In learning objective number two, we need to understand light, and that's why I began the unit with a picture of rainbow. To understand electrons, we have to first understand light. So, in this learning objective, we are going to see the inner conversion between wavelength and frequency of electromagnetic radiation. We're going to back up a little bit, so that we can see what energy was thought of prior to the understanding of light. The classical view that, physics view of energy is that energy is a continuum. Your experience would probably give you that feeling as well. Think about the drive in your car. Now, that's not energy but we can associate that with the energy because of the speed that your car's travelling. You can go zero miles an hour, or zero kilometers per hour depending upon where you're from, and you can be sitting still, you can then start traveling and get up to 50 kilometers per hour, or 100 miles per hour. Whatever the case may be. And as you're going from sto, the stop to that speed, you're going to be travelling through every speed in between. That was a classical view of energy as well. Well Maxwell Planck came around, and he was studying taking a solid object and heating it up until it glowed. So think of a electrical burner on your stove. What he found was that the light that's been produced from that if you measure the energy of that, it was in discrete little quantities which he called quanta. And this was the beginning of quantum theory. Now, some things that you run into are a quanta system. For example money. In United States we have a penny, which is our smallest quanta of money. And you could pay something, buy something for a penny, although I haven't done that a long time. Two pennies, three, pennies, get 100 pennies, we call that a dollar. So that is a quanti system. Some things are quanti's, we're very thankful for it. A cat gives birth in, to kittens in quanta. Cat might have one kitten or two kittens but we're really glad that that cat never has 2.46 kittens. But energy was never thought that way, until the beginning of quantum theory. So let's look at waves to begin with, properties of waves. Now this is not necessarily light waves, this is any waves in general. A wave is a vibrating disturbance by which energy is transmitted. Now whether you think about waves on the ocean or waves that are sound waves or electromagnetic radiation. Any kind of vibration that transmits energy is a wave. So if you've thought about the waves in the ocean, you know that those waves can knock you down. They have, they're bringing with it, energy. The things that way are, that characterize waves are first off, wavelength. Now, wavelength is the distance between the identical points on successive waves. So if we look here, there is a peak to peak, these are two different wavelengths of, of a wave. Now you don't have to measure from peak to peak, you could measure from trough, that's called a trough, to trough, but that would be a wavelength. And it'd be exactly the same no matter where you measure from. You could do a midpoint on the way down, to midpoint on the way down, and that would be the same length. Over here, wavelength could be measured again at different places. The other thing that defines a wave can be amplitude. Amplitude is defined as the distance from the midline of a wave to its peak. So you don't go from trough to peak, but midline to peak. So there's a couple different ways that have different wave, I mean, they have the same wavelength, or do they? Don't know if did they know, they don't. But they definitely have different amplitudes. Midpoint up to the peak or, you could say midline, to the trough. It's the same amplitude. We generally associate energy of a wave with its amplitude when you're thinking about waves on the o, ocean. The taller the wave, the more it'll knock you down. Some waves can get so tall that they'll knock buildings over. So the amplitude is what classical physics would have associated with the energy associated with that wave. Too many uses of associated, [LAUGH] but you get my meaning. So our next property we're going to discuss is frequency. So frequency is the number of waves that pass through a particular point in one second. Now if you look at a wave drawn like this, it's hard to understand what we're discussing. But let's imagine that this thing is moving by. So, I'm going to draw me. Here I am. Okay? And I am watching these waves go by. What am I going to see? Well, what I'm going to see as I watch only this one fixed point. Okay? So I'm only watching right there. As I watch that fixed point, what I'll see is it's down. And then it'll come by, and it'll be up. And as it travels forward then it goes down. So what I'm seeing from this vantage point is simply down, up, down, up, down, up as I go through watching this wave go by. How many of those down, up, down, up patterns I see in one second is the frequency. Now, we're looking at it in one second. Okay? That's key. And, we call them cycles per second. How many cycles of a wave from a down up to a down. How many cycles per second are there? So some waves will travel, and waves on the ocean maybe one, maybe a