Atoms and Light: The Interaction and Nature of Light and Matter

Hello, and welcome. This is Jason Kendall to one of my introductory astronomy lectures, and this time we're talking again about the nature of light. Light is that thing that allows us to see things from here to there, there to here. We don't emit light out of our eyes, unlike certain kinds of superheroes who beams of light come out of their eyes. No, light comes to us from sources. Those sources might be hot objects; they're so hot that they glow, or they're so hot that the atoms in them emit light as they jump between orbits in their atomic shells. There's lots of ways for light to be emitted, um, but let's just see what light is as a thing.

And as we've always seen from, like, the album cover of Pink Floyd—now, like we're looking at here—when light passes from one medium to another, it changes direction, and depending on the medium, it has a frequency dependence for the speed of light inside that new medium. But the speed of light that we're going to care about comes up really shortly. In any event, what is light? Well, light is electromagnetic radiation, and electromagnetic radiation is a way of saying that energy is being transported through space without there being a physical connection between the two things. There's no actual physical link. So electromagnetic radiation is a transfer of energy.

Examples where the other two examples where energy gets transferred are conduction, where you heat something up and the vibrations of the molecules and atoms inside of that object that you're heating up—they vibrate against each other—and eventually all the atoms move very fast. And if you happen to be heating up a skillet or a pan on sort of an open fire or a heating element, then eventually the handle gets hot too. So that's called conduction. Conduction is the vibration and the in the collisions of atoms inside a solid object or any object where the atoms and molecules inside it are close enough together that their vibrations can impact each other. So that's physical contact. Another way that physical contact can occur is through convection. Convection is where you take a hot body of some sort, a hot bubble of gas or liquid or what have you, or even a hot solid, and you move it from here to there by some physical process. The heat then is transferred; the energy is transferred because now you've got something with a greater amount of energy, and you take it from here and you put it there, presumably to a place of lower energy or lower heat, or you could place it to a place of higher energy, but then it would gain more energy, so it doesn't—that's not really the flow that we think of in terms of convection. So a good example is a boiling pot. You heat the butt—heat the pot; the bottom of the pot gets hot, makes a bubble of hot water. That water then rises in the pot, releases it as steam or heat into the surrounding—to the kitchen—and then that cooler liquid then sinks back down. It makes a roiling pot. So there's actually a flow of water, a flow of water inside the pot as it goes. So that's convection. Um, also happens with air; that's how we get storms because there's convective cells in storms, and so we've seen that happen all over the—all over the earth with the creation of hurricanes and so forth.

But with electromagnetic radiation—radiative transfer of energy—does not require physical contact. Convection means you transfer objects that are physically moving through each other; this bubble that's high moves through a region until it gets to a region where it's cool. Conduction is where electrons bounce against other electrons right next to each other. But if it's radiative transfer, electrons and protons don't go, "I'm going to touch you and move along." No, it's light. Light actually transfers its energy from here to there, so there is no physical contact that the photon does; it's just the thing that it transmits energy. And so light is something, but let's get to it in just a little bit. It's a very complex question, but light's everywhere. The reason you could see me now is because light's bouncing off of me, getting recorded by the uh—by the—by the camera. The camera then holds it as an electromagnetic impulse, and then I transfer it to the computer. After I transfer the computer, I play around with it on the computer, manipulating the electric and magnetic fields on the computer, and then I upload it using electromagnetic fields to YouTube. After I have transferred it to YouTube, you then turn on your computer and, using more electromagnetic energy that creates light that comes out of the screen, which you then see. Interesting. But what is this light thing—this thing that is transmitting energy from me, through the magic of YouTube, to you?

Anyway, there are characteristics to light that we should discuss before we say what light is, because without—we can't discuss what it is without discussing these characteristics. And one of them is this wave motion. So light has—has a wave property, meaning that there's wavelength to light, and light's wavelength is a very important thing. So what do we mean by, like, wavelengths? If we take some sort of medium—medium—and we have an irregular disturbance in it, we get waves that go up and down, like water waves. Water waves are a perfect example of wave activity. When water waves—we see the distance between the crests and water waves, and those distances are the wavelength. So the wavelength is the distance between crests or troughs in a wave as it traverses, and so it's a cyclic pattern. It's just not one wave; there's many waves in a train of waves, and the train of waves has a speed with which they move through the medium. Say, the water waves move at whatever speed they do through water, and that speed is important because the speed of the wave is equal to the frequency—or how many waves go by you per second—times the wavelength of it. So if you have a high frequency, then if you have wavelengths of the same type—same length—and one of them is high frequency, then, of course, the waves are moving faster by you. If the—if the same frequency is occurring, but one of the wavelengths is much shorter than the other—than the one that's long—then the—then the smaller wavelength thing has a short—has a—at the same frequency—has a much slower wave speed. Now we're going to see something interesting about the nature—we call the period of the wave is how—what the time is between individual—individual cycles.

All right, so in terms of the speed of light, the speed of light is a constant in a vacuum. It only has one speed; there is no other speed to light. It either is not existing—meaning there is no light—or it's going this speed, which is very interesting. There's no acceleration or deceleration to light; light just simply goes at this speed, the speed of light, which is just shy of a thousand kilometers per second or a just 186,000 miles per second, but specifically it's 299,792.458 kilometers per second, which is a lot—which is a very fast speed. That means it gets to the moon and back in two seconds. That's why those pings on the—in the Apollo missions where they have that little ping sound, because you know it's rude to talk over people—you actually want to know—so you send the ping; they say, "I'm done with transmission," because it takes a second for the light transmission to get from the earth to the moon, and that's why they had the ping sound at the end of the Apollo mission transmissions when they were talking back and forth between the moon and Houston. So what does that mean? So if you have the speed of wave—the speed of light being a constant—then the product of the frequency times the wavelength gives you the speed. All right, so if the speed is always the same, then if you have a long wavelength, you have a short frequency, and if you have a short wavelength, you have a lar—a high frequency, and so they're inversely related—one of—because the con—the speed of light is a constant. So once again, if you have a very small wavelength—lambda is typically what we use for wavelength—then you must have a very, very, very high frequency in order to maintain that speed, and if you have a very low frequency, then you must have a very long wavelength, and those are radio waves; the other one are gamma rays. So light goes in all sorts of flavors, but it all travels at exactly the same speed. All right, so how do we know what the speed of light is?

Well, the speed of light, as we discussed in a previous lecture, was first investigated—or at least investigated many ways—but only Rømer looked about it by looking at the timing—the timing—the uh—the transits of Io across Jupiter over a long period of time—over many months—and actually noticing that the times that it was expected to be were wrong. But another more direct way to do it is with Fizeau, who actually did use mirrors on tops of mountains and actually bounce light all the way across and through a rotating toothed wheel, and the toothed wheel spun and spun and spun, and as the light passed through the wheel and bounced off the mirror and came back, it had to make it—had to do the—had to make that trip while the rou—this—the uh—the wheel was rotating, and the light had to come back through the same tooth it left or else it would be blurred. So Fizeau made it a pulsing beam, and that pulsed beam had to have the same speed as the light going through—as the light going through it—or else it would get blocked. And so you either get blocked light or you would get—or you'd let it through, and the disc—the how you determined the speed of light was how fast was the gear—how fast is the rotary wheel turning—what's the length of space between the two—between the teeth—and so you could say, "Well, how long did it take for light to go all the way down and back such that you don't have—such you don't get a distortion—you don't get a blurred view," and that's one way of determining it—how fast the wheel's rotating and the size that it's rotating through. In any event, the wave nature of light was determined uh—because you can actually say, "Well, what are some features of wave—wave light is that light diffracts around boundaries, just like water waves do." So when water hits a boundary, like a jetty, it curves around that jetty; it doesn't actually stop; it doesn't go around it—when it goes past it—it doesn't not go around it. You don't see waves not propagating. Waves have a way of actually spreading out, and so they don't stay trained on one place; you uh—they just spread out until they thin out across their—their breadth if it's a water wave, but uh—but in terms of like a jetty going around, as soon as it passes the jetty, it starts to spread back out around the jetty. In any event, you can have multiple—you can have interferences of waves where waves can constructively interfere and destructively interfere, and if the waves constructively interfere, that means the two waves merge together, and if their peaks match at the—at a given place in space, then the—and then they add together. If they—if their peaks are counter—if they're p—if one wave's peak matches another—the same wavelengths—wave's trough, then they cancel out. So you can either have what's called interfering constructively, meaning they add together, or they can destructively interfere and subtract from each other. Basically, the waves superimpose and add to each other, and the trough acts like a negative number, and the peak acts like a positive number. So if it's a wave height of two and the other wave height is two, and they happen to be at the same place—that the peaks are the same place at the same time—then the wave height is four, but if the wave trough is at the same place as a peak, then the wave height is zero, and it's flat. So you can have waves passing through each other and not make a noise; it's kind of a weird thought, but it can happen. So constructive and destructive wave interference can be seen pretty easily if you look at—drop two stones in a—in a puddle of water. Those—you can see two outbound ripples. It helps to have some nice sunshine so you can actually point out the troughs in the water and the peaks in the water, and it's pretty easy to see as you—as you try it out at home, because what the heck—everybody's got puddles of water around them—maybe something deep—and you can see the reflection of water on it and see the constructive and destructive interference.

Another thing to look at is back in 1901 or so—or the early part of the 20th century—uh, Young did a—was famous double-slit experiment where he put a slit inside a barrier to make an image of a slit as a single uh—as a single sort of a—as a single source—and then allow that image of that slit then to spread out because light spreads out from a source diffractively to impact on two other slits, and those two other slits—then they each act as sources—but those sources—um—then the—what we see on the far side are a constructive and destructive interference pattern on the—on the far side of it. So you have a source—a continuous source—going through a slit; that slit then goes through a double slit, and that double slit then makes constructive and destructive interference patterns, which can only occur if light is doing a—his life has wave properties. So Young's experiment actually proved that light actually did have wave properties. So what are some effects of wave properties? Well, let's say you were moving towards or away from something. We've always heard of the nature of the nature of wave properties. So let's say you're going to see a Doppler effect, and Doppler effects occur because let's say you see a car driving towards you and it's honking its horn; the pitch will be slightly increased as the car is driving towards you, and if it's driving away from you, the pitch will be slightly decreased. And I had the benefit of going to the Indy 500 a long time ago with my good friend and best man for my wedding, Ralph Haesner, and Ralph got tickets for us to go see it, and you could really hear the effect of the Doppler effect as the cars flew by you. You know, okay, so just to say it—when cars in the Indy 500 are driving, they're these little things; they're extremely loud. All right, they're driving like that; they're driving really fast—really fast. Now that sound is what you hear if you're inside the car. Now what do you hear when you're watching them go by on the track? What you hear is—that's what you hear. Now inside the car it's, "Oh," because that's the sound of the engine; they're really whiny, but outside—your hair—as it approaches you and then as it goes by you, and the pitch changes. So the wavelength of the sound changes to the observer. So I'm the observer sitting on the stands in the fourth row above the finish line going, "Yeah, there's the cars," and I hear this sound, and everybody who's ever watched these kind of things has seen and heard this sound; it's a really cool sound. In any event, that's a Doppler effect, which is the change in wavelength or frequency as a result of a movement of—of the source towards you or away from you. So the Doppler effect is just that you have the true wavelength, which is inside the car—the sound of the engine—but then there is the perceived wavelength or the apparent wave like which depends on the relative motion of the source. So the faster something goes by you or towards you or away from you, the greater the Doppler effect is. So that's all dependent upon both the speed with which it's moving and the speed with which the wave travels—the sound wave. All right, so for light we have a slightly different thing, but it works the same way because light has a wavelength. So if it has a wavelength, then we can see if there's a Doppler shift, and there is. So light has a wavelength, and there's a certain wavelength at which the light is emitted, and there's a certain wavelength at which the light is received. So if I were to actually take a red light—maybe it's uh—6,500 nanometers in wavelength—maybe that's the wavelength I'm looking at—and that wavelength source of light—which, by the way, would be a cloud of hydrogen gas—if that wavelength of light is traveling towards me—or actually, let's say—let's make it go away—if it's going away from me at uh—say 90 percent the speed of light—or maybe 80, just to keep it easy—if we said—if the light was going away from us at 80 percent the speed of light, then the total speed—then the wavelength change would actually change the wavelength to almost twice its wavelength—almost twice—so it would be well into the infrared—roughly about 1200 nanometers—uh—yeah, 1200—yeah, 1200 nanometers as opposed to about 600 nanometers. So it'd be well into the infrared, and you wouldn't be able to see it. So if something's emitting—if it's a hydrogen—class gas—and it's rushing away from you—whatever reasons—hot hydrogen rushing away from it—80 percent the speed of light—normally, if we're still, you could see it, but if it's rushing away from you that fast, then the light gets redshifted down to the infrared, and you have to use infrared to see it. That will be important when you're talking about the Big Bang, but in any event, Doppler shift is important in light because if the source is moving, then there is a Doppler shift, and that occurs in every direction. You can have a slightly change—but aversion from it—away from it—if you're looking at it from the side; there's a—there's a—there's an—there's a part—the part of the motion that's towards you changes it. So effectively, the light bunches up in the direction of it that it's going, changing the frequency to a higher frequency, and—and gets stretched out away from the source as it—for things behind it. In any event, they're—for wavelengths of light—like uh—like—like it shifts it, but the thing with—the important thing about the Doppler shift with respect to—say—let's say up—that cloud of hydrogen gas was talking about—is that all the wavelengths get shifted by the exact same proportion. So the spacing between the wavelengths—if that is not dependent on the speed—so the pattern stays the same; it just gets shifted by the same amount—either blueshifted, meaning if it's going to shorter wavelength, or redshifted if it's going to a longer wavelength. And if something's receding at like—say—one percent of the speed of light—uh—if it's receding, then it'll be slightly redshifted; if it's re—if it's running towards you—approaching at a much faster rate—maybe uh—twice—two percent the speed of light—then it'll be much greater, but on every case, all of the emission is simply just shifted by that same amount to the left or to the right by the same amount, and they don't get stretched out or pulled out in any direction. All right, where can we measure this? I just said, "Gas cloud, hydrogen rushing away." Well, you know what—if it's rotating—let's say you've got some rotating, glowing object. If it's rotating and glowing, then the side that's—of it—that's rotating—maybe a big hot glowing ball—that's kind of weird—big hot glowing ball rotating really fast—when it's rotating really fast, the side that's approaching you would be blueshifted, and the side that's retreating away from you would be redshifted, and so you can have a Doppler shift on a big hot rotating ball of gas—maybe a super fast rotating star or something—or even a moderately rotating star can—can show a Doppler shift. In fact, the sun shows a slight Doppler shift from—at physical wavelengths, but you've got to be really sensitive to see it. If you have two stars that are orbiting each other and they're part of a binary system, then those two stars then also show this Doppler shift because, hey, maybe one of them is approaching—one of them is receding—so all of the spectral features of the star that's approaching you get shifted to the blue, and all the star features—the spectral features of the star that's receding away from it get shifted to the red, and then they swap back and forth as one's receding and one's retreating, and the other is retreating and the other's receding. So that's another thing—look for binaries that do this. And finally, is the—as the earth goes around the sun—it's even very interesting—is that there's a slight Doppler shift as the earth goes around the sun, with…

