Particle Physics - A-level Physics

We talk about charge a lot in physics. Now we haven't always known about electrons. The first evidence of electrons was cathode rays, but we now know what the charge of an electron is and we know what the mass of an electron is, but there was a time when we didn't know either of those things individually. The first thing that we knew about electrons was something called specific charge. Specific charge is equals to charge divided by mass, also known as charge to mass ratio. Charge has the unit coulombs, mass has the unit kilograms, so therefore the unit of this is going to be coulombs per kilogram. In other words, how much charge does a kilogram of a certain type of particle have? If we know that electrons and protons have the same charge, for an electron, that's equals to E over M. Like I just said, we knew the specific charge of electrons before we knew each of them individually. Once they knew one of these things, then they could use it with a specific charge to find out the other. If you really want to know about that, have a look at my turning points discovery of the electron video. But for an electron specific charge, it's going to be 1.6 times 10 to the minus 19 divided by its mass, which is 9.1 times 10 to the minus 31. To 3 sig figs, that gives us 1.76 times 10 to the 11 coulombs per kilogram. That's a massive number, but that makes sense, doesn't it? If we had a kilogram of just electrons, then of course they would all together have a massive charge. For a neutron, it's obviously zero because the charge is zero. But for a proton, also known as a hydrogen ion, then we know that it's going to be the same charge, 1.6 times 10 to the minus 19, but it's going to be divided by this bigger mass. That gives us 9.58 times 10 to the seven coulombs per kilogram. So electrons have a higher specific charge, charge to mass ratio, than protons. So if you had a kilogram of electrons, it would have a much bigger charge than a kilogram of protons. So you need to know how to calculate specific charge, but apart from that, it's not that important until we look at charged particles moving in electric and magnetic fields. If you want to know more about that, then have a look at my videos regarding those. What is charge in reality? Well, it's just a number that we assign to something because we can see certain particles be affected by certain forces. So if charge is just basically a number that we assign to particles, are there other numbers that we can assign to? Or rather, are there other numbers that we must assign to particles? The answer is yes. Now it turns out that energy and matter are interchangeable. Specifically, when we talk about matter, we're talking about particles with mass. When we talk about energy, strictly speaking, we're talking about photons, EM waves. Now, because energy can be turned into matter, photons can spontaneously turn into mass. More on that a little bit later on. That means that if we create some particles, similarly to conservation of momentum when we have recoil, there must be things about the bits of matter that cancel each other out, and that is true. Now we're talking about matter and antimatter. From there, we can start splitting our matter and antimatter, our particles, into different categories. The first split is into hadrons and leptons. Leptons are fundamental particles, at least as far as we know. In other words, they can't be subdivided into smaller particles. An example of a lepton would be an electron. Hadrons, though, can be split into smaller particles. And what we found out through the Large Hadron Collider and other such experiments, we find that they're made up of things that we now call quarks. But because hadrons are made up of quarks, there's actually different ways that you can arrange quarks. So we split hadrons into two more subcategories. First one we call baryons, and they're made of three quarks. And the other type we have are mesons. Now they're made up of two quarks, but in order for them to work, they need to be made up of a quark and an antiquark. We'll talk about what that means in a minute. An example of a baryon would be a proton or a neutron. Mesons, we'll look at some examples later on. Like I said, an example of a lepton would be an electron. I'm gonna put E minus there. So we're not only talking about particles like electrons and protons and neutrons, we're actually talking about their antimatter equivalents. And we call these antiparticles. Antiparticles are exactly the same as normal particles. They have the same mass, but they have the opposite. And we have four things. We have charge, lepton number, baryon number, and something called strangeness. So this here is what all of particle physics or quantum electrodynamics, QED for short, is based on. Antiparticles are written with either the opposite charge to the normal particle or a hat on top. For instance, a proton is a normal particle, that's matter. It's antiparticle equivalent is a P with a hat on top. That's an antiproton. An electron, we write as E, but now we're going to write it with an E minus. Now we could have an E with a hat on, but that's not how we write it. We write an E plus. We could call this an antielectron, but it has its own name. It's called a positron. It has the same mass as an electron, but its charge and all its other numbers are the opposite to that of the electron. Like we said just now, energy and matter are interchangeable. We see that happening in the real world. So what happens when we get matter turning into pure energy? What we get is annihilation. It's when a particle and its corresponding antiparticle collide and the mass disappears and it all gets turned into energy. So this can happen with an electron and a positron. And