half of a wave every second, you know, it's kind of slow coming to the shore. But some things will have thousands, and thousands in a second, very, very rapid of transmission of that energy with its frequency. So, cycles per second is abbreviated with the H-Z, that stands for hertz, okay? So we have a hertz is a cycle per second. Very often when we're doing our calculations, we will write our unit as simply 1 over seconds. Or seconds to the minus 1, and not write the word cycle in there. Now, the speed of any wave is defined by the two things we just discussed. The frequency, which is this, that's a nu. That's a Greek letter nu. And wavelength, which is the Greek we, letter lambda. So any wave would be defined its speed by how long it is and how many cycles pass through in a second. So let's say that this is measured in meters. And we said cycles per second, or 1 over seconds is our frequency that would give us meters per second and is that not a speed? Yes it is. Now let's get to electromagnetic radiation. Electromagnetic radiation is the emission and transmission of energy in the form of what are called electromagnetic waves. Now electromagnetic waves have got two components. They've got an electric field component, and running perpendicular to it with exactly the same wavelength is the magnetic field component. So both of these are manipulated, manipulable and observable by scientists. We won't go into or separate out ever again the fact that it's got the two components. But I just wanted you to know why it's called electromagnetic radiation. Now we know that energy is a capacity to do work. So this is the transmission of energy, which is the capacity to do work. Knock you over if it were a wave on the ocean. The units of energy that we will be dealing with as we go into this section will be in joules. And for unit conversion purposes, and so that units will cancel as we need them to, you need to make sure you know that a joule, if you broke it down to its SI units, was a kilogram meter squared per second second squared. Okay, so now if we go from the speed, which was u earlier equals lambda times nu for any wave. When you're getting to talk about electromagnetic radiation, the speed is always abbreviated c. So that would be the speed of light. The speed of light is there. Of course we've got our wavelength and we've got our frequency, lambda nu. [SOUND] When you're in a vacuum, the speed of light is 3 times 10 to the 8th meters per second. Now it's hard for us to even imagine how fast that is, to travel. But if you were to stand at one point on the earth and be able to shine the light around the world. It would travel around the world several times in a second. If you had a way of hitting mirrors and having it come back around, you could see it. So in a second's time, you can travel around the world many times, several times. Less than ten but more than five, somewhere in that range if you could do that. So this is really, really rapid. This is very fast speed. Now you're not going to always be working problems where the speed of light is in a vacuum, but this is a number that you can use for all your calculations, unless we tell you otherwise. But light does travel different speeds depending what's travelling through. It travels through water different than it does air, which is different than it would in a vacuum. Now, what we think of, when we think of light is just the visible spectrum. So we've expanded visible spectrum out here and we see all the colors of the rainbow. You might have learned a mnemonic, ROY-G-BIV, along your [LAUGH] And really, let's erase that, and let's do it the opposite way because of the way my rainbow is. [LAUGH] ROY-G. I can actually write backwards. ROY-G-BIV red to the violets. anyway, that's just a very small portion of the electromagnetic spectrum, and that's the visible region. Now when we use the word electromagnetic radiation, we're talking about this full of spectrum. Way down on the high energy of gamma rays, down to lower energy, very low energy of radio waves. All of it can get the name light and this just be the visible region, but we usually use a word in, electromagnetic radiation for the whole range. High energy gamma rays, you don't want those passing through you. They're very damaging. They can use gamma rays to help kill cancer cells. X-rays, you don't want a lot of x-rays. It used to be that they'd x-ray, I didn't realize this, they would x-ray kids, in shoe stores when they first came out, so that they would be certain to give them right fitting shoes, and then they found out that they do cause some damage. Down here on the radio wave range, we have those passing through us all the time and does not cause any damage. Okay, so now we're ready to use this equation that we learned. C equals lambda nu to work this problem. They're giving us a frequency of light. They're asking for the wavelength of the light. And that's the job of this equation, to convert between wavelength and frequency. So when we're trying to find the wavelength, so we'll solve for wavelength. C over nu equals lambda. C is 3 times 10 to the 8th meters per second. Wavelength is, I'm sorry, frequency is 3.5 times 10 to the 5th, and it says hertz there. Well, we need there just write that as 1 over seconds for our unit work. A hertz is a cycle per second which is just how many waves per second we do 1 over second. That would leave us with meters, and when I divide those two numbers I get 857 meters. Now we can only really note to two significant figures. So we'll call it 860 meters. Now that's pretty long. Would that be in the visible region? Well let's look here. Visible region, wavelength, it's about 10 to 3rd nanometers. Well this is not a nanometer so, let's get this in nanometers as it asks. So we'll convert this to meters. We have 800 and, I mean, oh, we're going to convert to nanometers. 