Respect to all the stars in the sky, so that's a very small amount, and that has to be taken into account for being very sensitive with respect to spectroscopy. So the earth's motion of the sun can cause a Doppler shift in stars, all right. So is it real, what's real speed? So what's the real speed? I mean, I know I'm going fast with respect to, but what's the real speed? What's my real speed? Well, there is no real speed; there's only relative speed. The Doppler shift only cares about relative speed; there is no absolute speed, meaning okay, if I could find my reference frame such that I'm going the absolute speed, then everything is going to be fine. That sounds like something you might hear about in a comic book, maybe it's like, "Oh, I'm going the absolute speed," kind of a Flash thing or something. So you're going at absolute speed, but there's no absolute speed. That's an odd thought, but there is one absolute speed: the speed of light, but that's the speed that the light's going, and it only goes that speed, so that's kind of weird to think. So there's really no such thing as a as a uh, as as a true speed, meaning the speed with respect to space and time, because there because all space and time is relative. So you have to measure Doppler shift with respect to your speed with respect to the source or the observer, and if one's moving, the other one could be moving in exactly the same way, in the same sense that the Doppler shift would occur if in the Indy 500 everybody in the Indy 500 stands were simply moving by the car and the car was standing still. The Doppler shift would still occur for the for the people in the stands. That would be very jarring uh, to to realize that the car is standing still and the entire city of Indianapolis is moving, but it would have the same effect in terms of the Doppler effect.

All right, so what do we mean by the wave nature of light, and what do we get out of it? And wonder for the nice things that we see is that you get pretty rainbows, and pretty rainbows are part of the wave nature of light because as light enters a prism, the speed of light changes, and in a prism in glass, the speed of light is of is a function of wavelength and frequency. So the blue light is bent more than the red light, and so the chain there is a there is a frequency dependence, and so the light spreads out as it passes from air into glass and then from glass back into air. The uh, the change in medium actually, because it goes through the glass, it actually gets spread out by the glass. Anyway, our more important thing is the pretty rainbows that are caused by by water droplets in the air or by or by pretty prisms hanging in your window. Is that the visible spectrum, the visible spectrum that which we can see is called the visible electromagnetic spectrum. The invisible electromagnetic spectrum is roughly between about 4,000 angstroms and about 7,000 angstroms, or 400 nanometers to 700 nanometers, and it spans from the violet all the way through the deep, deep red. And if it's shorter wavelength than violet, we call it ultraviolet, and if it's longer wavelength than red, we call it infrared, and their frequencies are very high; they're on the order of 10 to the 14th cycles per second. But the wavelengths, let's look at what the wavelengths are for just a second: 400 to 700 nanometers. We already know that there's wave properties about light, and since light has wave properties, it does diffraction. So why don't we see diffraction everywhere? Why isn't everything fuzzy? Because waves of light are which should make things fuzzy. I mean, we have eyes, and as light enters our eyes, it's an aperture, and the aperture then means that inside your eye the light must spread out. So why does why isn't everything all fuzzy? Well, because the wavelength is very small with respect to the aperture of your iris of your eyeball. So your iris of your eyeball is a couple of millimeters; right, it's a few millimeters. That's really big compared to nanometers. So there's an order of tens of thousands of them. So uh, if you're looking at like 700 nanometers or 500 nanometers, let's keep it simple, and that's many thousands of times smaller than the apert the size of your iris, and so waves don't really notice the diffraction, so the diffraction effects are not very noticeable. However, if you wish to see them, take this little experiment: take two of your fingers together like this and just barely close them, so there's just a tiny bit of light between them. Hold them hold them close together so there's just a little bit of light and bring it close to your eye and look at some bright light source, and you'll see in between your fingers dark and light bands. That's some diffraction patterns happening because of the because of the diffraction around the edges of your fingers. So it's really kind of pretty; you can see that with just your fingers.

All right, so the fun thing is is that the light comes in frequencies and wavelengths and packets of light called photons do that, and that's what we call light. Well, here's the funny thing: because individual packets of light called photons have individual frequencies, then there's really no such thing as color. Color is a construct; it's a biological construct in your brain. What does that mean? Well, it means that there are right there are cells in your eye which are which are receptive to certain ranges of color uh, and if they're receptive to say maybe 15 nanometers from say 500 nanometers to 550 nanometers, maybe that's the sensitivity of that cell in your retina in your eye, and the rods and cone the cones in your eye are receptive to many wavelength bands, and so if you can see many many colors and you are gifted to see many colors, then you have lots of different sensors, and they're very fine, and they can see lots of different things, and you have lots of ways that you get that very narrow bands of frequencies to which these cells are um, are sensitive. So your brain then takes this information as the cells are fired off by the light and they say, "Oh, I can see this; I get a photon; I get a photon; I get a photon," but then your cut your brain then says, "Oh, that's the cell that makes purple; that's the cell that makes green; that's the cell that makes red," and where'd you get those words from? Those words came from what everybody called that thing that we call red, and that redness is what we culturally call red. Isn't that interesting? So color is in your brain; you construct it because you add photons inside of a filtered frequency receptor, and that scepter is called a cell, and the cells can retrain can see lots of different bands, and it's the difference in brightness between your yellow receptors and your blue receptors or your blue receptors and your red receptors that tells you what the color is. If your red receptors are really firing off and your blue receptors are not, then you'll call it red. If your green receptors are firing off and neither the other two are, then you'll call it green. That's how color works, and we call that thing green. Now people are colorblind; their blue receptors and green receptors are fired equally, so you can't tell the difference, and that's kind of a sad thing for them because they go, "What the heck is that? I don't see grain; I don't see blue; I just see kind of a gray," and that's what people have got with their color blindness; they can't tell the difference between the colors. All right, so that's pretty good; we'll see you next time.

Hi, this is Jason Kendall, and welcome to the next of my introductory astronomy lectures. We're still talking about light. Light, what the heck is that stuff? Light, light is well, the thing that we see things with, so we want to know exactly how light does what it does. Last time we reviewed the concept of the speed of light. You're here; the concept of Doppler shift, we reversed the concept of what the electromagnetic spectrum is and how it varies with wavelength and what visible light is. We didn't say what it was and how it's created; it's kind of weird. We know that it has these wave properties and it acts like a wave, but what makes it act like a wave and exactly what is it? Well, to understand that, we need to know how light is created. So let's take an example: how does matter create light? That's an interesting question. Let's start and go back and say, well, we've talked about Maxwell's laws and the nature of electromagnetic interactions, but we also talked about the nature of fundamental particles like electrons and protons. An electron and proton has a charge, like an electric charge. A proton is how the electric charge is distributed inside; it has quarks inside it, but really from the outside far enough away, meaning about 10 to the minus 10 meters, it looks like a point charge with a plus sign, and that's pluses by convention; we just call it a plus; it could be a minus; could be a plus; it doesn't really matter; it's just what we call it. Um, but then the electron has the exact opposite charge, the same exact amount, but exactly this different exactly opposite sign. So two like charges, plus plus, will repel each other, and two uh, opposite charges will attract each other. That's the nature of it, but what do we mean by charges and why do they repel each other? What's going on? Well, let's think about this concept, an incredibly important concept to all of physics, and in fact, the incredibly important concept, the element of what we call electromagnetism, is the idea of an electric field. An electric field is the influence in space by an electric charge to everything around it, and it doesn't have a limit; it just keeps going; there's no limit; it's just its intensity drops off as the distance squared, but there's no real like limit where it says, "Well, now I'm done, and it stops, and it's the end of the line." So really this picture of an atom that is out there or a plus charge that sits there, and that plus charge just has these what we call field lines, and if you place something, say another plus charge at a location on a field line, the total number or density of field lines at that location determines how much it's getting it pushed away. So the field says, "Give me a test charge; I'll tell you what force I'm going to exert on another get off due to the charge at the source." So I placed a little test charge at the at the source of the um, at the at the field line, and we can place another test charge, maybe once plus one's minus, but if it's plus, it gets pushed away, and if it's minus, it gets attracted towards it. So the field lines also determine the direction of motion that the test charge will go, and from a plus charge, we can think of it as being outbound, and a minus charge it can be considered inbound, and by convention it doesn't really matter what direction, but we can just do it that way. So a plus charge, if you place another plus charge on a field in an electric field next to a plus charge, and the test charge is very tiny, so incredibly tiny or positive to be tiny that it actually is the thing that's moved and not the source because they're pushing against it, remember Newton's equal and opposite forces; one of them just has to be a big enough charge that it doesn't get affected by the other charge as much. So the test charge can be infinitesimally small, and then it just gets rocketed out on those field lines, and it goes very, very far away. But if you place it closer, then the field lines are denser, and that means it gets a harder push, and if it's an electric if it's a negative charge, then it'll be attractive in the same way; it'll be attracted, not as much if it's far, and the closer you put it, the more attraction it shall be. So it gains energy as they fall towards each other because they're pulling on each other, and the closer they are, the harder they pull each other because the force of attraction is increased as their as their distance as their distance is is made small, and the force of attraction or repulsion is decreased as they're farther and farther apart, and so at some point they can be so far apart that that the the electrostatic or electrostatic or electromagnetic force between them, the electric the electrostatic force between them can be minuscule and not taking into account. However, if you have loose charges around there, they really true this; the electric force is very strong and is going to really try to actually make it so that there's that the charges get neutral. In any event, opposites attract, like charges repel, and if you've got one, you got the other. So that's really what we're talking about. So plus charges repel against plus charges, and minus charges delegate minus charges. Protons have a plus charge; electrons have a negative charge; they have exactly the same amount of charge; they are just opposite and equal magnitude. The electron has a much smaller mass; a proton has a much larger mass than the electron, so the proton tends to stay still where the electron tends to whizz about.