because they are antiparticles of each other, they annihilate each other and what we get are two photons being made. The opposite of this or nearly the opposite of this is pair production. But of course we don't have two photons making two particles. No, we only have one photon spontaneously turning into a particle and its corresponding antiparticle. In both these cases, energy has to be conserved. But hang on a second, it seems like we're getting energy from just mass. So hang on a minute, that must mean that there must be energy in the mass of this electron and positron. And that is true. How much energy is that? Enter Einstein's most famous equation of all, and that is for rest energy. In other words, mass energy. Energy stored up in the mass of a particle. If you destroy that particle, get rid of its mass, how much energy would that create? That's equals to E equals MC squared. I'm sure you've all seen that equation before. Mass being the mass of a particle in kilograms, C being the speed of light and we square that. Here we have a particle and an antiparticle colliding, annihilating and making two photons. What energies do we have going in? Well, we have their rest energy from their mass going in, but also they're travelling quite far. So they also have kinetic energy. So it's fair enough to say then that the energy of the photons, total energy of the photons, has to be equals to the rest energy of the particles plus the kinetic energy. Now the energy of a photon is equals to HF. F being frequency, H being Planck's constant. But because we have two photons being made, we have to put a two in front. Two lots of that. Rest energy, well, we've got two particles. So it's gonna be two MC squared. And then we have the kinetic energies as well. We're going to assume that they are travelling the same speed, so they have the same kinetic energy. So I'm gonna say two lots of half MV squared. So that ends up being just MV squared. That way you can figure out what the frequency of the photons is made if you know what particles are colliding and with what speed. For pair production, however, we only have one photon going in. So it's gonna be energy of photon makes the rest energy of both particles plus any extra energy that's left over is given to the particles as kinetic energy. So it's just gonna be HF, that's the energy of the photon, equals two lots of the rest energy plus two lots of the kinetic energy. Sometimes you'll be asked what is the minimum frequency or the minimum energy required to make two particles, to make a particle and its corresponding antiparticle. In that case, you say, well, I know there's not gonna be any kinetic energy left over. So it's just gonna be HF, energy of the photon, equals two lots of the rest energy. And that's it. Now in particles, we talk about the energy of individual particles a lot. So the thing is, is that that ends up being a tiny amount of energy for an individual particle. If we expressed energies in joules for particles, they'd end up being very small numbers, obscenely small numbers. We're talking of the order of 10 to the minus 17. So it's not really that useful to talk about energy in joules. So we have another unit for energy when it comes to particles, and that is the electron volt. Now let's just think about our definition for voltage. Voltage is energy divided by charge. So for an electron, that's going to be energy divided by E, the charge of an electron. Therefore, energy, if we rearrange it, can be given by its charge times a voltage. What is this voltage? So one electron volt is the energy of one electron accelerated through a PD, a potential difference of one volt. So like I said, you don't really need another definition, but you do need to be able to convert electron volts into joules. So what is one electron volt? One electron volt is equals to 1.6 times 10 to the minus 19 joules. So the conversion factor is the charge of an electron. Quite often people get confused as to whether we times or divide by this conversion factor of 1.6 times 10 to the minus 19. To get from electron volts to joules, electron volts are small and joules are big. So we should always have fewer joules than electron volts. That's a good way of remembering. You've always got fewer joules. And because 1.6 times 10 to the minus 19 is a very small number, to go from electron volts to joules, all we have to do is times by 1.6 times 10 to the minus 19. Going from joules to electron volts, it's the other way around. We want more electron volts, so we divide by 1.6 times 10 to the minus 19. So let's say that we've got something, doesn't necessarily have to be an electron. Let's say that we do have an electron that has two electron volts of energy. To get to joules, we want fewer joules, so we times by 1.6 times 10 to the minus 19, and that gives us 3.2 times 10 to the minus 19 joules. Sometimes, instead of electron volts, you'll be given mega electron volts because that's an easier number to deal with, mega being times 10 to the six. So this is 1,000,000 electron volts. So if we go from mega electron volts to joules, so to go from mega electron volts to joules, we could times by 1,000,000 first to get the number of electron volts, or we could just cut out the middleman and instead times by 1.6 times 10 to the minus 13, and then vice versa going the other way. So we always have to convert energies into joules first before we use them. So chances are, more often than not, you'll get an energy in electron volts or mega electron volts, and then you have to convert that into joules. And usually, that energy ends up being the energy of a photon, or it can be the kinetic energy of a particle. And so then, once you've got it in joules, you can pop that number into the necessary equation