AS Physics - Matter and Radiation

Ok, today we will be having a quick lesson on particle physics, because while that shit might seem easy, it'll sneak up on you, and you don't want to be let down by one of the most fun parts of A level physics, do you? Aight then, lets do this thing.

First off, the basics you should know. This is only a refresher post, or at least it plans to be, before I inevitably start digging into really interesting but ultimately irrelevant articles. Anyway. Atoms: Really fucking small. Made up of even smaller things called nucleons. These are your garden variety neutrons, protons. They make up the nucleus. Nucleon, nucleus, you see what they did there? Fucking genius. And of course we can't forget electrons. No, those little bastards will come into nearly every aspect of physics ever, somehow.

Now, we all know that protons, neutrons and electrons have charges 1, 0, and -1 respectively, right? Wrong, motherfucker. Those are relative charges. Relative to what? Doesn't matter, because you're now going to forget them. Same goes for those masses of 1, 1, and negligible. In fact, you can super forget them, because they are just plain wrong. No, now we break out the metric, wherein the proton has a charge of +1.6e-19 C (e means x10 to the power of...), an electron has the same, only -ve, and a neutron, well, the neutron still has 0, being neutral and all. Masses are 1.67e-27, 1.67e-27, and 9.11e-31 kg.

Isotopes you should know, atomic symbols you should know...ah, here we go. Basically, after realising that the nucleus was made up of nucleons, physicists considered than maybe something existed that was holding these things together, overcoming the electrostatic force that should be pushing them apart. A force, that effects the nucleons, a nuclear force, if you will. They called this the Strong Nuclear Force, and I have another fun little analogy for you. See, the force only actually works within 3-4fm, and beyond 0.5fm. It's like when you see someone from a distance, and you think "Hey, she's pretty cute. Attractive even!" But then you get a little closer and BLAM. She wasn't nearly as attractive as she seemed from a distance. She is actually kinda repulsive. Got it? Aight. Next song.

Ok, I'm pretty sure we all did radiation in GCSE. Here the only real difference is a small, but important addition to β radiation. When it happens, you get your high speed electron, your atom with +1 proton number, but you also get a neutral antiparticle called an antineutrino, specifically an antiELECTRONneutrino. Because it came with an electron. get it? These were discovered when scientists worked out that in β radiation, energy was being lost. This meant that either Conservation of Energy was bullshit, or another particle was being released here. They went with the latter, since the former had been so good to them in the past, but this went unproven for a further 20 years, when in 1956 there was executed the Cowan-Reines neutrino experiment.

Cowan and Reines used a nuclear reactor, as a source of 5×10¹³ neutrinos per second per square centimeter.

The neutrinos then interacted with protons in a tank of water, creating neutrons and positrons. Each positron created a pair of gamma rays when it annihilated with an electron. The gamma rays were detected by placing a scintillator material in a tank of water. As mentioned in the Discovery of the Nucleus article, and scintillator is a doohickey that flashes, scintillates, when it is hit by something,  in this case gamma rays.

However, this experiment wasn't conclusive enough, so they came up with a second layer of certainty. They detected the neutrons by placing cadmium chloride into the tank. Cadmium is a bitchin' neutron absorber and gives off a gamma ray when it absorbs a neutron.

Most of this paragraph has been ripped from Wikipedia

The arrangement was such that the gamma ray from the cadmium would be detected 5 microseconds after the gamma ray from the positron, if it were truly produced by a neutrino.

Music break! Have one of the greatest pieces of soundtrack music ever composed.

To be honest, you don't need to know most of that shit. I just think it's interesting to know where our ideas come from. Point is we now know that neutrinos are everywhere, even more so than my claimed ability to play the guitar. Billions of them bombard us EVERY SECOND from our very own sun. These are grim days, friends, where our closest ally could also be our gravest threat. But I know that together we can be strong. We will prev--Oh, what, they're harmless? Well never mind then. Next!

Ok, most people know of photons as particles of light. However this is, well, not wrong, just inaccurate. Photons are actually the name given to bursts of electromagnetic waves, which, as you know, visible light is an example of. The idea was established by Einstein when he was working on photoelectricity, where electrons are emitted from metal when light is directed at it's surface, but that's something for another time. For now all you need to know is that LASERS are beams of photons with the same frequency. Note that the energy of a photon is given by hf, therefore is the number of photons passing a point per second is given by n, then the energy per second, i.e. the power of the laser of the specific frequency is given by the simple equation P=nhf.