All right, so distant charges feel the effect of other charges, so all charges feel the effect of the other charges through the electric field that they generate. So really space is permeated by the electric field due to charges, and if they're all standing still, all these electric fields are don't move; they're just kind of sitting there. If everybody's held in place, they're all pinned down, let's say all the charges in the universe are pinned to one place to wherever they're at, doesn't matter where they're at; there's a pin, then everything will be pushing on it, but then they're pinned down, so they can't move, but they're pushing with the electric field or they're pulling depending on their charges and or the signs of their charges, and that tells us how they're going to move. All right. Now let's do something very strange: we then jiggle one of them. If we jiggle them, then the then the field must change, and how does the field change? The field may change in a regular way. Let's say you instead somehow take an electron and put it between let's say you staple it between two springs, and if it's between two springs, it might go up and down between the two springs, or it's stapled to between two boards on two springs, and so it can go up and down, and as long as you don't touch it, it's not going to vibrate, just like anything that's held by two strings between two boards, right? But if you come along and flick it, then the electron will bounce up and down, right? Now the electron has an electric field that's associated with it, and the electric field is inbound by convention, and the field lines are drawing towards it. So let's use a proton, so this outbound, I like the outbound arrows. So a proton is staying put and it's staying itself between these two springs between the two boards, and you kick it. Now it's going up and down, and if it's just going up and down, bouncing up and down like this, what do we notice? The field doesn't stay fixed in space; the field follows the proton. So the proton was here, and the field radiates out from wherever the proton is at that moment. So then the way those from the field lines aren't fixed in space; they're moving; they have to be moving up and down. Wait a second; if you make something move up and down, then you've got a wave. Now what does the pro what happens to that? Well, then there's a disturbance in or disturbance or a wave motion of up and down of the proton. So now the electric field is going up and down. Now how long does it take for something very far away, a distant charge, to feel it, huh? Well, those changes in the electric field propagate at a particular speed: the speed of light. So really what is light? Light is a disturbance in the electric field of a charged particle that makes a disturbance; it vibrates; it moves; it accelerates; it changes, and as it changes, the electric field disturbs, and that disturbance propagates along. That disturbance is called a photon; that's light. Light is that disturbance. Now why doesn't it propagate forever like these like these vibrating strings that we see or like you can pluck a string and have a standing wave? Well, photons propagate from here to there in the same way that if you take a jump rope and you flick the jump rope, when you flick the jump rope, it bounces, and if you if the jump rope bounces, then you you see the pulse go up down the jump rope, and the pulse comes back from the jump rope. Now you can make it so there's a nice regular pattern to it; you can do double dutch by having two the jump ropes go around; you can make it have a nice even string where you have wave patterns in the rope, but really if you flick the rope, then the disturbance goes down the rope and back the rope, and that disturbance in the electric field line as it propagates due to the previous motion of the proton is what the photon is; it's a disturbance in that electromagnetic field. That's really something. So a photon is a disturbed magnetic field that was disturbed say some time ago by a very distant thing, and then that distant thing that propagation of that electric field from there to here gets to us eventually. Isn't that weird? If that's what light is, if that's what light is, and that's probably a very close analogy to what we call it from claw from from great from deep studies of what the nature of space and time are, then light then the just when you look at some distant galaxy, maybe millions of light years away, there was some electron that shook, just a tiny electron or a tiny proton, a very, very, very lightweight object shook, created a disturbance by its shaking that made a disturbance in its electric field, and that electric field disturbance propagated out through space on the electric field of the proton and eventually reached your eye three million light years away. Wow, that's interesting. So it propagates through space radiatively carrying the energy of the disturbance that created it across space vast two areas of space as a packet of as a packet of a disturbance as a wave packet, a disturbed wave packet in the electric field lines as it propagates through space. That's an interesting picture of a photon, and that's what we call that. So that packet of waves, that disturbance, is called a photon, and electrons don't vibrate forever; protons don't vibrate forever; they take a certain amount of time, and then they stop vibrating, and when it's done vibrating, then guess what? That's the end of the wave packet train, and there it goes, the photons on its way.

All right. Now that's essentially a very meat and potato sort of elementary way of talking about photons. Photons have a certain amount of energy; an amount of energy is related to the frequency or the wavelength, whichever you like to use in order to say how much energy the photon has. So the wavelength of the photon determines its energy; the short wavelength photons have high energy; the long wavelength photons have low energy. Radial light has long wavelengths; it's low energy; gamma-ray light has high weight; it has short wavelengths, so it has high energy. Um, next, because it's a wave motion, and if you do something really interesting, if you take because we learned this through electromagnetism, if you go taking a collector statics class, you learn about Faraday's law, you learned about the nature of of of the of the beatles of art law, you learn all these interesting things where if you take a current, take a current of of electrons, which is now an electric flow, a flow of charges in a circle and make a circular charge flow, you create a magnetic field. A magnetic field flows through the charge. So if you want to start your car, you use what's called a solenoid, and a solenoid is a many, many, many turns of electric coil. You then put a charge back and forth; you change an electric current back and forth through that solenoid, and it moves a piston that then that then starts the engine running, and that start and that forces gasoline into the into the engine and then starts the engine up. So you can take an electric force from the battery and do an alternating current through it that then shakes the solenoid and shakes and it creates an alternating magnetic field and tar starts a car. So an electric field going in a circular motion creates a magnetic field. Likewise, if you take a magnetic field, a fixed magnet, a fixed magnet that has a magnetic field like a like an iron magnet or a bar magnet, and then you spin it, it will create an electric field. That's part

Of the way that we get electricity out of hydroelectric dams, you create fixed, large bar magnets. Then, as the water goes over the waterfall, it turns turbines. The turbines then spin magnets which are which are which wrap around coils of of of a wire. And those wires then have an electric current that is created out of them by the by the twisting tur by the spinning magnetic field. Wow. So there's a link between the electric the emotion of an electric field and the creation of a magnetic field, and the motion of a magnetic field and the creation of an electric field.

We've just learned that when you vibrate an atom, you create an electric field. You always have an electric field, but if you vibrate an atom, then it creates a disturbance in the electric field. That disturbance is called a photon. But if you have it but the photo but maybe you're accelerating it, and you then have if you have any kind of motion that can be determined to be cyclic with respect to an electric field, then there is a perpendicular magnetic field to that. So it is predicted that the map that the photon has a magnetic field that runs perpendicular to the electric field in the direction of propagation. So as the magnet as the photon propagates maybe with the direction with with a wavelength like that going that direction, it will also have a magnetic field that goes this way as it propagates in that direction. So electromagnetic fields, magnetic fields are linked to electric fields.

For the earth as another example, the earth is it has a liquid metal iron core. And as the earth spins, that magnetic that liquid iron core has a strong magnetic property because of ferromagnetism. And that creates an electric field which then creates a magnetic field. We have a dynamo effect, and thus the earth has a product a protective magnetic field around it. Really quite interesting. So magnetic fields are created by the movement of current, and the movement of current creates magnetic fields, and they're linked. All right, and that's the nature of a photon: is that oscillating electric fields create magnetic fields, and the same thing, an oscillating magnetic field creates an electric field. And as that propagates through time, we call that a photon as well. So the wave packet of a photon isn't just an electric field; there's also a magnetic field component to it as well.

Uh, so the direction that we call that magnetic field is called polarization. So there might the the photon might be oriented up and down; the electric field might the vibration might be like this because of how we shook the proton; it might be going like this. And so the orientation, the polarization of the light might be in that direct might be up and down. This is also a reason why when you wish to have good sunglasses for the summertime and you wish to see the road while you're driving, you use polarized sunglasses. Because when light reflects off the road, it reflects off of a flat surface, and when it reflects off a flat surface, it bounces off that flat surface, and all the vertical components of the polarization are gone from the scattered or randomly oriented light in its polarizations to only having the ones that are parallel to the road. So all you need to do to have good glasses to drive with, which are called polarizing sunglasses, is to have something that blocks out the light that goes like this. And how can you do that? Not too difficult. You think of a picket fence. Picket fences: you can throw a frisbee through on its edge because the slats are vertical, and so there's a hole that's vertical between the slats, and you can't throw a frisbee between the slats of a picket fence; however, you can throw it on the angle, uh, throw it when it's on the side through the freaking fence, but not flat through the prickett do through the picket fence. Well, if you want to change if then take that principle aside, so a polaris polarizing sunglasses are simply very small slats that are printed inside the glass that then block the light. And how can you see it through it? Because the size of these slots is on the side is on the order of the size of the wavelength of light, and so the polarized light that's coming up and down, it's going side to side, is blocked because all the slats are vertical. So you get to see only the vertically oriented light, which is minimized because of the reflective property of the asphalt. So light comes as polarized as well as being as well as being electromagnetic and has an orientation of the electric field and orientation to the magnetic field 90 degrees. The electric field has a direction of motion at the speed of light that we talked about.

So what is light? Light gets emitted in copious quantities by hot objects, by electric fields that are being made by vibrating electrons and protons inside of atoms and molecules inside of dense objects or inside of hot objects or inside of a inside of things that are simply energy, and they re we see that energy coming off of them. So the light's really there, and it's all sorts of different frequencies, and it's all sorts of different wavelengths from very very high energy to very low energy. And how it propagates from one medium to another, whether it can penetrate a wall or penetrate only air or whether it gets absorbed by water or whether it gets absorbed by nothing and passes through everything is all dependent on the properties of the material through which it passes. So light is everywhere; it bounces around the room knocking about, and as it hits a wall, it reflects off. How does it reflect off a wall? It goes a little bit in, and it shakes the electron inside of there, and the electron says, "No, I don't think I'll need that sandwich today," and shakes back, and the photon comes back out. So really what happens in a reflection is it goes in and gets turned around. You can think of it as getting trapped in a in a turnstile; the light gets pulled in and swung around; it doesn't actually it gets absorbed very briefly and then re-radiated back out the same direction it came. And these kind of ray tracings were done by Newton a long time ago. So we have predictions, and in fact, quantum electrodynamics actually accurately predicts by by some really interesting arguments that I'll leave to Richard Feynman if you go look up at his videos about this exactly how that works, which is really fascinating. Um, you can look that stuff up; this is not really for an introductory level thing, but you look up quantum electrodynamics, and it'll tell you exactly how the nature of the phase shift of the frequency of light interacts with the phasing with how the electrons move inside of inside of a material. So it's a very I I won't be able to do it justice in a short video, so I'll just leave it to to others who have done that with Richard Feynman videos. Go look his stuff up; it'd be fantastic; you'll love it. Um, but be that as it may, the study of how light actually interacts with material is an incredibly important element to all of astronomy and all of physics; in fact, it's central the because one of our more key ways to understanding the nature of materials and physics is actually through spectroscopy.

All right, so let's finish with the electromagnetic spectrum. The electromagnetic spectrum is the all the possible wavelengths of light. There are many different wavelength regions from radio to infrared to microwave to visible to ultraviolet to x-ray to gamma ray, and they span an enormous number of wavelengths and frequencies. The total number of wavelengths that we call infrared is is I think about almost a thousand times bigger than what we call visible light, and radial light is pretty much everything short and longer than like a centimeter or so. Uh, ultraviolet light is shorter than 300 nanometers and goes down to a few tens of nanometers when we get into soft x-rays, and soft x-rays go up to uh go up to angstrom level to go up to single angstrom sizes and even harder when you talk to gamma rays, which are on the size scale of 10 to the minus 12 meters in terms of wavelength. So the higher the energy of the light, the shorter the wavelength and the higher the frequency, and there's no real theoretical limit to the low lower limit to the wavelength of light, but there is kind of a theoretical upper limit to the total energy of light that can occur in terms of energy because at a certain point the light becomes so energetic that it can actually fall apart and become other particles like it actually can just turn into matter if the energy is great enough, and that's a study for nuclear physics. So the electromagnetic spectrum is simply all the different forms of light in all their different wavelengths, but the total amount of light and different kinds of light that exist in the electromagnetic spectrum is vast, and it's the best way to the best analogy for it is look at the key the keys on on a grand piano. And if we could only look at the sky in visible light like we had for centuries all the way up through the night uh the early 1960s when we finally got the technology looking radio light and when we finally launched satellites actually to look at ultraviolet and gamma ray and x-ray and infrared, the analogy is almost completely accurate that looking at the light looking at the universe with only one indivisible range is like playing a piano concerto uh by only listening to one middle c one note middle c on the piano, and that's what it's like. So imagine hearing a gorgeous symphony, and somebody some crazy composer says, "Well, this is a symphony; this is this is so and so symphony, but I've removed all of the notes except for middle c." And so you might hear this 25-minute um you might hear this wonderful piano concerto that lasts for half an hour, and all you ever hear is when they play middle c; that's what it's like, almost. You're missing the whole thing if you don't see in these other wavelengths of light. So the electromagnetic spectrum looks at so many local things, and we get to see so many more things, so many different processes that occur as a result of it. And what are those processes? That's what we'll talk about next time.