1 nanometer is 10 to the minus 9 meters. So that would be 8.6 times 10 to the 11 nanometers, okay? So if you stopped with the 860 and that's back here. You might have said sure 860 well that's kind of just beyond here. It, oops. No, there we go. 860 is just a little bit beyond here. But, that's in nanometers. What we're dealing with is a frequency over in this region and that is a radio wave. So, definitely not in the visible light, but it is in the radio wave region. You going to try one here, and you're going to determine the frequency given that it's 490 nanometers. So, take your time. Work through that after you pause it, and then see if you got it right. Well, did you get this value? If you did, you did everything correct. The most common mistake students make is not to watch their units. This is in nanometers. So when we have our equation, C equals lambda nu, in this case we're going to be solving for frequency, so C over lambda equals nu. You don't want to just put in your numbers. And 490 and divide those, that’ll get you the wrong answer. If you watch your units you know that this speed of light is in meters per second, and this is in nanometers. So you can’t leave it in nanometers. Units will cancel. 1 nanometer, to the minus 9th meters. And now the nanometers are cancelling, the meters are cancelling. And you're left with 1 over seconds. And that will give you the correct answer. Okay. So let's learn some other things about waves. There's something called an interference pattern that we're going to look at. And the interference is the waves that, way that waves interact with each other. There's a couple points that we want to look at. There's something called a constructive interference. And if the waves align like these two waves right here do. We have a, with the troughs lining up, the peaks lining up. When they align like that, then we end up increasing the amplitude. So the, you think about waves on the ocean, that's the way that works. Destructive interference is if the peak of one wave aligns with the trough of the other wave. And when they're what we call out of phase, they will annihilate each other and you will have no wave. So, let's look at diffraction. Now when a wave passes through a slit. Now this slit has to be about the size of the wavelength. So let's imagine. Let's look at our top picture here. In our top picture, we have got the waves travelling this way and hitting this slit. So you're seeing peak, trough, peak, trough. If we looked at it, if we could look at it from the side, 'kay? The wavelength is from here to here. And that slit is about the distance of that wavelength. It's gotta be about that size for this to work. That slit's just right. As the wave passes through that opening, it bends the wave, as it passes through. Now particles wouldn't do that. You were to throw sand at the slit they'd just pass right through the particles. I mean, through the slit. There's not a diffracting pattern. Now, an interference pattern, what you have is two slits, okay. And always will have this property. If you have two slits, as a wave approaches those slits, you're going to have them passing through. So we have them passing through here and we have them passing through here, and bending in both cases. Now as they come forward, and they start bumping into each other, in some places they're going to be out of phase. And when they're out of phase, we're going to get no light. So say this was light or something that is there you'd get nothing, you'd have a dull, a annihilated spot where no waves are seen. And then you'd have areas where the waves are actually reinforcing each other. And we have this constructive interference. And when you have the constructive interference, then you might have a bright spot if it were light or a huge wave hitting that area. So this is a way waves behave, whether it's light waves or waves on the ocean. You're going to get some, you're going to get this pattern of no waves. Big ways, no ways, and it's going to be going from an increasing to decreasing pattern. Meaning from nothing to a bunch, from a bunch to nothing. So that'll be an important property that we're going to study as we move forward. We've got our wavelength and frequency interaction. We've got this notion of a defracting pattern or an interference pattern of our waves. And now we're going to ready to take this to our next learning objective, where we're going to start seeing how light helps us understand electrons.
