make it himself from scratch even all the glassware which is really funny because in high school he was famous for breaking everything in the chemistry lab anyway so he gets going to with this experiment and he actually improves it but he gets so destructive by doing the experiment he seemingly forgot to write the report until the dead the Day of the deadline no matter how great the project is for Max extra credit don't forget to spend just as much time on the written part and at this point his mom and his brother come to help him and so he dictates the report to them and they write as quickly as they can and while everyone submitted they're nice and carefully typed written reports with the grabs and everything and everything uh Boar's admitted rosh handwritten one and he still won he's just I I just imagine everyone in the living room just like seriously writing and then boar being really sorry that he forgot to make the report until the deadline but also really grateful that his family is helping is helping him anyway I would love to just tell you stories about boar and other scientists I like but let's get down to business and if he yeah so in 1912 Bohr was having a bad time looking at lamps and trying to imagine why don't electrons spiral down towards the nucleus but how did Bohr even knew that atoms have nuclei in the first place and why was he trying to solve this by looking at lamps well to understand Bohr's Discovery first we need to understand what people at the time knew about atoms and about light back in the late 1800s early 1900s atoms were less than a theory they were a full Theory they were a really good hypothesis so and so chemists have noticed that certain elements combined in certain proportions to create new substances and they thought they could explain this by atoms coming together into new structures they called molecules and they had been able to classify elements based on their properties in an early version of the periodic table but no one has been able to prove atoms existed and even if they did no one could explain how they formed these new structures nor why they have the different properties both electrons were a different story they were discovered by JJ now another Canadian YouTuber I wish no JJ Thomson so back then they had this device called a cathode ray and there are many demonstrations of how it works in YouTube like this one from veritasium but don't go watch it right now I need the views Derek doesn't so anyway the point is that this device consists of two play two metal plates in a vacuum and so when you put a lot of electric potential between them eventually you see this substance flowing between them and with a clever use of magnets you can figure out that this substance has negative electric charge and then uh Thompson was able to figure out that this substance was made of individual particles with the same charge and mass the electron that we know today now this had enough evidence to be a theory the discovery of electrons led many chemists to suspect that maybe atoms interacted by exchanging electrons and if that was the case it seemed that the number eight kept coming up over and over and in fact some chemists proposed that atoms were in fact like little cubes that could hold one electron in each corner it was a cute idea but the most popular vision of the atom back then was the raisins and pudding model proposed by Thomson himself so this model said that atoms were like a cloud of some primordial substance with positive electric charge this was the pudding and then In This Cloud electrons were floating and electrons were like these solid objects with negative electric charge like the raisins I just love this model because it has the right combination of seriousness and silliness and you can tell that Thomson was hungry when he came up with it in this context in the year 1900 a scientist named Max Planck would answer a seemingly unrelated question and in doing so he would change how we think about light that question was why do hot things glow this observation is as old as Humanity I mean Embers in a bonfire can keep on glowing long after they are done burning because they are still hot and humans have been smelting Metals for thousands of years and noticing that molten metal glows in the late 1800s scientists were beginning to notice this is not limited to Embers and molten metal but it applies to everything everything emits light based on its temperature even you you are glowing right now literally granted it this light is too thin for your eyes to see it but it is definitely there and it can be measured that's how thermal cameras work they are to solve this mystery is called ultraviolet catastrophe and it is quite good but the mathematics plank used to solve it are not very relevant for qft so I'll just give you the highlights otherwise this would be like a Naruto level flashback besides the next episode will be all about the map so spoilers are here for ultraviolet catastrophe in case you haven't seen it movement creates Heat so it stands to reason that heat is just atoms and their electrons vibrating in place this is interesting because when an object with electric charge moves around it Jiggles the electromagnetic field and this jiggling creates light because that's what light is light is an electromagnetic wave and so when things get really hot their electrons vibrate a lot more and they create a lot more light this was the model everyone was using and they wanted to use it to predict how much light a completely black object would emit baits only on its temperature what they called the black body radiation but the problem is that the model predicted there should be an infinite amount of ultraviolet light being produced regardless of the temperature of the black body which is not what we observe I mean otherwise we would need like a lot of sunscreen like a bottle at least plan tried to solve this problem a bunch of times tweaking the model in different ways but he always got it wrong until he found the answer thanks to the power of friendship because his friends were also working on this problem and they sent him letters showing him their progress one of his friends had found a model that only worked at high temperatures and another friend had found a model that only worked for low temperatures Planck wanted to combine these models into a single model that worked at all temperatures but to do that he had to modify the model in one strange way he has to assume that instead of light being a continuous wave it was made of particles then if the energy in these particles is proportional to the frequency at which electrons were vibrating when they were creative you get this equation this is Planck's law and it correctly predicts the light emitted by an object depending on its temperature by the way plant called this new strategy of modeling nature in non-continuous