Hello, this is Jason Kendall. Welcome to the next of my introductory astronomy lectures. Great to have you back. We're now going to start diving deeply into technical aspects of astronomy and how they relate to the physics of astrophysics. So to this time we're going to be talking about the nature of stellar brightness and luminosity and luminosity distances. So let's start with the concept of what we mean when we say the words, "How bright is the star?" Usually when I take people outside and go to a telescope, they're going to say, "Wow, look at that bright star." What they won't say, "Look how bright that star is," they'll say, "Look how big that star is." And people mean big, but they really mean bright. And so what do we actually mean by the word bright? And so brightness is a thing that we actually try to quantify. Brightness is an amount of energy we receive in terms of photons per second and given white brightnesses um, and so that can over in a detector such as an eye or a camera or something like that. So when we talk about that, we're really talking about the nature of brightness is the perception, but really if we want to know about the nature of the object itself, we need to talk about luminosity. And luminosity is the intrinsic amount of energy the object such as a star is putting out every second over whatever wavelength band we wish to care about. So how bright is a luminous asaurus? How bright is it? Well, that's the number of photons that arrive at a detector, and so that's what we call the apparent brightness. And frequently in the literature we call that B, capital big B, is the apparent brightness, and what we measure that in is some so really odd units, but strictly speaking, everything that we ever measure brightness in is essentially either photons per second in a surface area or energy per second in the surface area. Photons per second: we already know what the energy of the photons is, so we can just deal with that. So our real question is we want to know the energy that we're receiving per second over a surface area, and that's what we call the apparent brightness. The thing we're trying to hunt for though is what we call the luminosity; that's how bright something really is. So we're getting these two words, brightness and luminosity, a little mixed up, but we're going to resolve that shortly. Luminosity is the entire luminous output of the star. When we say luminous output, that's where it comes from. Luminous means light, so luminous output is the total amount of energy output by a star in the form of light per second. Now we can measure that in energy per second or more commonly we use the word watts, such as light bulbs. Light bulbs have a 100-watt light bulb or a 500-watt light bulb, etc., etc. Uh, the sun's a lot brighter than the average light bulb, so the energy we met the units we measure luminosity and our energy per second, and that's what the production amount of energy is happening by that object. So these two things are of course related because brightness is how bright you see it to be, and luminosity is what it's actually putting out, and how bright it appears to you is actually the depends on the luminosity divided by 4π times the distance to the object squared. Because let's assume that the light is being spread out uniformly across a sphere such as like a a bulb light. So if it's a bulb light, we expect it to be tr going across a sphere, and so it spreads out evenly, and so the brightness drops off as the distance squared to the object. So the luminosity gets dimmed by the distance squared. So that's where we get the units of energy per second per square meter or watts per square meter if we're using SI standard units. And when we're talking about that, that's where that 4π comes in from; it's not just the distance squared; it's the 4π because it gets spread out over a surface area, and it drops as it goes. So if something's twice as far, it's four times as dim; if it's three times as far, it's nine times as dim; if it's five times as far, it's 25 times as dim; it's 11 times as far as 101, 21 times is dim, and so on. So the 4π comes from the fact that we're assuming it spreads out evenly over the surface of a sphere. So what do we mean? Does the star look bright simply because it is intrinsically very luminous, or is it faint but nearby? So we have to measure the distances to things, so distances become a very important thing. Luminosity is not dis distance dependent; it's a distance-independent property; it's a property of the object itself, whereas brightness is dependent upon our perception of it. So we need to be able to know how to measure brightness, and that science is the thing we call photometry. And we express that photometry is really the measuring of photons. Photometry: the measuring of photons. So we're counting the total number of photons we receive, and there's there's a couple of ways we talk about it. We can express it in terms of the old familiar thing that we learned from parkas a long time ago in stellar magnitudes, or we can express it in absolute fluxes, meaning the energy that we receive in the detector per second on top of the surface area. And in astronomy, we use both of them interchangeably. So the magnitude system is something that you'll hear very commonly if you go outside with a bunch of amateur astronomers; they're all up in the sky; that's a 5th magnitude star; this is a great night; we can see down to 6th magnitude, and you'll hear things like that. Or, "Wow, the brightest star in the sky is a zeroth magnitude star," and you'll hear such things. Well, the tradition of magnitudes dates a very long time ago; it comes from Hipparchus, which was a Greek philosopher, and he actually of Nicaea, and he lived roughly about roughly roughly in the second century BC. He lived about 70 about 190 BC to 120, and he classified stars and ranked them into magnitudes. He said the first magnitude stars in the brightest, the second magnitude stars the second brightest, and the other ones are dimmer than that. So we rank them into three groups. Later on, Ptolemy of the Almagest, who gave us the Ptolemaic system of the cosmos, which is the sun-centered Ptolemy came along and made it more qualitative and added them into six separate buckets so that the magnitudes could be divided in the first magnet right all the way down to the sixth sixth brightest stars, six magnitude being the sixth the sixth brightest type of stars. So these were all relative brightnesses, and they were done by eye; there's no detectors; there's no photometric detectors; no cameras in 100 BC. So that was kind of a tricky thing. So you had to say, "Well, this one's a little bit brighter than that one; this one's brighter than that one; that one's brighter; this one; this one's around that one." So they rank to them in terms of their apparent brightness, and that was called their magnitude system, and magnitude simply meant to them it looked bigger because magnitude means size. So my goodness, it's actually not a size thing. So our stars are so far away that we can't actually perceive their size from Earth very easily; only a few stars have actually been measured in such a way, but the point is is that magnitude means size, but here we're using it as the word for brightness, and magnitudes are a measure of relative brightnesses between stars. Now the modern magnitude system was developed in 1856 by Norman Pogson, and Norman Pogson at Oxford, who was a also uh who's considered to be uh he's also from he went to India; I believe he was from India originally um, and he developed what we call the modern system magnitudes, and he codified this ancient idea of Hipparchus into a separate set of definitions. He said, "Well, every five steps of of the stars is of every five magnitudes is a set of 100 brightness in times." Now he actually was able to quantify this because it's very close to the truth in terms of the old idea. So Hipparchus's idea modified by Ptolemy was actually very close to the eye, and the eye acts logarithmically in terms of what their brightness is that we can measure. And so he said that if a difference in five magnitudes is a hundred times brightness, and so he also said the standard star of brightness was Vega, which is zeroth magnitude. So for example, a ninth magnitude star is a hundred times brighter than a fourth magnitude star, and a zeroth magnitude star is a hundred times brighter than a fifth magnitude star, and so forth and so on. So the faintest stars that we can possibly discover with any aspect aren't really necessary stars; they're probably galaxies or quasars; that's about 30th magnitude, and those have been detected by the Hubble Space Telescope. Ground-based equipment, the best ground-based equipment diameters is roughly 15, 16, maybe 18th or 19th magnitude on the ground. So you can get some pretty faint stuff. Remember, every difference of five is a hundred times, so zero magnitude is 100 times brighter than five, which is 100 times brighter than 10, which is 100 times brighter than 15, which is 100 times brighter than 20. So a difference between zero magnitude and twentieth magnitude is a hundred times a hundred times a hundred times a hundred or ten to the eighth; that's a hundred million times brighter. A zeroth magnitude star such as Sirius in the sky is a hundred million times brighter than a 20th magnitude star, and there are 20th magnitude stars that have been observed in the Milky Way; they're just really dim and really far. All right, so Pogson's definition, it can be codified numerically by saying the ratio of the brightness is equals 100 to the difference in magnitudes divided by five. And so the difference in five magnitudes gives us a hundred times brightness, and that allows us to define the magnitude system, but still it's a relative magnitude system; it's always relative. What's nice though is that it actually allows us to codify if we can get the brightness in energy per second on a surface area; we get the brightness of one star, and then we can actually translate brightnesses between each other. The this also allows us to roughly guess by eye the brightness of something and then allow us to get very close to what we actually get with it with some sort of formal detector. Nicely enough, the standard star is Vega, and Vega is prominent to most people in the sky, and the standard for vague is a little tweaky because very Vega is a variable star, but in terms of things, Vega was defined in many magnitude systems to be zero, and so you can you can basically start from Vega and

Go everywhere, and you compare and compare and compare. Oh, how am I right? Am I compared to Vega? I'm brighter, I'm dimmer, I'm brighter, I'm dimmer. Vega is useful because it goes across the zenith for most of, for many North American and Northern European and north northern hemisphere observers. It doesn't go across the zenith for people in the south hemisphere, so they got to use secondary standards of some kind because the entire system has been centered around the northern hemisphere. So we can codify that, and so basically we can say the star compared to Vega's brightness could be a hundred to the the stellar magnitude divided by five. And that allows us to actually compare a star's brightness with respect to Vega and give us a numeric value.

If somehow you can get the energy received per second at Vega from Vega as you can perceive energy per second on top of surface area, that gives you that thing. Now you can do that both ways because your detector detects in energy per second; that's how it detects. So you're going to translate this into magnitude. So magnitudes tend to be a pretty handy system because there's something visual; also, they're logarithmic. So therefore, the apparent magnitude system ranges from from negative 30, which is well negative 30, which is roughly around the sun. The sun's a little bit dimmer than negative 30, but uh the apparent magnitude of the sun is negative 27. It goes all the way to Fulton, which is about negative 12 and a half or so. Naked eye limit is about six. Binoculars go down to about 10. Uh, the typical one-meter scope is around magnitude 18 or 20. And anything bigger in the meter class scope than its car—that's uh that's almost out of amateur astronomy land. Uh, there are some amateurs who have bigger scopes than this; there's not many of them. They're expensive equipment to use and work with, but then we're talking in terms of large-scale observational qualities, and you get to four-meter class scopes which can observe down to 26 magnitude, and the Hubble that can observe to about 30th magnitude.

So the science of flux photometry—and what we call flux is not the flux capacitor from Back to the Future—but flux photometry is the total amount of energy, meaning flux. Flux is another name for brightness. It is the total flux that we perceive on top of it through a detector. Sometimes you wish to use fluence, which fluence is the total amount of energy, not just energy per second, but total energy on a detector. So it's energy per second, and that's been integrated over time; it would be called the fluence. So flux photometry says, I'm going to measure the brightnesses between various stars using various standards, and I'm going to use a filter wheel on top of this thing and check the differences of brightness between various filters. And then I'm going to start from Vega or whatever standard stars I have, perhaps anything in the land old set that'll send me over to uh to brightnesses of stars. So the science of flux photometry then says, Good, I'm going to try to get these brightnesses as accurately as I can, and I'm going to difference them against known standard stars; or if not this, not Vega, then standard stars that are agreed by the entire astronomical community in order to say this is how bright a star is with respect to this. So these standard stars have had their energy output carefully measured and repeatedly measured for non-variability, so they can be called standard stars. That's how Vega was discovered to be a variable star. It's kind of it's a slightly variable star, so it's harder to use. The sun's a slightly variable star in terms of if you were looking at it from every distance; in fact, it is a variable star. So we have to take into many accounts when we're doing the science of flux photometry. We have to do; we have to detect whether or not there's clouds in the sky, how high the object is in the sky, where the if there's a lot of things, the detector itself, how the how your your camera works, how your telescope works, um whether or not you have you have your the readout of your camera is good or bad, the temperature of your system. There's a whole bunch of things that can affect the brightness of your measurement. So that's for another day, and I'll allow you to go dig around the internet to walk down that very deep rabbit hole to see what you have to do in order to calibrate to to your telescope.

But in very general terms, we can then say the luminosity of an object measured through some brightness so is simply equal to four pi times the distance squared to the object times that brightness. And you just need two brightness; you need two measurements in order to get the actual luminosity. You need to know the distance, and you need to know the brightness. So if you can get one of those, you can get two of those. Brightness is pretty easy; that's just what you get at your detector, but you've got to back play it and remove all the effects of the earth's atmosphere and many other effects in order to make sure that you actually get really what you think is the real brightness. So you can say, Oh, there's all these things that took away light, darn it, and you take that into account, and then you'll get the brightness outside your detector and outside the atmosphere, and then you get a distance measurement, and guess what? You'll have the luminosity. So a lot of practical issues associated with this; there's a huge number. I described many of them to you, but when the biggest is distance, distance, distance, distance. Oh, it's the worst thing in the world, but a lot of distances can be measured um using parallax. And so parallax gets by the Park Coast satellite in the early 90s uh got the distances to about 100,000 stars, and the Gaia mission recently got distances to over a few billion stars. So this is a big, big, big improvement. So using these distances will allow us to get secondary things such as luminosities based upon appearances that can be seen without checking distance. So distances are incredibly critical, and once we get those things, there's a lot of things to go, and luckily the Gaia mission has done a lot of that, so it's fantastic.

So luminosity is either measured in watts or in this unitless thing that we will call absolute magnitudes. Absolute magnitudes or luminosity in watts; they don't depend on the distance. They all know stars have different absolute and apparent magnitudes, meaning the absolute magnitude is different than what we perceive it to be or see it to be. And the lower the number, uh the more luminous it is in magnitudes, right? And luminous just as how much light is coming out. So what we'll tend to do is we'll compare two objects' luminosities, and we see that they're relative to their brightness, and if they're and the inverse of their distance is squared, and that gives us that'll give us what we're going for. But we can create this concept called the luminosity distance, meaning how far is it based on how bright it is. So let's take as our example the sun. We can measure the sun to a pretty good accuracy, a very good accuracy; it's roughly 93 million miles. Um, that's a good accuracy, 150 million kilometers. So we can use that as a baseline. So if we know the the distance to the sun, and if we know the luminosity of the sun, which every with that's no variant, that's also very well studied. So if we got the luminosity of the sun, we've got the we've got the distance of the sun; we can make brightness measurements in the sun, then that helps us. Strictly speaking, we want to go across all wavelengths, and that would be called the bolometric luminosity, but we'll talk about that maybe later, but I don't think that's totally critical, but that's a real end result; it's a total output. So we're going to assume that we're going to upgrade; we're doing the bolometric luminosity in any event. So you figure out the brightness of the sun across the entire spectrum, and you know the distance to it, and you know the loop. Then if you can somehow derive the luminosity across the entire spectrum, then guess what? You can use that to find the limit the distance to other stars because if you can guess somehow their luminosity by hook or crook, maybe there's a way to do that, and there is; it's called spectroscopic parallax, but we'll talk about that later. So if you can get the luminosity of the star compared to the sun, or if you get the bright and get the brightness of that star compared to the sun, then guess what? You can get the distance to the star, and that's called the luminosity distance or the distance based on a standard object that you can calibrate against and then get the distance based on how bright you see it to be, knowing how bright it actually is. And the uh the standard way we talk about this in astronomy is using a thing called absolute magnitudes, and absolute magnitudes are a pretend concept that actually says, Pretend you take every star or every object in the sky and move it close or far to a distance from the sun of 10 parsecs. 10 parsecs, 32.6 light years, and then how bright does it appear? What's its magnitude? It's visual magnitudes; it's V magnitude; it's I magnitude. How bright does it appear when it's brought by magic or hook and crook or just imagination to 10 parsecs from home? And that is the definition of the absolute magnitude.