that you need to use involving energy. So we know that mass is conserved in any interaction between particles, but also charges as well. But we've got other numbers to take into consideration as well. Lepton number is also always conserved. Barrier number two. Strangeness is a weird one, hence the name. It's sometimes conserved. We'll talk about when it is and isn't a little bit later on. So let's have a think about lepton number then. Only leptons have a lepton number. That makes sense. Electron is the prime lepton, so it has a lepton number of one, plus one. Positron is its antiparticle, so it not only has the opposite charge, but also the opposite lepton number. Protons and neutrons aren't leptons, so they've got a lepton number of zero. It's similar for baryons. Baryons have a baryon number. Protons are plus one. Neutrons are plus one. Their antiparticles have the opposite charge. Well, it's still gonna be zero for a neutron, but they also have the opposite baryon number. So why on earth do we need these? Well, let's have a look at a specific example. Let's look at beta minus decay. Carbon-14, six protons, eight neutrons, turns into nitrogen. That's because one of the neutrons has turned into a proton. And we get a beta particle, which we know is just an electron, being chucked out. Let's look at the lepton numbers of everything involved. What's the lepton number of this carbon-14 nucleus? Well, it's just protons and neutrons, so zero. What about this nucleus? Again, zero. The lepton number of a beta particle, an electron, is one. But hang on a second, we said that lepton number must be conserved. So we need an antilepton with no mass too. And it can't have any charge either. They said, right, there must be a particle here with no mass, no charge, but it must have an lepton number of minus one. So they said, right, we're going to call this an antineutrino. If it's an antilepton, then it's going to have a lepton number of minus one. So now, lepton number is conserved in this beta decay. So let's talk about hadrons. Now, if you remember, hadrons are subdivided into baryons and mesons. Like we said, baryons, it turns out, are made up of three sub-particles, three quarks. Now, if this is a proton, then that must mean that its overall charge is equal to plus one. But if that's the case, if we've got three sub-particles, then the charge of these quarks must be split into thirds. Now, it could be that the charge of this is a third, third and a third, and they add up to one altogether, but that's not the case. What we find is that there are six types of quark that we can observe. And we give them different names. We call them up, down, strange, top, bottom, and charm. But we're not going to worry about top, bottom, and charm. For A-level, we only need to know about up, down, and strange. An up quark, just give it the letter U, its charge is plus two thirds. A down quark has a charge of a minus third. Turns out that a strange quark also has a charge of minus a third. Now, a proton isn't made up of any strange quarks at all. So can you figure out what combinations of up and down quarks we must have in order to equals plus one altogether? Hopefully, you've got this. An up quark is plus two thirds. Another up quark is altogether four thirds. And then if we have a down there, that's minus a third. Altogether, adding up to plus one. So that means that the quark composition of a proton is up, up, down. What about if we had a neutron instead? It's not made up of any strange quarks. So what combination of up and down quarks do we have to have in order to get to zero altogether? If you had up, down, down, you are absolutely correct. Plus two thirds, minus a third, minus a third. So the quark compositions of neutron and proton are NUD and POOD. That's the way I remember it, the NUD and the POOD. Now, you can also have three quarks involving strange quarks as well. And they give you other hadrons, but their charges always have to add up to an integer. So zero, plus one, plus two, or minus one and minus two. If you wanted to make an anti-proton, all you have to do is have the anti-quark of all of these. That way, instead of plus two thirds, we've got minus two thirds, minus two thirds, and plus a third. They're just the opposite of their counterparts. Same for an anti-neutron. Any particle that's made up of three quarks is a baryon. Mesons, on the other hand, are made up of two quarks instead. Now, if we have a baryon number of plus one for both protons and neutrons in any baryon, then that must mean that all quarks have a baryon number of plus a third. If that's the case, then anti-quarks must have a baryon number of minus a third. And if mesons have a baryon number of zero, because they're not baryons at all, they're mesons, then that must mean that we have a quark and an anti-quark. Again, you can get all sorts of combinations of these quarks and their anti-quarks. Let's look at one in particular. Let's get an up quark. So that's plus two thirds, charge, and an anti-down. Now, down is minus one third, so this is gonna have plus one third. So overall, whatever this particle is, whatever this meson is, it's gonna have a charge of plus one. But because we have a quark and an anti-quark, its baryon number is gonna be equal to zero. And that's good, that's what we wanna see. This is actually called a pion, specifically a pi plus meson. All of these different particles have several crazy names. If a meson has a strange quark in, so let's say that we got our up again, this time we have an anti-strange. And again, that's gonna be plus one third. It's very similar to this one. Same charge, baryon number of zero, of course. This is called a kaon, specifically a k plus meson, or kaon. You can also have k minus, and you can