Ok, here we go. I like this bit because it features a bit of Bristol talent. On 8 August 1902, one Paul Adrien Maurice Dirac was born in Bristol. 26 years later, two years ofter receiving his PhD from Cambridge, the same Bristolian predicted the existence of antimatter. 20 years earlier, Einstein had shown his whole fast particle=more mass thing, relating this with the infamous E=mc². He also said however, that when a particle is at rest, it's rest mass (m) corresponds with it's rest energy (mc²), and that this energy must be included in the conservation thereof. Using this, Dirac predicted that when a particle and it's antiparticle meet, they annihilate. Furthermore, he predicted the reverse, known as pair production, wherein a photon will split into a particle-antiparticle pair, both of which will then piss off from each other. The rest is just maths.

It's kinda difficult to come across image macros that relate to particle physics.

Ok, positrons. Let's do a little on their discovery. They are the antiparticles of electrons, and could just as easily be referred to as antielectrons. Similarly, I suppose, electrons could be referred to as negatrons, and funnily enough, that's what they used to be known as. In short though, a dude called Carl Anderson, one of the more boring names I've ever heard of, was firing beta particles into a cloud chamber. He was then surprised to find that  some trails were actually going in the opposite direction to that he has expected. Exciting stuff. Well, I suppose it was if you were there, but A Level seems to be specifically designed to reduce the most interesting stuff into grey sludge, which is a shame. Physics is such a beautiful subject, filled with elegance and wonderment, and this is lost on a majority of the population who just can't get past how god damn dull the initial learning of it is...Sorry, wrong meeting.

I'm going to leave it there folks. There is more about the weak nuclear force, and Feynmann diagrams, but that last bit kinda depressed me, so I'll leave that to you. Late'.

I was listening to the soundtrack through most of writing this.

(1902-08-08)

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A2 Physics - Capacitors

This is being done on a boat, and as such without internet. Thus I am typing this up in OpenOffice, and without the Blogger Draft's curious ability to know exactly what I want to do with my images. So let's do this thing. Today I will be talking about, oh, lets go for capacitors. I do not like capacitors. So, all the more reason to learn about them, I guess. I shall however be recording my state of boredom through judicious use of reaction images.

This is going to be much more factual than historical, no internet and all, so all I'm working with is my textbook. So let's start with an idea of what a capacitor is. It stores charge. Nothing much else. Get two metal plates near each other, boom, you gots yourself a capacitor. Connect it to a battery blam, you've got a charged capacitor, the two plates actually having equal and opposite charges. This I because the same amount of electrons leave the plates as they do jump on. It's like a water flume. One kid comes out the bottom, the guy at the top pushes another one in. Eventually the first kid gets back to the top of the flume to be pushed down by the guard guy, who I guess in this metaphor represents the battery.

Ok, so, charging one of these bad boys. This can be done by hooking it up to a direct current right? So what we are going to do is stick in a variable resistor, an microammeter, and a voltmeter. Exciting stuff right? Hold on, it gets even better. The voltmeter could be a data logger, which sends data to a computer, about the p.d.. Or you could use a regular voltmeter and use a stopwatch to record the p.d. at regular intervals. Pussy. So now we have some badass information in the form of amperes, p.d., and time. You know what we can do with these? Fucking everything. We want to know how much the capacitor has charged by? Q=It, bitch. We have I, we have t, so you know what that means? Yeah you do you BAMF of a physicist you. We have motherfucking charge Q.

But shit son, there's more. We still got a V hanging around. That's where shit gets interesting. You see capacitors have their own damn quantity called capacitance. This is defined as the charge stored per unit pd. You know what that means? You got it. C=Q/V. We have p.d. V and thanks to our braniac skills above we have charge Q. You know what's coming. Go ahead, tell me, Feel good about it. You got it, we have capacitance C.