So how can we use this? The brightness; we compare the brightness to the sun, and luminosity; we can rearrange it and get to say, Well, how if we then say, Let's look at one star, just one star. Then if we think, Ah, this when the star is far, it's dimmer than when it's near, and if the star but it's the same luminosity because it's the same star. So the brightness only depends upon the distance squared that we have. So the farther star the d it will be compared to the distance the nearest r squared will give us; well, that'll show us the distance between them. Remember, brightness is defined to be a difference in magnitudes, so we're going to use the magnitude system in order to get there. The brightness versus far is one thing, and then we can equate that to Pogson's equation for the magnitudes, and then we get the magnitude of the far star compared to the magnitude of the near star, and then that gives us the brightness difference, and we work out to this thing where we find that the difference in magnitudes is equal to a logarithm of the brightness. So a logarithm of the brightness gives a logarithm of the longer the brightness, and therefore a logarithm of the distance gives us the magnitudes. Now if we can get the distances, we we're good, but we've already established one thing; it's the same star. So the magic distance we're going to pretend it is is 10 parsecs. So if we instead of saying look at the two magnitudes, we say one of them is the absolute magnitude, and the and that is the magnitude if the star were magically placed at 10 parsecs away, then we end up with what's called the distance modulus equation, which says the apparent magnitude subtract, and then you take the apparent magnitude; they subtract it from subtract from it the absolute magnitude, and that is the same; that is equal to 5 times the log base log 10 rhythm logarithm of the distance and then minus some number 5, all right? Because remember, magnitudes have no units; they're really strange; they're just relative brightnesses between two stars. So there are relative brightness; so they have no units unlike luminosity, which does. So absolute magnitude is kind of a funny thing; it's a unitless way of talking about luminosity, but if we know the distance to something and we can measure the measure measure the brightness and apparent magnitudes, then we have the absolute magnitude, and that's really something we can use.

So absolute magnitudes are important. If we know the parallax of a star, the parallax is the inverse of the distance in arc seconds. So if we know the parallax, we can take the base 10 logarithm of the parallax, add 1 to it, multiply that by 5, and then add the apparent magnitude to that; we get the absolute magnitude. So now we take two measurable things: the apparent magnitude and the parallax, and then we do some magic, some mathematical magic, some arithmetic on that, and we get the absolute magnitude. So if we can get the absolute magnitude of a star and know how that absolute magnitude compares to the luminosity of the star, and we have a fixed way of doing that, then measuring the apparent magnitude and the parallax will give us the absolute luminosity. There's a lot of trickery that goes into the last step, but it is possible, and it is dual at the very minimum. So as an example, if we take the one of the nearest stars to us without the actual approximate Centauri, but Alpha Centauri, which has a parallax of seven 742 milliarc seconds, and it has an absolute magnitude of just a little bit brighter than zero, it's minus 0.01, then that means it's absolute visual magnitude, apparent visual magnitude, meaning what we see it to be, that's a visual magnitude, and then the absolute visual magnitude is about 4.3 plus 4.3, and that's what the math works out to be. So magnitudes themselves are things that also we measure inside of filters. So a filter will actually determine it what we use. So we can have a magnitude in the Johnson B or the Johnson V, the Johnson I, or the Sloan I, or the Sloan U, or the Sloan V, or the Sloan B. There's all sorts of things that you can measure it in as long as you have a standard filter system. So absolute magnitudes are a really great way to actually get um a great way to actually give us luminosities and roughly the solar luminosity in absolute magnitude is about five. It's recently been defined by the International Astronomical Union, and so the absolute magnitude system no longer definitively relies on the sun simply because the sun is slightly variable. So you don't want to try to tie a an absolute system onto a variable thing such as the sun. So roughly speaking, the sun is about an absolute luminosity of plus five, give or take a little bit, and that corresponds to a solar luminosity of one. So if we then go up and down, if it's a hundred times the solar luminosity, then it has an absolute magnitude of zero. If it's ten thousand solar luminosities, then it has an absolute magnitude of minus five. If it has a hundredth of a solar luminosity, then it is about a magnet an absolute magnitude of about 10. And if it is 10,000 110,000 of a solar luminosity, then it has an absolute magnitude of plus 15. So this kind of helps us get to get around because this you'll notice that the luminosity was whereas the uh whereas the magnitude system is linear, the luminosity of the magnitude system is is exponential; that's the nature of a logarithmic relationship. So that's how bright we can look at it, and it's another way of thinking about it. So brightness then becomes luminosity as long as we know the distance, and the best thing we can get for distance is called parallax. So parallax then gives us distances in parsecs, which is a geometric distance. So we can play lots of games and say, Oh, if something's 20 parsecs away, and what's the magnitude if you have an apparent magnitude of four, and if it's like five distant parsecs away, the apparent magnitude of four, what's the what's the absolute magnitude, etcetera. Lots of games you can play, so you know, and so what we find is that we can is that the relationships really lead us down a lot of different places, and we're going to use these relationships over and over and over again with respect to luminosity and brightness and magnitudes, and the distance modulus equation will come in many times in the future.

Hello, my name is Jason Kendall. Welcome to the next of my introductory astronomy lectures. Today we're going to continue the idea that we did last time when we discussed the nature of magnitudes and brightness and luminosity, but now we're going to formulate it in terms of an important thing that we call color. Color is an incredibly important thing to astronomy because, well, things have different colors, so we need to actually know how we can quantify this concept of color. But first, what we need to do is understand a little bit about where color arises and how light interacts with matter. So let's discuss that first before we get into the nature of what color is with magnitudes, all right?

So light and matter interact, and if you've ever been alive, you know that light bounces off walls, reflects off of things, comes from light sources like light bulbs, things that are hot, glow, and so forth. So what matter can do to light is it can allow it to pass through it, such as the glass that's passing through the lens that I'm looking at you with. Uh, it can also reflect light; light gets reflected off of various surfaces, and it can then bounce from one surface to the next. Matter can gain this energy by absorbing light. So if you go out on a hot day, the light from the sun you get absorbed, the light that light in the form of infrared radiation that reflects that goes into you and absorbs in your skin also is the ultraviolet light does the same thing, and then you absorb the energy of that light. Third, matter can lose energy by emitting light. So if it's warm or hot or hot in the surroundings, then light will spontaneously come off of matter that is warmer than its surroundings and radiate to the surrounding environment, and that's called radiative transfer of energy. Okay. So there are two things that are important with respect to color and temperature, and temperature relates to the internal energy of the matter. So the internal energy of the matter um is what we would call temperature. So the internal energy can have multiple forms: one is the structure of the material itself; that would be the phase of the matter, and the other is the average random motions of the material inside the matter, and that would be the vibrations of the mass of it. If it's a gas, how fast it's moving around the room. So the internal energy is a function of temperature, all right?

So let's look at the how color relates to temperature. So first and foremost, color is a funny thing. What is color? I mean, I'm wearing a little checkered red, white, and blue shirt. How do you know what I'm wearing is a blue shirt? Blue checkers and red checkers on it with a white shirt and some fun red and blue and yellow things in the background here. How do I know what color is? Well, color is a funny thing because it's defined inside your head. Color is actually a concept of relative brightness between sets of things that do reception of light. What do we mean with that? Okay, so your eyes are filled with cells on the on the backs of your eyes; it's called the retina. The retinal cells there's the cones and the rods. The rods are for nighttime, and the and the cones are for color and daytime. So the rot the cones or the color rods have various receptor cells, and there's maybe let's just over for an oversimplification; we know that there's maybe three. Let's just call it three. So you've got a set of cells inside the cones that are red receptors that receive a green receptor and a blue receptor. So a red receptor would only say fire off if red light lands on it or what light in a specific wavelength region, let's say. Then a green receptor only fires off if green light or this wavelengths of light in a specific wavelength region, same with blue. So then the relative brightnesses of these to these signals from the various cells, the pieces in each cell, determine the color. If it's if more of the red cell got fired than the green, then we would call it red. If more if the green and the blue got fired, then we would call it yellow compared to the red. So anything the red the color then gets constructed in your brain, and then we culturally decide to call red red and blue blue and yellow yellow yellow, but that's cultural. We want to quantify it. So what was done a long time ago is the Johnson filter system actually tried to mirror roughly what your eye sees, except it extends it into the infrared and the ultraviolet. So the primary filters that are used astronomically or at least the easiest ones are some of the oldest ones to use that are still standardized are the Johnson UBVRI filters. So we've got a blue filter, which is B; we've got a V filter, which is kind of yellow-green; and then we've got an R filter, which is red. So the R filter covers a wavelength region about 6,000 to 7,000 angstroms; the V filter covers roughly about 5,000 or 4th at 5,500 angstroms; and the blue filter covers

Roughly about 4,000 angstroms. So these three filters together allow light of only a certain wavelength to pass through to the detector. Notice how that's similar to what your eye does, but your eye does it automatically. The retina has these cells that only detect the light. Instead, now we make a nice photo detector, some sort of camera, and what we do is we put in front of the camera a filter so it blocks out all except the group, the blue light, or the green light, or the red light. And therefore, what falls on the camera is either blue light or green light or red light. That's different than the then then what happens in your eye. We don't have filters in our eye that filter things out; we have cells that receive certain things. So we can think of the cells as kind of like inverse filters; they absorb only specific wavelengths of light, but a filter transmits only certain wavelengths of light, and it's the specialization of this transmission that allows us to actually determine color. All right.

So the Johnson's cousin's filter response system it goes has a very specific wavelength, uh, transmission frequency transmission wavelength dependency. So we don't expect to get pretty much any light that is more that is more blue than say 3,000 angstroms in the B filter, and we don't expect much light longer than 5,000 angstroms to pass through the B filter. And that's what we mean by these transmission curves. So the sun itself has a certain brightness in each one of these filters, and we can actually then look at things and do relative brightnesses of the filters. Typically, astronomy is done with relative brightnesses, so you say, "Oh, this thing is brighter than that thing, and that thing's brighter than this thing, and this thing's brighter than that thing." And the filter system like this makes it very easy because then you can use the magnitude system, which itself is a relative brightness concept.

The visible light bands are only covered by the B, V, and R sections of the Johnson's cousin's filter system. The U section, you're gonna have to go way up in altitude in order to use it, and same with the I section; you need to be a little bit high altitude in order to use these because the earth's atmosphere strongly absorbs ultraviolet infrared light. So what we got is we have these wavelength regions which the co which the filter system allows through. All right. Once again, just like we defined with Pogson system last time, Pogson originally said that every filter system in any filter system, including the Johnson's cousins, is the definition of zero magnitude is the star Vega. So we start with that idea and then say, "Oh, how bright or dim is the object with respect to Vega?" And the reason we use Vega again is because Vega is culminates; it goes across the zenith for many observers in the northern hemisphere.

All right. So what do we really mean by color? In your eye, it is the difference in brightness that you perceive in the red cells versus the green cells versus the blue cells in your retina of your eye. Likewise, in an astronomical sense, what we have is three filters. So the filters then say, well, what is the we can then make so we can determine the magnitude of the object, and that's our brightness. Remember, magnitude here is brightnesses, the apparent brightness in the U filter, the apparent brightness in the B filter, the apparent brightness and the V, R, and I. And so we do is it's kind of funny like we've defined magnitudes before where we have the distance modulus, little m and big M for absolute magnitude. Here we define the apparent magnitude of an object to be the capital letter of the filter that you're using. So here we say the the magnitude in the U filter and the magnitude and the B filter and the magnitude of the V and the R; those are just the letters. So we take those values of the magnitudes, the brightness in magnitudes on these things, not brightness in terms of of watts per meter squared or or that's not how we do it; we use magnitude system because we can easily do differential brightnesses between them. So the magnitudes become our reference point in astronomy, not necessarily flux. We will translate that eventually into flux, but we start with magnitudes.

All right. So color then is defined in astronomy to be the difference in brightness between two filters that are adjacent, and you always take the short wavelength filter minus the long wavelength filter, the magnitude and the shorter wavelength minus the magnitude and the longer wavelength. And it's typical that you only that that you look at adjacent filters and not necessarily span across, but there might be a science reason why you would actually do that, but typically you might take the difference in brightness between say the U and the B and the B and the V and the B and the R and the R and the I and then call those the colors. So a standard color that is used frequently throughout all astronomy is an observation in the B filter and an observation in the V filter, and then you take the difference in those observations being the magnitude difference between B and V, meaning what is the what is this if you take the magnitude of B and subtract from it the magnitude of V, that is the color, kind of a funny thing. So there's lots of different ways we can call color, and so therefore we can quantify color; it's not just calling it magenta or red or puss or aquamarine or any other names that you would find in a crayon box from Crayola, all those 64 colors with all those pretty names. We don't care about those names; those names are really nice and everything, and they're very fun to have, but really what we want to do is we want to use the definition of color in order to get us data and understanding.