ways quantization so whenever you hear me talking about it you already know what it means today we call light particles photons and the proportionality constant is called Planck's Constant and we still use Planck's law for many things like deducing the temperature of Stars based only on their light for example this is the spectrum of the sun according to NASA from here we can deduce that the surface of the Sun must be at around some 6 000 degrees Kelvin because it matches Planck's law at 6000 degrees Kelvin or well I okay they don't match exactly the same but that's because Planck's law is describing an ideal situation but in the real world there are many other factors altering or results like the atmosphere of Earth and in fact here you can see how NASA compares the spectrum of the Sun as seen from space and a scene from Earth these all of these factors we cannot control make these lines all jacked although although I do wonder what creates those large leaves hmm I'm sure it won't come up later blank's Discovery was controversial because it was well established that light is a wave and one of the experiments that proves this is called fresnel's dot it works like this so if you shine light just right in front of a sphere the light waves will continue to spread behind the sphere and rejoin at some point creating a bright spot in the middle of the Shadow or well it's not very bright but it is definitely there and this wouldn't be possible if light wasn't a wave for this reason and many others Max Planck the hero of the ultraviolet catastrophe himself insisted that photons were just a model he believed that light was indeed a wave although a wave with strange properties and once those properties were better understood photons would be replaced with another model one closer to reality but then this shows up Albert Einstein and there's an entire OVA called miracle year in which Einstein among other things uses photons to solve yet another problem called the photoelectric effect and again I'll just give you the highlights the spoiler alert for miracle year people have noticed that when you shine light on a piece of metal it creates an electric current but only if the light has the right color and this color is different for each kind of metal and if you don't believe me there's a really cool demonstration of it by the action lab oh um by the way when it comes to light color energy frequency wavelength are all very interrelated if you know one of these quantities you know all the others so I'm going to use them pretty much interchangeably first we need to put some extra electrons on the metal and this sounds really difficult but it's actually really easy just like take it alone roll it on your head and then touch the metal with the balloon what happens is that some electrons from your hair ended up in the balloon and then when the balloon touches the metal those electrons are there in the metal fine then you take a lamp that creates light with a right color and just for the sake of argument let's say that the right color is violet you shine this violet light on the middle and it creates an electric current what happened is that the extra electrons absorb that light and use that extra energy to move around next you replace the lamp with another lamp that creates green light with exactly half the energy but when you shine it on the metal there's no current okay so perhaps you need more energy so you take a second identical lamp but guess what still you will not see any current the amount of light energy in both cases with one lamp and two lamps is exactly the same so if light really was just a wave it should make electrons move in both cases but instead if light really is made of photons and electrons can only absorb one Photon at a time then it doesn't matter that two of these green photons have the same energy as one Violet Photon the electrons simply doesn't buy with them it cannot buy with them they don't have enough energy but when the Violet Photon comes along it does have enough energy and electron goes by with it it absorbs that Photon and that extra energy releases it from whatever force was holding it in place and then it becomes free to move through the metal and this is more or less how solar cells work now we have evidence that light is a particle but we also have evidence that light is a wave so which one is it particles or waves well why not both por quino Los Dos nature doesn't care about our expectations the strangest it might be nature can make objects with properties of both particles and waves now remember that up to this point people were still not sure that atoms were a real thing but then they were finally proven by let me check my notes anything again and then he also discovered relativity all in the same year talk about a Mary Sue it let's just fast forward to 1911. in 1911 Bohr was doing his PhD at the same University where thonson worked and this was not a coincidence board chose to go there precisely because he was a thumbs up Fanboy he was like nobody's missing pie but sadly Senpai didn't notice him Samsung was just not impressed by Bohr's work but this was just as well because in 1912 Bohr met Rutherford a scientist who had just performed a couple of very interesting experiments involving radiation people back then were just perplexed by radiation they have noticed that there were some elements that were constantly shooting out particles and they classified these particles as alpha beta and gamma but they didn't really understood what these particles were or where in the atom they were coming from I mean remember that they still believed in the pulling model both Rutherford had just come up with an idea to test that model he decided to shoot Alpha radiation at a thin gold foiled and see if the radiation could go through it this was his reasoning if the pulling model was correct then the only solid objects inside the atom were the electrons both alpha particles are like 7 000 times heavier than them so electrons should be steamrolled and alpha particles should pass through without any problems but if the pudding model was wrong something else should happen he set up a radioactive Source in front of a thin gold foil and behind it the most advanced particle detector in the world had ever seen it consisted of a fluorescent material that shines when it receives radiation on his eyes for real for real they have to count out loud when they saw a spark and then remember the number they couldn't even write it down because the note the room needed to be dark for them to see the sparks in the first place and then they needed to move the the fluorescent screen at different angles and repeat the whole process and let me tell you I've done similar experiments in the past and this light is not easy to see it is super dim and can agree you can see a modern version of this experiment in the YouTube channel