14.1 Quantum Mechanics

Ok, today we're gonna start our new chapter, Chapter 14. And we actually do a shift in physics up to the late 1800s. It covers everything that we've covered so far in Physics 20 and 30 – all of Newton's formulas and motion, acceleration, gravity, circular motion, all that kind of stuff. Plus, what we did in 20 and 30 on waves and EMR (electricity magnetism). Thompson did some work configuring what the masses of electrons, protons, all that kind of stuff is. So all of that stuff is considered classical physics. It's good, it all works, but it presents some problems when we get into some newer topics. The first topic we're going to look at that classical physics can't explain is called blackbody radiation. And what blackbody radiation is, think of it as a blackbody just being an object that can absorb all of the electromagnetic radiation that strikes it or that it strikes on. So, kind of think of it like being an empty box. So, if you have this empty box and we shine light on it, the box, think of the box as being open. It's gonna absorb all the light. And the box closes. And what happens is, it doesn't matter what the radiation is. So, if we shine light, radio waves, microwaves, ultraviolets, cosmic, a black body will absorb it all perfectly. And the reason we call it a black body is that the color black basically is the absorption of all light. We don't see any light reflected, so that's why we see black or the absence of light. So, kind of using that same idea, just seeing a black body absorbs everything, not just light, but all EMR. And we know that electromagnetic radiation, the higher the level of frequency, the higher the energy. So really, what's happening is the black body is absorbing energy and then if we heat it up, so a black body will absorb energy at cool temperatures and it'll then re-emit it when it gets heated and it will release that energy. Then, as it cools down again, it will absorb it once again. So, according to classical physics, the more energy that gets absorbed, the more it should get released. So, the higher the frequency, the higher the energy, the more that's going to get released. So using common sense, we should be getting sort of a graph that would look linear. We should get bigger and bigger as the frequencies get higher and higher. So, what happened when they actually tried this is it didn't work out. So, the higher the frequency, we think the higher the intensity. So, it should look like the red line. But in reality, they actually got that it was pretty linear for a point and then it sort of hits sort of a threshold and then came crashing down. So, what happened is when they were doing this experiment, they actually found out that the frequency that crashed was about UV. So, radio waves and up, once we hit visible light and all that, we started to fall apart. We hit UV, it crashed. And then when we got towards gamma, it definitely didn't follow the pattern that we thought. This black body caused perplexing issues for a lot of scientists. So, the best minds around at the time couldn't figure out why. All they knew is that when they hit UV, it sort of crashed. They called it the ultraviolet catastrophe. There's no explanation for it. They just had trouble. So, when they did different experiments, they found that that peak or that part where it crashed just changed as you change frequency. So, if we had more intense, it would just shift that thing one right the other. So, if we actually increase the temperature, the higher the temperature, the higher the frequency. But if we also increase the temperature, we actually get a visible shift in color. So, from the red end of the spectrum towards the violet end. So, that's why, when you have a fire, you know, you turn on your electric element on your stove and it gets hotter and hotter, it gets brighter and brighter red or turns to almost a yellowy sort of. Color, or you think of a campfire. Once it's burning, it kind of starts, yeah, reddish. It goes to a yellow, you know? And eventually, it might even get to a blue sort of color, or even white-hot. Like, it might get hot enough where it actually just kind of looks like a white glow off of it. So, it kind of explains why we get that, so that as it hits certain temperatures, we get a certain level. So, Max Plank was the first guy. He was in the early 1900s. What he did was he figured out sort of an explanation for this. He said the reason why we're getting these thresholds is that we think that as we have more and more energy, the electrons are just going to take that energy and start vibrating faster and faster. But, what he said is instead of it being sort of a straight curve like that, what happens is you have to get to certain levels. So the electrons have to take a certain amount—it's sort of flat—and then they're going to jump up to the next level. Then it's going to take more energy, more and more, and more. Eventually, it'll hit enough, and it'll jump up to the next level. So you said think of it as sort of like being stairs or where we got to go up in increments instead of it just being a continuous line. So, we need these minimum amounts in order to make it jump. So, he called these levels or these amounts a quantum. So, a quantum is just a thing but as a small bundle or small piece of energy. So, the idea is that if we have these bundles or pieces, that's going to explain why we're