All right. So the blue star, the blue color of say the star Sirius, so Sirius is by definition, well, by not by definition, but by your eye, you can see in the sky as being a blue star. So therefore, it must be brighter in the blue magnitude in blue magnitudes than in V magnitudes, and in fact it is. So if you take and likewise it must be brighter than the V than the R. So if you look at these numbers, the B number, the B magnitude of Sirius must be closer must be lower in apps in value than the V magnitude because remember magnitudes, the larger the magnitude, the dimmer it is. So the more negative it is, the closer towards negative infinity it is negative, the larger negative number or the smaller positive number, the the brighter it is. So if you compare a 10th magnitude star to a fifth magnitude star, the fifth magnitude star is brighter than the tenth magnitude. So let's say that a star like Sirius might happen to be uh in the B magnitude, it's pretty bright, so I'm just going to make up a number here, and the number I'm going to make up is that it has a B magnitude of say I one, let's call it a B magnitude of one, but because it's dimmer in the V magnitude, maybe it would have a V magnitude of two. So the color, C2, which is the color two, which in the Johnson's filter system B minus V is minus one. So there's the color of Sirius in the B minus V. B minus V color equals minus one. And let's say the R magnitude is four because it's a very strongly blue thing. So then V minus R is minus three. So C sub three, which is another color definition in the Johnson's color Johnson's system, that would be a minus three. So B minus V color is minus one, and V minus R color is minus three. Now I pulled all these numbers out of out of thin air, so don't bother looking them up; they're wrong. So but anyway, I invite you to actually go look up what the B minus V magnitude colors are of Sirius and the V minus R that are standard, and if you look at the American Association of Variable Star Observers, you should be able to actually see that.

All right. So let's take a different star also in say in in the winter sky, Betelgeuse, which is in the constellation Orion, very beautiful red star. So therefore, the B magnitude would have to be dimmer than the V magnitude. So and we also know that Betelgeuse is also roughly a magnitude one-ish sort of star in visual. So let's say the B magnitude is say three because it's much dimmer in B then in V, and we'll say that V is say a one. All right. So that makes sense. So B minus V for Betelgeuse would be three minus one is plus two. So now we see that a color that is in B minus V if it's positive, it's red; if it's negative, the star is blue. So a positive C2 color, B minus B, means the star is pretty much red. If this if the B minus V color is negative, it's probably blue, and if it's zero, it's probably kind of whitish yellow like the sun, which is makes sense anyway. So with the same thing with V minus R, maybe the V minus R color is more significant for Betelgeuse, but our magnitudes tend to be a little bit tweaky for a lot of reasons. Then we said we tend to see B minus V is roughly as a pretty big standard, the American Association Variable Star Observers. All right. So the B minus V color will be more positive, the V minus R color will be more positive for a red star. So we can construct all of these colors, and this is like an extraordinarily low resolution spectroscopy. What is spectroscopy? Spectroscopy is where you take the light from a star, say, and you pass it through a prism, and when you pass it through that prism, the light then gets broken out into a rainbow, and you see how bright it is; it gets raised frequencies. So you really care about how bright it is at various frequencies; that's what you really care about when you're doing spectroscopy. Um, but the nice thing about doing filters like this filter photometry is that pretty much everything you look at is pretty bright. So you know spectroscopy; it can be pretty dim; you need a lot of light in order to make a decent spectrum, but you can do pretty well at lower at lower resolution spectroscopy with uh with Johnson's filters with with such B minus BVRI and filters, UBDR filters.

All right. So this color is important because it does relate to temperature. So let's find out how that is. In general, if we look at the types of stars, we break out their spectrum. Remember that's what Annie Jump Cannon did at Harvard back in 19 the 1910s and 1920s with her team of computers under Pickering. The spectra of stars were classified according to their temperature, and their temperature was guided by the by their prominence of hydrogen lines. So okay, but if you look at the nature of how how spectral lines look, we see that oh stars in general are much brighter, well, in general always, O stars are by definition brighter in the blue than they are in the red, and M stars are brighter in the red than they are in the blue. Sometimes when we look at stellar spectral classification, we forget that O stars are inherently much much much much brighter than M stars, but we'll talk about why that is shortly. In any event, right now what we can do is look at the temperature of a star, and we see that as the temperature decreases, it gets it goes from being bright in the blue to brighten the red, and that's why we can say that a blue hot object is much hotter than a red hot object. Red is pretty hot to eyes if you're thinking about flame, but you don't want to get close to a blue hot flame; that's very very very hot in the event. So real spectra of real stars show that hot stars look blue because they're brighter in blue than they are in red. So let's say we put a fake B, V filters on top of some spectra and see what the impact of that would be. Um, we can easily see that the brightness in B filter for an O star, that's kind of BVO, right, the brightness of in the blue filter for an O star is the B magnitude is much greater than the V magnitude for the O star. So therefore, the color will be negative. And if we look at an M type star, the B magnitude will be dimmer and therefore larger than the V magnitude, where the V magnitude will be brighter and therefore a smaller value. So a big value minus a small value equals a positive value. So the color for the B minus V color for M stars is is positive, and the B minus B color for O stars is negative.

All right. So that's kind of what we were talking about. The O and B star stars are all over the place, and in general, a star like the sun, the G stars, right in the middle, their B minus V colors tend to be roughly about zero because the magnitude difference between the two filters is roughly nothing; there's almost nothing. So there is a transition point, and that is roughly around the middle of the spectral sequence and roughly at the G's. Okay. So let's say we instead instead of looking at it from like a pretty picture rainbow type of things, we decided to look at it from a spectral sequence where we actually measure the total brightness of a star numerically instead of using like uh like our eyeballs or magnitudes, but we start with say flux, which is watts per square centimeter; that's flux falling upon a per square square watts per square meter. Well, you know, I could have a meter-sized detector, but anyway, the uh we then say what's the absolute what's the absolute flux or the amount of light that is the luminosity falling on our detector and count the real energy that was being deposited by that light, and we get what we call a spectrum. So that spectrum can be numerically related to the Johnson color system, and we could say, well, what is the B minus V colors for the various objects, and then we see that O stars are of course brighter and in exactly the same way that we discussed with them we looked at simple spectra. So the next question that we have is a rather interesting one, and so we see that stars are organized by their temperatures, and O stars are hot and M stars are cool. How do we know this? Why do we know this? And the answer is in the spectra themselves. So the spectrum itself determines the temperature of the star, and we just are lucky enough to be able to use the Johnson's filter system to actually determine that much more easily.

All right. So when we're looking at the spectra of a star, notice the shapes of the spectra. In general, the shapes of the spectrum of a star, the blue one looks kind of nice and sloppy; it starts off in during in the visible part of the way of electromagnetic radiation; it is bright in the blue and the ultraviolet and dim by the time it gets to red in infrared, and the situation is reversed for the M stars. So what do these curves mean? What do these these plots of of intensity as a function of wavelength mean? Well, they just mean that is that is what we're seeing is if we look at a star, it's really far away, so we're not taking the image of a particular patch of a star; we're looking at it over averaged over the entire star. So we're looking at the average, say, temperature and the average spectrum of all the regions of the star; some might be a little hotter, some might be a little cooler; that's what sunspots are in the sun; some spots are slightly cooler areas; prominences are are a little bit cooler. The sun radiates and X-rays, but if we took the sun and put it really far away, maybe tens of parsecs away, then we wouldn't be able to resolve the sun, but we would still be able to get the average spectrum of all the light that is that comes to us from the sun. The most important thing though about a star is that no matter how far away it is, no matter how tiny it seems in the sky, it is a big thing. Stars are enormous objects; they're much bigger than planets; uh, even little M dwarf stars are bigger than the planet Jupiter. So if we take something like the size of the sun, the sun itself is a hundred earths could fit across it, and a million earths can fit inside it. So these are enormous objects, and an enormous hot dense body is opaque, and an enormous hot dense body that is opaque means the light bounces around inside it. If light is being generated inside of there and it bounces around inside it until everything becomes the same temperature, once everything's the same temperature inside the star, then it's at the same temperature, and what we see at the surface of the star is that average temperature of all the light then all the material being all the same temperature at the surface. So that's interesting because it's opaque; everything gets to the same temperature. So temperature is a funny thing because it's measure it is a measurement of the internal energy of the object and the solid; it's just the things vibrating in place and how much vibrational motion it has inside of the structure of the solid. If you give it enough heat, then there are bonds that must be broken down in order to turn it from a solid to say a liquid or a solid to a gas, but we'll ignore that for just a second because that's a that's a that's a different kind of uh of temper a different kind of change in latency and heat latency, but if you have a gas that's much easier, and stars are gases; they're not solids. So a gaseous ball, a star, a gaseous ball, the higher the temperature, the higher the average motion of the molecule, the atoms that make up the star. So they move faster. So temperature itself in a gas is related to how fast the atoms are moving inside it or ions if it's too hot. The way we can then relate temperature itself as a measurement to the speeds and therefore energy because speed is like kinetic energy; it's the energy of going fast. So therefore, the temperature must be an average measurement of all of the speeds of all of the objects in it; it's not everything's going exactly the same speed; that would be kind of weird, but what we see is it's an average speed over the entire uh over over the entire set of molecules and atoms. So we can relate it to the average kinetic energy of an atom inside of there, and that thing that we call its movement is what we call heat, and heat has a lot of different things that we can talk about, and that would be a thermodynamics course, but let's just start with a relatively easy concept and begin from there. And so heat is something that you measure; temperature is something you measure with a thermometer, and heat is a measurement of how much wiggling there is occurring inside of the atoms, a little bit loose definition there, I know, but off we go; we'll just kind of keep with it for now. So but cold can be defined as the lack of motion. So an absolute temperature scale, we might want to say absolutely cold; we want nothing moving. Well, we'll call that temperature equals zero. And so as you give it more and more heat, it the things move faster and faster. So therefore, there the temperature gets higher and higher because not everything's at the same motion; it's the average speeds of the object that determine the temperature. So the Kelvin temperature scale was defined a long time ago by Lord Kelvin, and it's related to zero is the absolute zero of it, and at that time there is no motion whatsoever on the part of anything that's inside an object that is at absolute zero. Um, the cosmic microwave background is at three degrees above absolute zero, which means it is very cold, but still there's some actually an incredible amount of energy associated with that, but we'll let that go for a second. The pure water boils at 207; it freezes at least if you cool water below 273 degrees Kelvin, it becomes a solid. If you warm it above 273 Kelvin, then as it first does it was a funny thing first when it becomes it's a solid, and then there is heat as you can apply heat to ice, and it'll change phase from solid to liquid at the same temperature until you've given it enough heat to break down the bonds that make it go from a solid to a liquid, and then once it becomes a liquid, then the temperature again begins to rise because when you apply heat to a to a phase that is in the phase transition mode, you actually that's what phase transition means is that you could have the same temperature, but yet there you don't change the relative the relatively average.

Motion of it, a phase change, simply changes the arrangement, or the these, the fundamental arrangement of the atoms and molecules inside of it. So it's a pretty loose definition, too. But once we get to 373 Kelvin, then it boils, which then the bonds that make up a liquid that are broken down, and you add heat into the liquid to make it become a vapor. It stays at that temperature, 373, until you've given it so much heat that all of a sudden nothing's left in the liquid state; it's all a vapor state, and then the temperature can increase again. Temperature then becomes, and it still is in all of these cases, a measurement of the average motion of the objects. But heat is, as you can see, slightly different because heat can be applied to something and it doesn't necessarily raise the temperature, which is interesting. And that's about phase transitions, and that should be done within a separate video. But for our purposes for this, all we really want to say is that at the Kelvin temperature scale for gases, which make up stars, that is a measurement of their average speed.

And uh, the Kelvin temperature scale has some basic things we already talked about: water boiling and so forth. But then fusion of hydrogen occurs when the temperature is approximately uh 13, approximately 10 million degrees, or 10 million Kelvin. So we don't say degrees Kelvin; we say degrees centigrade, we say degrees Fahrenheit, but we just say 10 million Kelvin because it's unit like watts or meters. We don't say 10, we don't say 10 million lengths meters. We don't say we don't say oh that's uh that's 10 million uh times seconds, right? Because we don't say seconds or a time; we know it's a time. We know a Kelvin is a unit of temperature, so we just say that's 10 million Kelvin; that's the temperature of that star anyway.