And oh shit, you know what? These capacitors are used in tonnes of everyday items, including smoothing circuits, back-up power supplies, timing circuits, pulse producing circuits, tuning circuits and filter circuits. Shit man, this last paragraph is like an electronics student's wet dream.

Ok, so we have the basics. Capacitors are like temporary batteries. And you know what batteries store? Energy. So you know what capacitors store? Energy. Excitement abound. Specifically Electrical potential energy. So, picture this. You have a bunch of electrons on a plate. You know, one of the plates the capacitor is made of. So the plate has a charge, yeah? Then you try to put another electron on the plate. This requires work do be done on the electron/charge. So you put that energy into putting that electron on the plate, and this becomes electrical potential energy. For a comparison, think about gravitational potential energy. You put energy into lifting an object onto a table, thereby giving the object E_GP. Do you get it? Because I kinda do now. This actually feels kinda good.

But how much energy? Consider this in graph form. You mathsy people out there, you know what a graph gives you? Two things, other than the values it already represents. Yeah, the gradient and the area underneath. So now we are going to imagine a graph of charge Q against p.d V. Q is on the x axis and Q and V are directly proportional. You know what that kind of graph looks like I hope. Got it? Good because I'm not going to be mocking up one just for you. Besides, you were already doing so well. Feel free to draw your own if needed. Lets do this. Ok, think in graph terms, we have a capacitor with charge q and we want to add Δq to that value. This is represented on the graph by a vertical strip over Q. This area is the energy required to force that charge onto the plate. (Think of a particularly heavy kid in that water flume).

Excuse me, the original Pokemon theme tune came on iTunes. Just need to rock out.

That was awesome. Where were we? Right. Consider the strip on the graph. Now consider lots of those strips leading to 0Q. The energy still is represented by the area under the graph, but now its hella easy to work out. You know who to work out the area of a triangle? And shit brother, look what we have in that graph. Half base times height that shit, and what do you get? The equation for energy is what. E=½QV. Magic.

Christ I'm bored. And just as we get to the important bit. Charging and discharging these bad boys through a fixed resistor. OkOk, this tenuous metaphor represents the discharging of a capacitor, where the insults and general ill demeanor represent the resistor. So where as before the electron kids were continuous as long as the battery guard kept pushing, the resistor guard just doesn't care. As lots of kids that have built up are now spilling down the flume and possibly over the side of the rails. It's very messy. But the amount of kids falling down slows as there become less of them, and word goes around that this guard may have a thing against kids. Ok, it's not a perfect metaphor.

The point is that the decrease in kids happens exponentially. If we have Q₀ kids at t=0, and then at t=1 we have 0.9 Q₀ then at t=2 we with have 0.9*0.9Q₀, etc etc.

Ok, just a couple more pages. Why is it exponential? Pretty much because some rearranged equations tell us so. Skipping some stuff, some how you end up with ΔQ/Q = -Δt/RC. This tells us that a fractional drop in charge ΔQ/Q is the same in any short interval of Δt during discharge. Rearrange that bastard a bit and you get ΔQ/Δt = -Q/RC. Δx/Δy? Its a differential equation mother fucker! But physicists leave maths to the mathemagicians. We just do some trickery and end up with Q=Q₀ e^-t/RC. Voila. We have created the time constant, RC. Let's just do a final check of my boredom.

Wonderful.

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A2 Physics - Radioactivity: the Discovery of the Nucleus

Well Christ, that 30 day thing really did a number on this blog, didn't it? You got bored, I got bored, and then I just stopped updating. Well, I officially declare that a failed experiment. Clearly I cannot adequately differentiate between various favourites without narrowing it down to a single point, without getting overwhelmed and pretending it doesn't exist. Instead I might suggest a track or two on occasion, but all in all I will now be going back to the Pokemon chronicling/regular blog format.

Currently however I am revising, and I thought it might be a good idea to use this as a tool to help me. So get ready for some edutainment, folks! Today's picture heavy topic is Radioactivity: the Discovery of the Nucleus.