getting black body radiation and things like that. So, his formula that he used is pretty simple. It's just equal to HF. So, our energy equals H (his constant) times whatever the frequency of the EMR is. So, Planck's constant is 6.63x10^-34 (or remember we can change from Julis to electron volts just by dividing by 1.6x10^-19). So, if we do that, we can actually get Planck's constant as 4.14x10^-15 in electron volts. So, it just depends whichever way the questions give it to you, pick one or the other. And also remember, this is for one quantum. So, if we just have one quantum of energy, that's how we're going to use equal to HF. Obviously, if we have more than one, it would be a 2, we double it, or we have 10, 2 times 10, and so on. Okay, so that's the key thing. The idea is that energy is not continuous; it's actually bundles or little amounts. So, kind of like when you look at a picture, we think of it on the big picture, we just see the entire picture. But, if you look close, we see a whole bunch of dots that the printer makes up to make a picture. So, it's sort of the same thing. He's saying EMR is like these whole bunch of bundles that, once they're all together, that's what makes what we see, the light or the radiation or whatever it is. So, let's go through a couple of formulas. You heard a couple of examples using this formula. So, the first one is asking what's the smallest amount. The smallest amount would be for one quantum. So, all we have to do is go E equals HF. So, our H is 6.63x10^-34. Multiply it by our frequency, 4.5x10^14. Multiply those together, and we get an answer of 2.98x10^-19 joules. Okay, so if we would do this with joules for the H constant, we get 2.98. If we would have done it with the electron volts, then our answer would be an electron volt. So, it doesn't matter which one you do, it's just one or the other. You can always convert back and forth just by dividing by 1.6x10^-19. Okay, so let's do another one. This one says, "What's the minimum energy to get 212 nanometers wavelength?" So, we know that E equals HF, but we also know from an earlier formula that velocity equals frequency times wavelength. And we know velocity is just the speed of light. So, we can actually determine that frequency. That is speed of light divided by wavelength. So, that's How are we going to do this? Instead of using lambda, we're going to use the symbol HC. Since we have electron volts, let's use the other symbol H. So, for 0.14 x 10^-15 times c divided by our wavelength of 2.12 x 10^-9, we get 5.86 electron volts. So, if you use H and electron volts, you'll get an answer in electron volts. If you use H and joules, you'll get an answer in joules, like we did in example one. The last bit for this topic is Albert Einstein. He came along after Planck and took it one step further. Planck's theory was basically using the idea of quantizing energy of electromagnetic radiation (EMR). So what Einstein said was, well, if light (visible light) is a section of EMR, then it should also apply to light. And if that's the case, it means that light is actually made up of individual particles, not just a solid wave that we've been dealing with. If we think back to the start of the last unit, we said that guys like Newton felt like light was made up of particles. Later on, guys like Huygens and Thomas Young figured out that light had to be waves because it was refracting and diffracting and all those kinds of things. So, Einstein is going back to that idea and saying, maybe light is actually a particle. If it's working like quanta, then it's actually a particle. Einstein called those particles of light "photons" and he said, well if light is made up of photons, then it has to be a particle. Obviously, the scientific world didn't like that idea because they had just come to the conclusion that light was a wave. But since Einstein's time, we now think of light as being a wave but made up of little particles that travel in a wave pattern. So, we think of light as being photons or particles that travel together as a wave. It's kind of a combination of the two ideas. Now let's calculate how many photons are in a light wave in a laser. If we have a laser with a frequency of 4.38 x 10^15, we can calculate its energy using E = hf. So we have (6.63 x 10^-34) times (4.38 x 10^15) which gives us an answer of 2.9 x 10^-18 joules, which is the energy of one photon. The next question asks how many photons we would get per second. They tell us that the laser emits a power of 4.06 milliwatts, which is just energy per time (joules per second). So, we want to take 4.06 x 10^-3 (think of it as joules per second) and divide it by 2.9 x 10^-18 joules per photon. If we divide these numbers, we get 1.4 x 10^15 (joules divided by joules cancel out). When we flip the fraction around, we have photons on top and seconds on the bottom. So, the laser is emitting 1.4 x 10^15 photons per second. This is why we don't see light as particles, because it's happening so fast. The photons are coming at such a fast rate that it looks like a solid continuous light source. But in reality, they're small bundles being emitted every now and then at a certain frequency. They're following a wave pattern, so that's kind of where we've come with this now. As we're taking light as a wave, but now we're breaking it up individually into a bunch of photons that are being emitted. And that's all.