have k zero as well. Now, let's talk about the different forces that we have in the universe. We have electromagnetic forces. What does that affect? Any charged particles. No matter what they are, if they have charge, positive or negative, they're gonna be affected by electric fields and magnetic fields. Now, this can be attractive or repulsive. You know that if you've got positive and negative, they'll be attracted towards each other. Positive and positive repel, et cetera. We also have the force of gravity. What does it affect? It affects all particles that have mass, so in other words, all matter. It's always attractive. Gravity never pushes things away. There's a problem when it comes to nuclei. Let's say that I have a nucleus here with a bunch of protons and neutrons together. Now, we know that gravity is going to pull ever so slightly in like that. It's gonna pull the particles together, the nucleons. The thing is is that positive and positive charges, they're going to repel each other, so they should just fly apart from each other due to the electrostatic force. Should repel the protons. But that doesn't happen. Nuclei stay together, but that isn't due to gravity, so there has to be another force keeping nucleons together inside of a nucleus, some unknown force that attracts nucleons together. And this has to be pretty strong, so we do call it the strong nuclear force. But here's the thing, is that the nucleus also doesn't implode. So whatever force we have here stands to reason that it has to attract nucleons together, but once they get too close together, then it stops bringing them closer. So we say it's attractive and repulsive. Weird. At what point does this necessary strong nuclear force become repulsive instead of attractive? If I draw a graph of the strength of the force against how far away nucleons are, what we find is that nucleons have to be very, very close together before the strong nuclear force starts acting. So we are talking about times 10 to the minus 15 meters. That's also known as femtometers. This incidentally is why you have to have nuclei with very high energies in order to get them close enough to get within this range for the strong nuclear force to take over and for fusion to happen. So what we see is that if we get closer and closer, these nucleons get closer and closer, what we find is that it does attract nucleons below about three or four femtometers. But then once they get too close, then it actually becomes repulsive. This happens at about 0.5 femtometers. That means that its range is below three to four femtometers. But then we know that it's attractive above 0.5 femtometers, but it's repulsive below 0.5 femtometers. So when we have a nice stable nucleus, it means that the attractive force of the strong nuclear force balances the electrostatic repulsion of the protons in the nucleus so we get no overall force. Incidentally, this is why we need nuclei with very high energies to fuse because they need to get close enough to overcome their electrostatic repulsion and get close enough for the strong nuclear force to attract them together, to fuse together. Now talking about particle interactions, having two particles just coming into contact with each other and maybe changing can be awfully confusing. But Richard Feynman, one of my favorite scientists, still around, came up with his own diagram to make things simpler. Called it the Feynman diagram, obviously. Now we draw it in 2D, but you must know that it only really has one axis and that's time going upwards. Let's do a beta decay, beta minus decay. We know that for beta decay to happen, what happens inside of a nucleus is a neutron turns into a proton. So what we're gonna do is have a neutron going off into a proton. And we know that during that process as well, we have an electron that's given out, or beta minus. And we also said that we have to have an antineutrino being made as well in order for lepton number to be conserved. Now technically, this should be an electron antineutrino because it's involved in an interaction which involves an electron. We give it the subscript E. You can also have muons, which are another type of lepton, basically a heavy electron. If that was the case, if a muon was being made, then we'd have a muon neutrino. We'd just have antineutrino with a little mu. Now technically, this arrow should be going backwards because of reasons, but we're not gonna go into that. But if you did this in your exam, then you'd still get the mark. Now in order for our QED model, that's our purely particle model of the universe to make sense, then even forces need to be represented by particles. So how do we explain forces in terms of particles? Well, we say that when objects or particles do interact in any way, shape or form, the momentum that's transferred, which of course is to do with force, is supplied by something called a gauge boson. The gauge boson is different for each fundamental force. And with Feynman diagrams, we always draw the gauge boson as a wiggly line, which doesn't have an arrow on it. So there has to be some source of force going on here. Is it gravity? No, that doesn't change neutrons into protons. Is it a strong nuclear force? No, because it involves things that aren't to do with hadrons. We've got electron and antineutrino. Is it electromagnetic? No, because we've got a neutron coming on, which has no charge. So actually we are introducing a new force. The weak nuclear force is involved in interactions involving leptons. Whatever this thing is here, it's actually taking negativeness, negative charge, away from the neutron to leave it positive. And then it produces an electron and an antineutrino from there. So we know whatever it is has to be negatively charged. We call this a