See, the thing is, until relatively recently, we didn't really know what we were made of. Some philosophical ideas had been thrown around for millenia that if you keep halving something that you would eventually get to a point where the cheese could no longer be halved. This tiny bit of something was referred to as "Indivisible", or ἄτομος (átomos). This was known as Atomism. The origin of this thought is widely credited to Democritus and Leucippus, though there are some (Isaac Newton, Robert Boyle, to name but a couple) who attributed it to Moschus the Phoenician, who they believed was Moses. Of the biblical fame, yes. The guy who laid down the basis of a majority of the world's religion may also have sparked the thinkings that created a good large chunk of modern science.

This guy strikes me as being significantly more badass than that Jesus prick.

However people still believed that we were made up of the classical elements, and while such a theory is still prevalent in modern popular media, most college textbooks tend to prefer teaching the periodic table. This was due to the foundations laid by 17th century "natural philosopher" Robert Boyle with Corpuscularianism, similar to atomism, except "corpuscles" could in principle be divided. While he didn't create the idea, Robert Boyle argued in 1661 that matter was composed of various combinations of different "corpuscles" or atoms, rather than the classical elements of air, earth, fire, water and dragon.

Things didn't really progress for a while after, Corpuscuthingy being the prevalent thought of the time, until the science of chemistry was developed. In 1789, French nobleman and scientific researcher Antoine Lavoisier discovered the law of conservation of mass and defined an element as a basic substance that could not be further broken down by the methods of chemistry. Later, in 1805, discovered the John Dalton proposed that each element consists of atoms of a single, unique type, and that these atoms can join together to form chemical compounds, prompting him to become thought of as the originator of modern atomic theory. Further lines of reasoning were made by one Johann Josef Loschmid, who in a scientific landmark, worked out the size of molecules in air, and botanist Robert Brown, father of what has come to be known as Brownian motion.

In 1869, building upon earlier discoveries by such scientists as Lavoisier, Dmitri Mendeleev published the first functional periodic table. The table itself is a visual representation of the periodic law, which states that certain chemical properties of elements repeat periodically when arranged by atomic number.

Now bear with me, if you haven't left already, because here is where we finally near the content of the A2 syllabus (assuming you haven't found the last 4 paragraphs as fascinating as I have). In 1897, the electron was discovered by J. J. Thomson while pissing about with cathode rays. In doing so, he discovered that they were a component part of every atom, thus overturning the then prevalent belief that atoms are indivisible. Thomson postulated that atoms were therefore made up of the negatively charged electrons distributed, possibly in rings around a uniform sea of balancing positive charge. Thus was created one of my least liked scientific names, the Plum Pudding Model.

Douse it in brandy and set it alight, then get back to me.

Thus it was that in 1909, under the direction of Ernest Rutherford, Hans Geiger and Ernest Marsden bombarded gold foil sheets with α rays, then known to be positively charged helium atoms. Lets take a more detailed look at that. What Geiger and Marsden used was an evacuated metal box, containing an alpha source lined up with a gold foil, and a scintillator (A zinc sulphide screen that emitted light when hit by an alpha particle). What was observed was that most particles travelled straight ahead with little to no deflection. 1 in 2000 were deflected however, and very occasionally, 1 in 10 000 would be deflected at a greater angle that 90°. Some would even bounce right back to the source, an action that would be impossible for a diffuse cloud of positive charges, as Thomson had suggested. It was, in Rutherford's words "as incredible as if you fired a 15 inch naval shell at tissue paper and it came back." to give you an idea of just how surprising this was.

vs

From this, Rutherford interpreted the results as suggesting that the positive charge of a heavy gold atom and most of its mass was concentrated in a nucleus at the center of the atom. This was the creation of the Rutherford model. He went on to use Coulombs law of force and Newton's laws of motion to explain his results, and through the use of different metals in the same experiment he worked out that the magnitude of the charge of a nucleus was +Ze, where e was the charge of an electron, and Z was the atomic number of the element.

So there we have it. The history of the discovery of the nucleus. I could go on to the size and density, but that's decidedly mathsy, and while I love maths, it doesn't translate very well into the historical documentary format I have going here, and I fear I would end up breaking into degree level stuff, which I just do not need distracting me this close to exam time.

At any rate, I hope you enjoyed it. It has probably helped me, if not you, at any rate, and that is really the main aim here. No offence.

Please note that this won't be a daily thing as it is entirely likely that I will be a) busy b) doing other things and more likely c) procrastinating

Ja mata ne!

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