backstage science which has been uploaded in the last 10 years so go show them some love but only after you finish watching this video of course the result of this experiment was that most alpha particles indeed went straight through the gold foil as predicted by the pulling model but some alpha particles were detected to the sides they had been deflective and since alpha particles have a positive electric charge they could tell they had been deflected by a positive electric field and even weirder some alpha particles were detected in front of the gold foil they had bounced back as if they had crashed with something and these deflections and these bounces just couldn't be explained by the pulling model building model pulling model pulling model pulling model building model it's it's I feel like a muppet where I'm saying it building model pulling mobile from this Rutherford concluded that the pulling model was wrong there was no cloud of positive electric charge but instead it seemed that all of the positive charge of the atom was concentrated into a single point along with most of the mats Rutherford had just discovered the nucleus now people were finally able to see the problem if the nucleus is positive and electrons are negative electrons should get attracted to the nucleus crash with it and sorta stay there it should be really difficult to separate electrons from their atoms but it's not it's really easy you can just go rub your socks on a carpet and touch a friend the shock you feel is electrons leaving your body and if you're lucky you might even see them another example is the photoelectric effect from before we were putting extra electrons on the metal and that was the easiest part of the experiment also electric current requires electrons to move between different atoms and so the line involves and static electricity and chemistry chemistry none of this would be possible if it wasn't easy for electrons to move between different atoms for this reason Rutherford proposed that electrons were actually orbiting around the nucleus much like planets around the Sun and that their speed prevented them from falling into the nucleus much like how Earth's speed prevents it from falling into the Sun but this doesn't work either electrical fields are different from gravitational fields in the sense that according to the laws of electrodynamics a charge moving in circles should jiggle the electromagnetic fields which remember create slides and this cost energy and that energy will come from the distance between the charges pulling them closer and from their movement slowing them down so electrons should slow down and crush with the nucleus anyway the idea of aronsa's little cubes it's not looking so bad anymore or is it in the following Year everyone and their mom had a new atomic model trying to make sense of all of these different observations but to be honest all of these models were actually really bad none of them really worked but thankfully Rutherford saw something in war that Thompson didn't and so he invited him to join his team and work in a new atomic model and Rutherford could afford to do this because he had a budget he was paid to do research even though research doesn't create any money and this is amazing because for thousands of years only rich people could afford to do research and this is the reason science was so slow and it is the reason I was so slow yeah this is the patreon blog look I have bills to pay like the 263 dollars I have to pay on student debt every month and these videos require a lot of time and work and I do earn some money out of them like from the previous big science video I've earned enough money to pay almost two months of student debt which is good it is a good thing but it's not enough it's not enough for me to justify the time and work these kinds of videos require but if I can start earning enough money from my YouTube channel from views and patreon and one time donations then maybe I can use an exploit called having a job which will let me speedrun the qfd series in the 100 no major skips category and what you will get from this is just more of this more often my dream is that if the video does well enough I will be able to hire an editor and an animator at which point this becomes like a small business uh but who knows maybe this video flops and I'll just have to keep working on this whenever I have time we'll see back to the show and so we come back to boar having a beach of a tie trying to make sense out of all the facts we've learned in this video electrons should be moving in orbits around the nucleus but the orbits are not stable but they should be so that electrons can move easily between atoms like when they form molecules and the properties of the elements are periodic so the properties of the orbits should be periodic and the number eight is important for some reason but the orbits are not stable but it should be so that they can become a mine in different ways that are periodic but the problem is that the orbits are not stable so but they shoot it but sure but they're not suddenly he got it okay it sounds kind of stupid at first but but follow me the problem is that the orbits are not stable right what if they are what if they there's a magical combination of distance from the nucleus and speed that makes some orbits stable and maybe in those orbits electrons can move without emitting light like the loss of electrodynamic Demands from them and maybe these magical combinations of distance and speed happen in some kind of periodic pattern and maybe that explains the properties of the elements in summary ball was proposing that instead of a Continuum of orbits the orbits were quantized remember that word from the beginning of the videos on 20 minutes ago I I really hope it's not more than 20 minutes for me it's been like four hours there was only a teeny tiny problem with this idea it still contradicts the laws of electrolynamics because a charge moving in circles just has to emit light no matter what and there are like a trillion experiments that prove that so if boar wanted anyone to take him seriously he would need to find a way to justify his ideas either theoretically or better yet experimentally and this is when a friend told him about the spectral lines of hydrogen do you remember how the spectrum of the sun has those weird dips in it people have been wondering what those dips were for decades and so in the middle to late 1800s scientists were doing this experiment where they shined a continuous spectrum of light onto a gas and they measure the spectrum that came from the other side and guess what those spectrums always have dips and these dips were in different places for each element from this they concluded that each element absorbed only some frequencies of light in other words the absorption spectrum of each element was quantized this is similar to the