W minus boson. So whenever we have an interaction involving this new weak nuclear force, if there are leptons involved, then it has to involve either a W minus or a W plus gauge boson. Now, technically there is one more as well. That's the Z zero, but you probably won't come across that one. To be specific, the weak nuclear force is involved in interactions involving leptons where leptons are changed, annihilated, or created. Because as we'll see next, if we have two electrons that are coming towards each other and they repel each other, but they both stay the same, then again, there must be some sort of particle, some sort of gauge boson that is involved in that force. That's actually a photon, or rather a virtual photon. Now, theoretically, the gauge boson for gravity is the graviton, but we haven't really detected that yet. Does the strong nuclear force have one? Well, yeah, but it's never involved in interactions like this where we can draw a Feynman diagram. Bit of controversy with this one. You ask some people, they'll say that the pion is the gauge boson for the strong force, but nowadays it's another particle which is given another name, which is called the gluon. Gluons are the things that keep quarks together inside of a baryon and a meson. So whenever you draw a Feynman diagram, all you have to do is make sure that at every single junction, charge, lepton number, and baryon number are all conserved. Incidentally, for strong interactions, that basically means no leptons involved, strangeness is conserved. And it turns out that a strange quark has a strangeness of minus one, anti-strange has plus one. An example of this is if maybe you had a kaon turning into two pions, that can happen. Kaon is a meson turning into two other mesons, no leptons involved, so therefore we know that strangeness must be conserved. So let's use this idea of conservation of charge, lepton number, baryon number, and sometimes strangeness to predict whether an interaction is allowed or not. What if we had a proton and an anti-neutrino interacting and they theoretically make a neutron and a positron? Let's check charge first. Proton has plus one, anti-neutrino has zero, neutron has zero, positron has plus one. Charge checks out. What about baryon number? One plus zero goes to one plus zero. Baryon number checks out. What about lepton number? Zero plus minus one, an anti-neutrino is minus one, goes to zero plus minus one. Yep, that all checks out. And what about strangeness? None of these things are strange, so it's just gonna be zero all the way, so that is conserved. All four of these things are conserved, so therefore this interaction is allowed. Incidentally, if this was a mu instead of an E here, this would make it an anti-muon neutrino, and so that wouldn't work. And so that wouldn't be allowed because we haven't got a muon being made. Let's have a look at another one. Here we have a pi plus meson decaying into a muon plus a muon neutrino. So let's check all of these numbers. So it turns out that a pi plus meson has a strangeness of zero, and these are leptons. They can't have strangeness. So let's check charge. Plus one goes to plus one plus zero. That checks out. Barrier number, zero, zero, zero. That checks out because that's a meson. These are both leptons. What about this one? That's gonna be zero because, again, that's a meson. And we have a mu plus. Because it's a positive lepton, it's gonna have minus one as its lepton number, and then we have plus one for a neutrino. So minus one plus one equals zero. That checks out. So that is also allowed. Let's look at something called electron capture. So when a proton and an electron interact, that turns into a neutron. And I'm gonna say that it makes an anti-electron neutrino as well. Let's check our conservation rules to see if this all checks out. So charge plus one plus minus one. So that gives me zero. And that's gonna be zero plus zero. Yes, charge checks out. Barrier number plus one plus zero. Plus one plus zero. Yes, that checks out as well. Lepton number zero plus one goes to zero plus minus one. Ah, that can't work, can it? Because I have a lepton number of one beforehand and minus one afterwards. So therefore, this is not allowed. That cannot happen in real life. What would I have to do to change this to make it work? Well, this just needs to be a neutrino instead of an anti-neutrino. And then it would work. And let's look at one more. So I've got two protons interacting and they carry on as is. But they also make two K mesons as well. That can happen. If they've got lots of energy, then they can create rest energy in the form of new mesons from that energy. So let's check charge. One plus one goes to one plus one plus one plus minus one. So two goes to two and then they cancel each other out. Charge works out. Barrier number one plus one goes to one plus one plus zero plus zero because these are mesons. Yes, that works out. Lepton number zero all the way so we don't care because we don't have any leptons. So it seems like this is going to work out. But let's just check our strangeness real quick. Strangeness for protons is zero. Strangeness for a K plus meson because it has an anti-strange quark in it. That's gonna be one and then it's gonna be the opposite for our K minus meson. So look at this. Strangeness is conserved. So that must mean that the strong interaction is allowed. If this wasn't the case but all of those worked out then this would instead be a weak interaction. So that's particles done and dusted as fast as possible. If you think I've missed anything because you've gone really fast or you have any questions then please leave it in a comment down below. Please don't forget to leave a like if you found this useful and I'll see you next time.