So light and heat is therefore a different thing, um, but yet they're all but they're related. So you may receive light from the sun in the form of infrared photons, and those infrared photons can go to doing one of two things: that he that can go to changing the internal heat of your body, and the internal heat then can be manifested in numerous ways. The most common way is to make the atoms and molecules in your body vibrate or move more quickly. It also can change the state from a liquid to a gas or a solid to a liquid, depending on the intensity, on the frequent, the wavelength of the light. So that all depends on how it absorbs and emits it. But from our perspective, what we really care about is that when light falls upon a gas, it it we can treat it as a heat input, and as it is it inputs that heat into the system, then what occurs is the temperature rises. All right. Now if it's an average, if it's completely opaque and everything inside there is at is at thermal equilibrium, meaning that there isn't a place inside the star that is significantly different compared to the compared to another place inside the star. Now that's kind of a tricky thing; stars have to be a little bit out of thermal equilibrium because they emit light and emit heat, so there has to have a source coming in there. But if the source the source of energy inside the star equals the amount of energy that's coming out of the star, then it can be said to be in thermal equilibrium.

So as long as the star is in thermal equilibrium, meaning in general it's not getting a lot hotter, and in general it's not getting a lot cooler, and in general there's no big areas where there's motion of heat going from one place to another, then that we call thermal equilibrium. If an object is hot, the same temperature at the same temperature throughout and opaque, then it would be called a black body. A black body is even a stranger object; it's kind of a theoretical, in fact it is a theoretical object that absorbs all light that falls upon it. And since it absorbs all the light that falls upon it, doesn't reflect anything, it reflects no light. It absorbs all light; that's kind of a that's kind of a stretch; there's nothing that does not absorb all light. So any light that falls on a black body gets absorbed and therefore gets mixed around inside the black body until then it become it thermalizes with all the other light inside that all the other matter inside of that and then re and then the black body then, because again perfectly absorbed, it can perfectly emit, and it doesn't hold back certain wavelengths of light. If a black body held back certain wavelengths of light, then it would also reflect those certain wavelengths of light, which is interesting to say. So once so a black body is a perfect absorber of light and a perfect emitter, which means everything inside it gets to the same temperature; that's what we care about. So uh, it's things that are very close to black bodies in mostly everyday parlons: molten steel at a foundry, the ingots of steel, those are those are most certainly uh black body objects; they're hot, they're very hot, they're glowing, they're all the same temperature. And in fact, if you look inside the foundry, it's hard to tell the color of the sides of the walls of the foundry from the actual molten steel itself. In fact, when they put it in there, you can't see the difference because the steel and the walls and the gas inside of there are all glowing at the same exact temperature, and since they're glowing at the same exact temperature, they have the same exact spectrum because it's the black body spectrum. Okay.

The next thing we can look at that's a very familiar thing is the coals of a fire. Look deep inside the coals of a fire, and on some camping night that you might go out to, and the coals of fire, not the fire flame above, but deep inside the coals where the below the wood, you can you can't tell where the fire begins and where the coals end if you look carefully. In fact, they all have the same temperature, they all the same color. The only reason something has a slightly different temperature is if it's darker, it's cooler, but if it has the same exact temperature, it'll have the same exact color. So the cool is the hot area that's being shielded inside of the cavity of the black body of the of the fire deep down in there; that's a black body, too. Now a welder's arc is a very very hot object, but what actually is the thing that might happen to be a black body? Remember the welder melts uh melts something else, the steel at very high temperature, and so not the sparking stuff, because that would be an emission spectrum; it would be a gaseous form of it, or but the sparks coming off the actual sparks themselves, they're reddish, but if you look at the center of a welding arc's light, the light itself is where the metal has been turned to blue hot, and now blue hot that area is very small. Remember the foundry look is this enormous thing, and you can still look at it; it's bright, but it's not used to look at it, but the intensity of light goes up rather rapidly as the temperature goes up. So the melted iron that is being focused on by the arc welder, that's the thing that's incredibly hot and incredibly blue and incredibly bright. So there's something about it getting hot that means also getting bright, too. All right. Oh no, now we get to throw equations at you. So equations are a funny thing. So the entire shape doesn't matter if it's a black body; any black body, every black body has a theoretical curve that has the shape that kind of looks like a an off-kilter uh normal normal curve or a bell curve. Take a bell curve and like stretch one side long, and that's kind of what the black body curve looks like. The only thing that that make that can be different or from one black body to another is the temperature, and so it just basically scales everything up by a factor of the temperature. So as as if it's hotter the blood the area of the black body curve scales up by a factor of the temperature, the third power, and so as you get hotter and hotter the but the area gets hot the the temperature gets higher and higher, so it's a very well it's actually the fourth power is really what it comes down to, but but still. So the um the the point is is that every black body has the same shape, doesn't matter what its temperature is, on the same shape, but yet whether it's brighter at one frequency or another, that's a different thing. So different black bodies at different temperatures peak have peak wavelengths at different wavelengths. When they're very very cool black bodies, as we saw in say the iron foundry or even a very cool star like Betelgeuse, it peaks in the red or even in the infrared, um, and then as it gets hotter and hotter it starts peaking in the visible light, like say yellow or green, and but if you were to see such a thing that's like six five thousand or six thousand Kelvin to your eye, it would look white because it's roughly evenly balanced across the the uh the spectrum visible spectrum, but it peaks at specific wavelengths that we would call green if it were if it was peaking roughly around 6000 Kelvin. And once you get above 7000 Kelvin, uh the peak temperature the peak location starts going into the ultraviolet, so it starts from the red and infrared, moves through the center of the visible spectrum and all the way up to ultraviolet. It just so happens that stellar temperatures, stellar surface temperatures range in their peak brightnesses for most stars in the visible light range all the way up through the blue light and all the way up through infrared. So infrared to ultraviolet, that's where stars seem to peak in their ultravio in their black body radiation.

All right. So when we take the curves for black bodies and we isolate only the sections that our that are that are visible light, if we isolate only those sections, it just so happens that the actual spectra of stars very closely match the theoretical predictions of what a black body curve of that temperature looks like; they're really really really close. It's not perfect, and the reason it's not perfect is because atmosph stars have atmospheres, and the atmosphere of the star acts to absorb light from that star, and when it absorbs the light from the star, it takes the light away from the star, and then we don't see it; we see an absorption feature, maybe we see even emission features, but typically it'll absorb it in one wavelength, and then that those atoms and molecules will re-radiate it in some other location, and it'll escape in a different way; it doesn't hang on to it, it just re-radiates another direction into other wavelengths. So the sun itself, well specifically the black body for it would peak right around fifty-five hundred, eight five thousand, uh roughly roughly the middle of the spectrum, but yet the actual curve because of this redistribution is a little bit more blue. So that's kind of interesting; it's real, but even so the curve for the black the solar spectrum is really close to a black body spectrum. So what are some other astronomical objects that we see that have a black body spectra? Remember it has to be dense and it has to be thermalized; it has to be all the same temperature; it has to be one object that's at the same temperature. All right, that's cool, and if it's not, and we'll see what kind of things we have. So if we look at dark dark dust clouds deep in interstellar space, the places where stars are being born, dense enough so that they barely collapse under gravity, they might be a parsec or two across; they're very very cold objects; they might be 60 degrees above absolute zero. And so even if it's 60 degrees above absolute zero, it can still have a black body curve because that's the average temperature. So if it's an average temperature of that, what's the peak wavelength? Well, the peak wavelength is deep in the infrared, deep in the infrared, if not even in the radial wavelengths. So when you have something at 60 degrees Kelvin, if you look in infrared light, you'll see it glowing. So therefore, that's why the Spitzer Space Infrared Space Telescope has been built and watched, and why Space Telescope has been built to look at objects that glow in the infrared and things that are cool objects, very cool objects. A dark dust cloud does not glow in any light in the visible light, and therefore we see it to be dark. If we then look at say something like a proto stellar object, like what let's say now a star has formed inside this dark dust cloud. Once it's formed inside there, the star itself is pretty warm, but yet it's not hot enough to call itself a star; maybe it's a bit warmer than the cert maybe it's much warmer than the surface of Jupiter, and it might be a few hundred Kelvin; therefore it seems to be a dull red, but it peaks in the infrared, in the in the near infrared. Near infrared means just a little bit further red than the about 7000 uh angstroms or 700 nanometers. And you'll notice also that something that is 600 Kelvin is a thousand times brighter at the peak than something that's 60 Kelvin. So the hot the warmer it is, the much more the much brighter it is. So by multiplying by a factor of 10 gives you a lot lot larger factor of luminosity in terms of temperature and luminosity. So we go to the sun now, and the sun is about 6000 Kelvin, and so it's about a thousand times again brighter than say some dust cloud that's at 600 Kelvin, and it peaks roughly in the visible wavelength region, but it has significant output in infrared, radio, well not really a lot of radio, but significant infrared output and significant ultraviolet output. The sun's spectrum is pretty close to a black body, and we can use that as a measurement. And what we feel is warmth on a summer day is the infrared light that passes from the sun through the atmosphere to us as part of the black body spectrum. The ulti the sunscreen you wear is for the intense ultraviolet light that uh that that drops off rapidly at hot shorter wavelength.

All right. So then the next thing we can look at is something even hotter, say the the accretion disk around the black hole. So there's material falling into a black hole, and as it falls into that black hole it gets hotter and hotter and hotter, and just before it falls into the center of a black hole it gets to be tens of thousands of Kelvin, uh actually it gets much hotter than that, but we're talking about the outskirts, or maybe we're even looking at an extraordinarily hot O star. So an extraordinarily hot O star might be tens of thousands of Kelvin, and those things are even more luminous than the sun, thousands of times more luminous than the sun, and they their peak wavelength is way out in the ultraviolet, and they emit even more visible light than the sun does; they emit even more infrared light than the sun does, but they emit even more ultraviolet light. So in general, the hotter something is, if it's a black body, which is mostly a star, stars are mostly black bodies or really close to black bodies in terms of their spectra, then it's brighter overall wavelengths, and the peak of the brightness moves to be shorter and shorter and shorter wavelengths. All right. So the law for blackbody says the wavelength maximum, the maximum wavelength of the peak of the curve, just depends on some little number b, which is a measurable number, and then you divide it's the inverse of the temperature. So the hotter it is, the shorter the wavelength is where the peak exists. And finally, these and how much energy does get gets dumped out of an object that has a particular temperature in Kelvin? If it's a black body, the temperature of an object goes as the temperature, the the energy output per surface area on the surface of the object goes like the temperature of the fourth power. So we take a standard sized patch, and we take that patch, maybe it's uh the size of your hand or something, we put it on various and things that are hot or cool, and we measure the total energy output through a standard patch, say you know it's like five ten centimeters by centimeters or five centimeters by five centimeters, whatever it happens to be, the energy output through that standard patch will go like the temperature to the fourth power. So something that's twice as hot as something else will emit 16 times as much energy; something that's ten times as hot will emit ten thousand times as much energy; and something that's a hundred times as hot will emit a hundred million times as much energy. So the hotter it is, the more energy it puts out, and it's a very fast function of of temperature. So these are our basic concepts of stellar of of stars, if and it makes them pretty easy; stars are pretty close to black bodies. If it's hotter, it's brighter; if it's hotter, it's bluer; that's really what we really care about. So when we take about these, when we look at all the stars that we see in the sky and then we look at their stellar spectra, we now have a pretty good firm foundation of what we can look at, and we take the spectra of a star, we see that O stars are bluer compared to M stars, so we know what that means, and now then we can use the Johnson's filter system to uniquely determine the temperature of a star. All we have to do is calibrate using the spectra on high level calibration what the spectrum of a star is like an O star and M star, G star, whatever, and we learned what the typical the average spectrum of those are, what their temperatures are according to spectra, and then we can step it down, and you do it easier by saying, well, look at the colors in the B minus V, the B minus V color uniquely determines the temperature of a star. So all we have to do in order to learn about something very important about the top of the star, meaning how much how fast the atoms are moving on average at the surface of the star or inside, right at the inside of the star, is take a picture in with two filters in front of it, say the B filter of Johnson and the V filter of Johnson, put pictures in front of those things, and difference the brightness between the two, and once we do that we know the color index; the color index is uniquely determined by the temperature. So this is an amazing consequence, and those colors, the B minus V colors, transition relatively smoothly from from the hot to the cold; there's some lumps along the way, but in general the more negative the color, the bluer, the more positive the B minus V color, the redder and cooler. B minus B negative, hotter hotter hotter bluer; B minus B positive, cooler cooler cooler redder. So we can go on and on with those kind of stuff, and we will. So this is a really interesting thing where we take the concept of the magnitude system and apply it to some deep physics about the nature of how atoms move inside an object, and we'll talk more about that next time.