photoelectric effect we saw earlier except now we don't need an electric current to see what is happening of course the scientists back then didn't know why this was happening but they understood that they could identify any element and in fact any molecule by looking at what colors of light it can absorb what they called the Spectrum and here you can see the spectrum of most elements except acetone and francium for some reason and up to no no no no no no okay no I mentioned the photoelectric effect and I saw on him no no Einstein go away go away this video is not about you it's not about you this is called spectroscopy and it is objectively cool as this is how we figure out the composition of the sun even though taking a sample is impossible the sun emits a continuous spectrum because of its temperature but then it reabsorbs some of that light because of its composition and that creates the dips although of course we have to correct for the composition of the atmosphere but that's relatively easy but then these beautiful 18th century nerds kept doing weird and they realized you don't need to hit something for it to emit light you can also shock it with electricity and this works particularly well with gases when they analyze the light created this way they realized this wasn't a continuous Spectrum but rather it was quantized too only specific colors of light were emitted and wouldn't you know it gosh darn it if there isn't the same colors of light that element absorbs if you want you can see a very good demonstration of these in the channel physics demos okay but why does this happen why are the colors quantized they have no goddamn clue part of the problem is the complexity of the spectral lines I mean can you see a pattern in the spectrum of iron no and if you say you can you are lying but the spectrum of hydrogen on the other hand is it still pretty complex but perhaps it's just simple enough that you can just plot the values and use brute force or I guess in this case brute thought to find an equation that just fits the data this is how Balmer was able to find an equation that fits many but not all of the spectral lines of hydrogen and then read bear came along and he found the general formula that correctly predicts all of the spectral lines of hydrogen but here is where it starts getting really funny this formula has two variables N1 and N2 and they have no idea what they represented honestly had no idea like finds general formula gives no interpretation of the variables refuses to elaborate leaves but wait it gets better do you know how many scientists want to have stuff named after them well it turns out that a bunch of people took reverse formula they gave one specific value to N1 and then they gave their name to the series of values you get by changing N2 like Balmer at least found his formula before real work all of these guys came after like Lyman my man you want me to learn your name just because you use a formula that already existed and this is a scam this is a scum and I don't know why anyone Falls for it they appear in textbooks they appear in Wikipedia why what's going on anyway it seems that boar was unaware of rayberg's formula there's a scene in which one of his friends comes and tells him about it and he gets really inspired and I always thought this was just part of the adaptation because Bohr was not living under a rock and everyone interested in physics at the time should have been aware of it right and so I went to the light novel which is a much closer adaptation to the source material and it has the same scene so I guess that yeah it is true boar was unaware of reverse formula but then when someone talked him about it and they explained how it worked boar had this moment of epiphany of Revelation where he understood what the variables in Reverse formula meant they represented the different orbits in the hydrogen atom let's say we have a hydrogen atom in an electric field this electric field adds energy to the electron which becomes potential energy pulling it away from the nucleus but it also becomes kinetic energy making it go faster let's say the electron ends up in orbit number nine this orbit is stable but it is less stable than lower orbits so at some point the electron will fall from this orbit down and down until it stops at a lower orbit say orbit number two but it doesn't just stop it's like it crashed against a wall and this crash creates vibrations in the electromagnetic field which becomes a photon of light and the energy of this Photon will depend on the different energy between the orbit 9 and orbit 2. giving us the ninth number in the Balmer series finally poor could understand the true meaning of redberg's formula it tells you the frequency of light an electron will emit when moving from orbit N2 to orbit N1 if you multiply by the speed of light this explains why elements can only emit some colors of light when their electrons are excited by Electric shocks light is quantized because the orbits are quantized from here it is relatively easy to find the formula for the total energy of each orbit it's just this en that is the energy of orbit number n is equal to E1 that is the energy of the first orbit over and square pretty easy but I want to focus on this n number here this N is a quantum number in fact it is the principal quantum number you'll see why in a bit and do I think that this is just like a human invention we came up with to just keep track of the orbits but no in a very very real sins nature is looking at this number as well and like nature would agree with us that this is the first orbit that this is the second one you'll see you'll see it's it's very cool when you when you see the realness of quantum numbers but that will have to wait because this emission of quantized light also works in Reverse let's say that we have an electron in orbit number three and then a photon comes along with enough energy to take it almost to orbit number five but not white well then the electron will simply not buy with it it will not absorb the photon and no it cannot take some of the energy and go up to orbit number four and leave the photon with less energy that cannot happen is an All or Nothing deal as real as it may sound nature simply doesn't allow electrons to end up between allowed orbits also notice that the orbits exist even if they're empty see in summary there are three kinds of Spectra the first one is thermal Spectra which are continuous because heat makes atoms vibrate in a continuous range of frequencies at which point they emit light in discrete particles or okay well technically thermal Spectra are also quantized but what happens is that the separation between the different energies is so small so mini skill that for practical purposes they are continuous meanwhile emission Spectra are quantized because electrons can only move between quantized orbits with very specific energies finally if you shine a continuous Spectrum on some kind of substance it will absorb some colors of light more than others depending on the allowed orbits and this will create an absorption Spectrum which is the exact negative of the mission Spectrum based on these new ideas about light and the structure of atoms Bohr was able to perform experiments that proved hydrogen only had one electron helium have only two and most elements have a number of electrons that is roughly equal to half of their atomic masses when measured in atomic mass units it's crazy to think there was a time when people didn't know that hydrogen only has one electron and today everyone just gives it for granted right because everyone knows hydrogen only has one electron right maybe this is like that xkcv comic about how we overestimate how much people know about our special interests hmm anyway so using this new model Bohr was able to propose a simplified version of how atoms come together to form molecules by combining the orbits of their electrons okay so to recap at this point Borg have been able to explain why absorption and emission spectrums are quantized he had managed to explain the structure of hydrogen and helium he had been able to explain the number of electrons of most elements and she had developed a basic model of how molecules are formed and yet no one took him seriously okay some people took him seriously mostly his friends the friends of Rutherford and Song Jong scientists here and there but for the most part people were completely unconvinced violating electrodynamics was just too much of a deal breaker board insisted over and over that his Fury was at work in progress but I get impression that people just didn't want to hear any more of it actually one of his karsh's critics was Thompson he went from Senpai to yandere perhaps frustrated that he wasn't able to recognize Boar's potential but Bohr have to continue and at this point he noticed something strange about the speed of electrons and he wasn't the first one a mathematician named John Nicholson had also studied spectral lines and come to the same conclusion the total energy for any object like an electron is divided into two Parts some of it is potential energy which in this case is given by the distance between the nucleus and the electron and some of it is kinetic energy which is given by the amount of movement in this case the angular momentum of the electron around the nucleus but notice something interesting the fact that the total energy is quantized must mean that these two forms of energy are quantized too that's interesting but wait the formula for the total energy doesn't make sense if n is equal to zero this means that nature simply doesn't allow electrons to have less than this energy and cannot be smaller than one and so for that reason electrons cannot get closer to the nucleus than the radius of these sphere this is why electrons don't spiral down towards the nucleus although at this point I must add that today we have improved bores interpretation of the sphere because back then they didn't know about Quantum uncertainty what happens is that you can never know the position of something with 100 certainty so we know that the electron must be near the sphere but perhaps more to one side or to the other now at this point you could say something like okay you've convinced me there's experimental evidence that there's a minimum amount of energy for electrons in atoms but why is there a minimum amount and why should that minimum amount be 13.6 electron volts like why and okay the answer to that question is that Quantum field Theory can tell us it can show us that there should be minimum values for some properties of Nature and we'll see that in a future video but at the same time Quantum field Theory cannot tell us what those minimum values should be those are just constants of Nature and who knows maybe there's a deeper theoretical explanation for the constants of nature but maybe there isn't maybe when the universe was created those values were set out at random who knows but yeah it is the combination of those two things this begins to repair the relationship with electrodynamics because it's not that its laws are wrong they are right an electric charge in moving in circles will emit light you just as long as it has enough energy to do so and it just so happens that the minimum energy is not at zero but anyway let's go back to war because he was able to calculate the radius of this sphere and from there he was able to calculate the minimum amount of angular momentum the electron needed to stay in that sphere and that amount of angular momentum happened to be equal to Planck's constant over 2 pi all squared isn't that weird this constant that was previously telling us the amount of energy in light is now also dictating how electrons move now this is the minimum amount but of course electrons can have more than that just not too much in order to keep the orbit stable so for example if an electron is in the third orbit the maximum amount of angular momentum it can have is 12 times larger than the minimum amount in general all the allowed values for angular momentum are given by this formula where Corby L goes all the way from 0 up to n minus one so for the first orbit there's only one allowed value of momentum for the second one there are two allowed values for the third one there are three and so on look I told you that nature was looking at the quantum numbers too they are real also something very important is that you can have electrons with different values of angular momentum in the same orbit they have the same quantum number n but different quantum number core VL so let's call these different values of corvial sub orbits right the proofs of these facts about how quantum numbers work are beautiful and if you're weird like me quite fun but today I am your guide I am your SharePoint in this mountain of knowledge and my goal today is to take you to base Camp Spin and I can already see it behind the fog so we must not lose focus but if you want to explore on your own then I recommend you read one of my sacred texts introduction to Quantum Mechanics by Guru Griffiths he is as insightful as his wholesome and he takes a different route to get to speed through the forest of calculus but anyway going back to quantum numbers and orbits here we find a new question which is just now making me think I could have split this video into two videos anyway it goes like this so you can have more than one electron in the same orbit right okay so then why aren't all of the electrons in the first orbit because it is the most stable one right so that's it that's the question we will answer in what is left of this video please don't miss less than half an hour you know I don't okay so scientists begin suspecting that electrons weren't falling into those orbits because they couldn't in the same way that nature prevents electrons from ending up between orbits it prevents them from falling into orbits that are already full this means that there must be a limit to how many electrons can be in each orbit but they have no idea why there was a limit and the limits seem to be different for each energy level so for example the first orbit can hold only two electrons the second one can hold only eight electrons and the third one can hold I honestly I don't know the 14 I think so something like that the answer to this question is deeply related to the concept of suborbits uh but here I want to clarify that poor didn't discover suburbates or at least he didn't discover them alone like a true main character he has begun to a mass a full Harem of collaborators now I cannot name all of them but some of them were both gang Paulie Gregor venzel Varner Heisenberg Otto lapore a Walter last name not approved for monetization Peter Devi William Lanes Walter corsel and those aren't like the most important ones those are just the ones that I thought about when I was writing the script so if I'm missing your your waifu or who's Bando the best boy the best girl like I'm sorry the point is that young scientists all over Europe were reading Boar's ideas and they thought yeah them electrodynamics and they began working on improving Bohr's Theory so it was an explosion of research and just in time because Borg was busy getting busy he got married he started a family he started a new University and it strikes me that he was a bit tired although funnily enough the leader of this new wave of scientists wasn't young Arnold somerfeld was like 20 years older than boar I cannot be bothered to look the actual number but the point is that Summerfield was inspired by Boris ideas and so he began to teach them to his students and to develop them himself in fact he is the one who came up with the idea of the quantum number corviel in the following sections as I describe how new developments were made just keep in mind that this was a team effort and it becomes very difficult to untangle who did what especially because more than once there were several people who got to the same answer independently okay so this is the final stretch this is the final fight before the final boss of this level people were finally ready to discover spin remember spectral lines well there's one more observation they have done about them the semen effect it goes like this you excite the atoms of a gas to see its emission spectrum fine but then you apply a magnetic field what you will see is that the lines of the spectrum are splitting to understand what was happening we have to remember how magnetic fields work the way they work is that if you move at 90 degrees from the magnetic field you will feel the maximum Force but if you've moved parallel to the field you won't even notice that it is there and every other orientation feels a force proportional to the sign of the angle this means that electrons can experience different forces depending on how their particular suborbit aligns with the magnetic field and this gives the electrons in that suborbit different energies however since the orbits can be oriented at any angle this should widen the spectral lines creating a sort of gradient but since the splitting of the lines is quantized then the orientations of the sub orbits must be quantized too we can analyze the alignment of the sub orbit by focusing on its axis of rotation and the angle it makes with the axis of the magnetic field although to make things easier instead of saying magnetic field every time I'm just going to call it the set direction right or well I know some people call it C said I never know which one it is anyway set Direction okay so we can do a projection of this axis of rotation onto the set axis and we get a new Vector this Vector represents how much angular momentum there is in the set Direction and since the orientation is quantized the length of this Vector is quantized too and it turns out to be just a number times Planck's constant over to Pi and this new number n is our third quantum number and this number cannot be larger than core VL and in fact it goes from negative core VL all the way to positive Corey L the negative values represent when the axis of rotation is pointing down and the zero represents when there is absolutely no angular momentum in the set Direction before moving on something I want to clarify is that these different orientations of the suburbates already existed before the magnetic field came along all the magnetic fields did was just to give them different energies also remember how there was a limit to how many electrons could be in each orbit before that limit seemed very random but now thanks to quantum number n they could see that a maximum of two electrons could share the same n l and m and these will be very important to explaining why the number eight is important in chemistry although we'll see that in just a moment okay I know this has all being very abstract but now that scientists knew the energy momentum and orientation of the different sub orbits they could actually figure out their shapes and they turned out to be pretty weird nothing like the planetary orbits Rutherford had imagined electrons can always have the minimum amount of angular momentum regardless of in which energy level they are and if they do their suborbit will look like a sphere just a sphere although of course this sphere will be larger in larger energy levels but the interesting thing about this particular suborbit is that it has only one orientation I mean it's a sphere right you can turn it around all you want it's still just a sphere but if electrons have more angular momentum then their sub orbits take these Weebly wobbly shapes but strange as they might be they were nothing new these shapes are given by two functions one tells you the radius and the other tells you the angle if we look only at the angular component we get a set of functions mathematicians have already discovered a long time ago when they were studying the different ways that a sphere can vibrate these are known as the spherical harmonics huh Harmony spheres I wonder if the ancient philosophers were onto something when they talked about the Music of the Spheres but instead of the music being in the heavens above it was inside them and inside everything else okay let's move on before I'm accused of mysticism notice something interesting here we are using the equations for a vibrating sphere to describe the position of an electron we are using the equation of a wave to describe a particle does that sound familiar hmm I wonder if it has any deeper meaning this is Science Center welcome back to Science Center and we see board he is been following all of these developments about the orbits and suburbits and he makes a very interesting observation to their referee he says that if electrons can move between different orbits and sub orbits by absorbing or releasing photons with the difference in energy shouldn't the same be happening to angular momentum that's right John because when the electron was in an orbit that had larger anger momentum and then ends up in a lower orbit with less momentum that momentum not had gone somewhere and being realistic the photon itself is the only place that momentum could be you're absolutely right but now we see Boris he's going he's going he's going he fumbles it he says there's no way to measure the angular momentum of light and he does same thing to explore the idea any further oh my God so frustrating he was this close to discovering spin but I guess the solution to the problem is always obvious when you already know the solution moving on at this point it finally became possible to explain why the number eight is so important in chemistry although I am compelled to point out that through some Arcane means bore had already discovered this without using the orbital quantum numbers and I don't understand how he did it I just keep finding mentions of it in different places of the Lord but no explanations so I don't know how he did it and now neither do you you are trapped in here with me but but seriously like if anyone knows how boar figured this out please let me know the point is that we can use the orbits and suborbits to explain why the number eight is so important in chemistry but to understand this explanation first we must talk about the quantum numbers so sit down this will be difficult to hear look KIRO uh your mom and I know that the total energy doesn't match perfectly with the quantum number n it did at first but as you have more electrons with more suborbits and more momentum eventually think things get just more complex orbits start overlapping it's not your fault it's not your fault and I want you to know you can still use the same formulas for the quantum numbers L still goes from 0 up to n minus one it's just that eventually you have electrons moving so quickly they have more energy than electrons in the next orbit and in general this happens when you feel the third orientation of the second suborbit I know this might be confusing for a child but look it's just two electrons here to here to here and to here do you know how many electrons that is Keto eight and so if you want to complete an electronic orbit in this life your best hope is just making it this far because anymore and you have to start a new orbit before you can come back and this just makes the electron less stable I'm sorry also we are getting other words now it's 1922. that's right there was a time skip reitburg is dead there was a World War and everyone is more about us now Summerfield glascaro his face with a sword that's actually true boar compile the work he and his collaborators had done during all of this time and he presented the results in the both scale lectures these lectures were like the Woodstock of atomic physics in the 1920s a landmark in the history of Science in which war presented and improved and unified theory of atomic structure as he spoke the haters were banished to the shadow realm no one could deny this was a better description of reality and the finishing blow was correctly predicting the mission Spectra of nearly all the known elements this was such a roaring success it came to be known as course festival and that's not a joke that's actually how they called it strictly speaking these new mechanics that use quantum numbers these quantum mechanics if you will still was incompatible with electrodynamics and incompatible with even classical physics as a whole but now it has become clear that it wasn't because quantum mechanics was wrong but because classical physics is just another model another approximation of reality one that only works at large scales with billions of atoms but despite all of this there were still two big problems with quantum mechanics two observations it just couldn't explain one of them was the anomalocyman effect which had been known for decades and the second one was the steeringer lack experiment which was discovered just a few months before birth Festival let's begin with a sternger life experiment the they wanted to find more experimental evidence for the quantization of angular momentum and so they wanted to send a beam of atoms through a magnetic field because these atoms should move in different ways depending on the orientations of their suborbits but first they needed to know the Precision of their beam of atoms and so they needed to launch something that wouldn't be affected by the magnetic field and they decided to use silver the explanation is really easy we just have to look at the orbits of silver which chemists write in this very confusing way well don't worry I'm gonna translate it for you each of these blocks represents a group of electrons with a certain energy and they are written in order of ascending energy the first number in the block tells you in which orbit these electrons are and then the letter tells you how much momentum they have so for example s corresponds to curvy L equal to zero P corresponds to core L equal to 1 and D corresponds to curvy L equal to 2. finally the second number tells you how many electrons are in this group for example we see that in this group sp there are six electrons which makes a lot of sense because P corresponds to curvy L equals to 1 which means that there are three possible orientations and in each orientation you can have two electrons for a total of six electrons now we learned from the normal semen effect that electrons feel different forces depending on the orientation of the sub orbits with the magnetic field but check this out all of these orbits with m equal to 0 feel known force and for each group of electrons that feels force in One Direction there is another group that feels the same Force but in the opposite direction they end up pulling on the atom in different ways and so they cancel out making silver immune to magnetic field and in fact you can test this for yourself just take a magnet and bring it close to a piece of silver you will not feel any Force although silver does have one lone electron in orbit number five it has no one to cancel it out oh but wait it's fine because its n is equal to zero so it will not be affected by the magnetic field right I mean there's no reason why it should be affected and yet and yet when this beam of silver atoms pass through the magnetic field exactly half went up and health went down I want you to appreciate how much of a mind this was exactly exactly how went up and exactly half went down how is that even possible like if you were trying to do that on purpose exactly how the atoms will be extremely difficult like how like how could they be exactly aligned and in both directions to this specific magnetic field like who told them like the atoms didn't know presumably the atoms were aligned in random directions okay so at this point is turn anger luck decided to just rotate the magnet so that it would instead of being pointing up it would be pointing to the sides and guess what exactly half the electrons win right and exactly half went left it's the other way around I think I have mild dyslexia anyway but look at that he's like what is going on like how how do these electrons know in which direction they are going to be measured and how do they know to go exactly half each way then sterlinger like started doing successive measurements first they measure it up and down exactly half going in each Direction then take the ones that were already measured and measure them left to right and again exactly half go in each Direction but then they started trying some other orientations at different angles and it wasn't exactly half in fact they found the proportion of atoms that went in each Direction was proportional to the cosine of the angle between the different measurements somehow measuring angular momentum is changing it and that was the answer the act of measuring this angular momentum was changing it and sure that seems obvious to us now in the present but it's only obvious to us now because of all the work these people did in the past because back then Stern and Gerlach had no idea why this was happening and so they joined this long tradition of making experiments and getting results you simply cannot explain but as you can see from this video This Club was very crowded and even more thanks to the anomalousy man effect remember how people were looking at the semen effect well it seems that these nerds were just sticking any substance they could find into their spectroscopes and eventually they started finding substances whose lines were splitting more than they should want to mechanics could explain how these lines were splitting into three five seven and so on but instead these lines were splitting into 6 10 14 even the first suborbit the sphere The Prodigal Son the superbit with only one possible orientation it was splitting into two boar was finally stomped and so was everyone else I mean there were no more energy levels no more values of angular momentum no more orientations and yet the lines just kept on splitting this problem went unsolved for years until oh look who it is the boy's savior balls gang Paulie I'm gonna be honest with you I don't like poly he wasn't a bad person he was fine it's just that he was this rich kid who was also a genius and to whom everything just came easy when he was 18 he wrote a paper on general relativity and when Einstein read it he said that Paulie knew more about relativity than she did I mean if Einstein is a Mary Sue then Paulie is every black-haired isekai protagonist ever combined he was even born in the year 1900 the same year Planck discovered the photon he was literally born along with the quantum theory eventually Paulie got interested in the animal semen effect and the sternger Lash experiment and he solved it using the trick that would define his career making up not enough quantum numbers make one up not enough particles make one up the integrals need an extra term to converge make it up and it worked every time in this case Paulie just looked at these experiments and he said okay so we need a new quantum number right and it needs to have two possible values to explain the splitting of the spectral lines and the silver beams but also the value of this quantum number depends on how you measure it okay done here it is this is my new quantum number and before you ask no he had no idea what this number could represent much like River he found a mathematical solution before knowing what it meant physically in fact he went so far as to say that maybe this quantum number have no physical interpretation that this was a property of particles that could only be understood mathematically but then a student called Ralph chronic had an idea he went to Poli and I imagined their conversation went something like this I think the results of this sternger lash experiment could be explained if the quantum number you discovered is some kind of angular momentum in the last suborbit of silver oh yeah and pray tell how would you change the orientation of a sphere well you can't that's why I was thinking that maybe in addition of spinning around the nucleus electrons are also spinning over their own axes like the Earth spinning over its own axis uh listen uh crunk is it chronic whatever in order for electrons to admit the light we observe in the anomalocyman effect they would need to be spinning over their own axis faster than the speed of light which is impossible I should know that I know more relativity than Albert Einstein in summary is not that your idea is not right it's not even wrong but it's fine go away and sin no more huh the spinning over its own axis just like the Earth this planetary analogies just keep on coming don't they but in the end Paulie pulled a thumbs on and he this means a good theory just because it was incomplete thankfully George ulenbeck and Samuel goodsmith were outside police field of scorn and so when they got the same idea they were free to develop it and they concluded that maybe electrons weren't like racings they weren't solid spheres of some primordial substance with electric charge but rather they were just points points without Dimensions that contained some amount of mass electric charge and yes even angular momentum which is is weird it's weird to think about this dimensionless points that contained properties both nature doesn't care what we think is weird however credit where credit is due Paulie did admit he was wrong as any good scientist should even I both gang Paulie can't be wrong and then he continues to develop this Theory finding the poly Exclusion Principle and the poly matrices which we will derive from scratch in the next video I can deduce from the experimental observation that you are listening to this that you made it until the end of the video oh my God so long and you made it till the end thank you thank you so much and if you enjoy watching videos like this perhaps you would enjoy working on a video like this with me the next video is all about mathematics and I'm gonna need so many animations and I'm really bad at making them so if you can make animations like these ones please send me an email along with some of your animations and let's see what happens and finally my B best and deepest thanks go to my patreons especially too automaticum Carlos all my patrons thanks a thousand times thanks a million times

Channel: Highly Entropic Mind

Views: 100,389

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Id: AToXA0Molig

Length: 68min 16sec (4096 seconds)

Published: Tue Jun 20 2023