Hello, this is Jason Kendall, and welcome to the next of my introductory astronomy lectures. Today we're going to be talking about spectroscopy. Spectroscopy is the study help of how light interacts with matter and how light the interaction of matter with light betrays itself and gets transmitted through space to us so we can receive it. Spectroscopy is simply the way we take the light that's coming from a distant source and use some method by which we can break it apart into a spectrum to see how the intensity of the light varies with wavelength or frequency. So an easy way to think about this is allow normal white light to pass through a prism, and then you'll see a rainbow effect. Well, typically a rainbow effect is pretty hard to see unless of course there's a very narrow opening through which that that passes the light in a very narrow beam, and that narrow beam then goes through the prism. If it's a general wave of light that goes through it or an ambient, then the prism will not necessarily be to create a spectrum; well, it will create a spectrum, would be harder to see. So for us to make it better, we do is we take the source, whatever it is, send it through a narrow slit so that it becomes a ray or a beam; we don't care about losing all that light because we're just going to analyze the light that comes to us from there. We pass it through a prism; the prism breaks apart the light by because the inside of glass the speed of light is different for different wavelengths, and so it spreads the light apart into its constituent wavelengths or frequencies, and then we take a picture of the

Incident light on out after it goes through the prism, and that is the study of spectroscopy. Something divides the light up so that we can see the intensity at given wavelengths or frequencies, and that we know exactly how that thing is interacting with the light. Meaning the prism, so we don't have to worry about the prism's interaction of the light; we just worry about the origin of the source. All right. So if we then look at more common things, like if we take a prism—just a garden, household variety prism or a crystal—you notice that there's always a pretty rainbow that comes off of the sunlight.

Well, pretty rainbows from the sunlight are indicated here in this image from the McMath Solar Observatory down in Tucson, Arizona, run by NOAO. And this—this absorb—this rainbow that we always see has actually some darker spots in it, and those darker spots are the shadows of the slit through which we passed the sunlight. So that's what we call them absorption lines, because we make a—we make a line, a very vertical line slit through which we pass the solar—the sunlight, and that sunlight then passes into our spectroscope. And that spectroscope might just simply be a prism, or it might be some other device like an initial spectrograph or something like that, or reflecting off of the surface but at the angle. What we see is we see a series of dark lines on the spectrum, and those are places where it simply is dimmer than the surrounding continuum. So the rainbow itself, we call it the continuum or the continuous spectrum, and there are absorption features which are darker than the surrounding continuum. So the sun's spectrum is actually what we call an absorption spectrum, and absorb—there is light that's been absorbed from the continuum. All right.

So there's a different kind of spectrum as well, where there's brightness—there's bright emission on top of a dark background. So perhaps the material is not emitting light at all frequencies; maybe it's emitting light at specific frequencies. And if those—if the material is emitting it only at specific frequencies, not with a rainbow but with specific wavelengths of light, then if we pass it through a spectroscope, we see the lines of emission that—that we put here. What's funny—we call them lines, and that's simply because when we talk about emission lines or absorption lines, that's simply because we're using a slit type opening, and so we're actually seeing the image of the slit. So in an absorption spectrum, or—I'm sorry—an emission spectrum, such as these—the emission spectrum themselves—that's the image of the slit through which the light is going, and so you'll see that the image of the slit, the appearance of the line, is the same for each one; it's just the color is different, and the wavelength is different. So that's interesting. And we also notice that they're—that they're kind of distinct.

Well, emission spectra are fascinating because what you can—where you can get them is if you take, say, sodium—sodium chloride, table salt—and you hold it in a Bunsen burner, and you hold it like a bit of table salt in—in like a metal—is a piece of metal, and you put it over a Bunsen burner and heat it up till it glows, then the flame that comes off the Bunsen burner will have a particular wavelength. And if you look at the lights that is coming off of the burning salt that comes off of there, you get a specific set of wavelengths, and those are emission spectra. Now you'll get a sodium spectrum, and of course, since it's table salt, you also get a chlorine spectrum as well, but really we care about like the sodium spectrum. But you see that a noble gas such as neon will have a different spectrum, and mercury vapor has a different spectrum, and ubiquitous hydrogen throughout the cosmos has as a specific spectrum.

So what's funny about all these emission spectra is that it doesn't matter where you get the material from—say hydrogen or helium or neon or sodium chloride or something—or when you get it or from whom you get it; it doesn't matter. All you have to do is heat it up such that it becomes vaporous, and it will emit the same exact emission spectrum. And so therefore, everything has its own fingerprint. Hydrogen has the same thing no matter where you get your hydrogen from; sodium has the same fingerprint no matter what. And we call these things fingerprints because the emission spectra is at exactly the same wavelengths or frequencies every single time you measure it, which is very interesting, which tells you something about the nature of the matter. So what—what emission lines can be done, and specifically we're going to be talking about what are called Kirchhoff's laws of spectroscopy. And Kirchhoff—it was his full name is Gustav Kirchhoff—and in the mid-19th century, he was doing a whole bunch of experimental physics, and he worked with the guy who invented the Bunsen burner, Mr. Bunsen, and they did a bunch of spectroscopy, and what he found were the following three laws. Kirchhoff's laws first say that emission lines are produced at single frequencies of—behind in front of a dark background. If you're looking at a hot, rarefied gas that has no bright emission source or no bright continuum behind it, it's just a gas that you see with nothing right behind it. So you get specific wavelengths appearing at specific brightness at specific wavelengths, and that comes from a hot gas, and that is one of Kirchhoff's spectroscopy.

The next one is if you take a continuous source like a light bulb—like an incandescent light bulb, which gives a black body type of radiation—and that is in front, and that is behind a cool gas—maybe it's the same gas, maybe it's hydrogen gas that's cooler than the bulb—well, as the light from the hot—hot bulb passes through the cooler gas, the cool gas absorbs the light, and it—and the absorption then dims the light at specific frequencies, and those specific frequencies get—where it gets dimmed—then get passed through; we see—we see it as a spectrum, and we see something like the solar spectrum. But when we look carefully, we actually see something more interesting deeper in just a bit. And so we can actually relate Kirchhoff's laws to as a trio of things, because a hot—a hot opaque body such as a light bulb emits a continuous spectrum. If something hot and opaque emits a continuous spectrum, something hot and opaque that is behind a cloud of cooler gas that emits—that it—that we see if we look through the cooler gas to the hot—of—uh—source, we will see an absorption spectrum. Now if we look at a quarter to that and just look at the gas that did the absorbing of the light, we will see an emission spectrum. So really Kirchhoff's laws are our two sides—are three sides of the same situation. You can either look straight at the continue—straight at the hot dense object, and you'll see a continuous object—a continuous source. You'll look at the—uh—cloud that's sitting off to the side of the absorption of the hot object and look through the cloud at the hot body, and you'll see an absorption spectrum; or you'll look off to the side of just the emission line—just the hot cloud—that—cooler cloud compared to the hot body, and you'll see an emission spectrum. So they're all part of the same thing, and that means that as we look at these objects, that the emission lines and the absorption lines are at exactly the same wavelengths, and that makes sense because the—let's say it's a hydrogen cloud gas—and hydrogen will absorb and emit at exactly the same wavelengths. It's not like it absorbs at one wavelength and emits in another—no, it emits at the same exact wavelength that it absorbs. That's interesting. So that's telling you something about the nature of matter—the nature of matter itself. And Gustav Kirchhoff did all the work in spectroscopy well before the advent of quantum mechanics and the model of the—the Bohr model of the atom. So as we look at the nature of what matter is, he didn't know about all this stuff, so he derived these laws empirically, and these observations then had to be accounted for with the advent of quantum mechanics, which they were.

So most importantly is that the setup of the spectroscope tells us an enormous amount about the nature of the material. So we can tip—it depends on what you—how you wish to view things or what is possible for you to view. You can set up an experimental apparatus in many, many ways in order to do spectroscopy, but it's typically pretty easy and dirt—well, not easy—typically it's helpful to start with an emission spectrum in order to identify exactly what material you're looking at, and then hopefully through some chemistry you can determine really what you're looking at. But spectroscopy itself is considered to be probably one of the most prevalently used science devices—scientific tools at our disposal to understand exactly what makes up an—uh—some kind of object. So Kirchhoff's laws were—were—were developed in the—uh—early 19—mid-19th century and refined until the early—were not understood of why they behaved until the mid-20th century.

Now what can you get out of spectroscopy? Well, the first thing is because every chemical element has its own particular fingerprint or signature—every single element that must be present in there must emit light or absorb light—so you can tell the composition of what's in the—what's in the gas that you're absorbing or what the nature of the cool gas in front of the hot body is. In addition, the spectrum changes a little bit if you're looking at ionized gas. So if you ionize a gas—meaning the electron gets blown out of the atom—and if it's blown out of the atom, then the electric field changes a little bit, which changes the spectrum just slightly. And so not only do you have to—to make all these fingerprint catalogs of emission spectrum, but you also have to try to get the emission spectrum of ionized gases as well, which really becomes kind of a pain because the more you ionize a heavy element, the—cha—the actual—the spectrum itself changes—uh—considerably. And then if you then take it—and we're just talking simple atomic spectra—atomic elements—if molecules are involved—like such as water or carbon dioxide or carbon monoxide or—uh—deoxyribonucleic acid or RNA or anything—if you wish to do spectroscopy on complex molecules or even simple molecules, every single molecule has its own individual spectrum, and some of them can be incredibly complex. And then we know that—that polyaromatic cichlid—polyaromatic cyclic hydrocarbons are actually present in space and can be observed because of their spectrum. In fact, ethyl alcohol has been found in space, and some extraordinarily simple amino acids have been found in space. So this is really interesting; we can know something about the nature of which molecules are present not even having to go there. It's really fascinating.

Now the other thing that's interesting about the nature of spectroscopy is that because it takes energy in order to—we have a hot memory—in a hot bulb in front of a cool gas—that hot bulb provides energy into the gas, and that gas then reacts to it. Well, if the temperature of the gas is not hot enough, then it might not react, or it might not absorb certain—that we might not—might not get the wavelengths of light it needs in—or it doesn't get the energy it needs in order to hop up and down—or—we can also then determine that by looking at how the gas is absorbing or emitting at different wavelengths or frequencies, we can actually determine the temperature of that gas. So an ion—if you have a gas full of hydrogen, and it's in front—it's above a star—if that gas is above—right above the star—maybe it's the atmosphere of the star—and the atmosphere is cooler than the star, then we might see a big absorption feature for say hydrogen. But let's say the star is extremely—extremely hot, and the electrons are ionized off of the hydrogen atom, then you won't get any absorption at all, even though hydrogen is present. Or maybe the star is very—very—very cool, and you don't get any absorption of hydrogen because the star doesn't have enough energy to kick the electrons out of the lower orbits of the—of hydrogen into higher orbits. Well, this can also—and spectrox—with the spectroscopy—can tell you something about the temperature of it. If you then look at the nature of the lines themselves, we can find that sometimes the lines—and—are not exactly as narrow as we think. So maybe you're in a laboratory; you measure the frequency of hydrogen—the emission lines of hydrogen—and then what you do is you take that hot gas and put it under extraordinary pressure. If it's under extraordinary pressure, you're going to find that the lines themselves—these emission lines—will be broader because as it's under pressure, the atoms of the—hydrogen atoms—are moving at a higher speed, which means that some—some of them are Doppler shifted towards you—away from you—from your emission—which means that as the energy goes into—and out of the—the—uh—the energy—as the small—as the atoms of hydrogen are moving fast as they're emitting—then that can Doppler shift it either towards you—away from you—and thus broaden the lines. That's called pressure broadening, and the same thing happens with density. So if you have a high-dense atmosphere, you can get different kinds of broadening. So each of these things can be studied inside of the spectrum of the star, and different kinds of broadening—or different profiles to the line—meaning not just that the line is like, okay, it's totally—uh—dark, and then think—I've got this one bright thing—like a spike—maybe it's shaped like a—like a—like a funnel—maybe you have funnel type shapes—maybe you've got wings and then a funnel—there's all sorts of ways that this—that matter can interact with light, and the profile of the line—meaning exactly how does it vary around that particular wavelength—can tell you a lot about the nature of the star itself or whatever you're looking at. And there's an incredible amount of information that gets carried along with it, and that gives us the physical data about what's happening at the conditions of the matter when the light was emitted. Because now we can understand the elements of—such as pressure and density and temperature and composition—now we can do physics, and the physics then allows us to understand what's really going on, and that's what we—that's what—tr—

Spectroscopy and the invention of the spectroscope and if the—uh—the invention and Gustav's laws as they began introduced the concept of astrophysics to astronomy, because up until the concept of astro—us—at—until the concept of—of spectroscopy really took hold, we could never really know anything about what was going on in the stars. All we could learn is that this thing's moving—it's going across the sky—it's bright—but we didn't really understand the spectrum. So it took some time before we said, well, look, if there must be an absorption spectrum coming from that star—well, stars are very dim—so it took a long time for the technology to come around—such as you could actually make a spectrum of a star photographically at least—but once we understood the nature of the spectrum of a star, we now then could transform astronomy into astrophysics, and that allows us to learn exactly how something is happening even though it's hundreds of light years away or thousands of light years away or millions of light years away, because we trust that all of the physics that happens here in the laboratory—and this is a really big assumption—this is one of the most important underlying assumptions about all astrophysics due to spectroscopy—is that since all the laws of the physics are the same everywhere in the universe at all times of the universe's existence—meaning from all the way ago to all the way today—that the laws of physics themselves are the same, then we can trust spectroscopy because we only get a messenger of light. So that's a really interesting assumption—that all of light and all of matter is the same here as it was there—and as we measure the laboratory wavelengths of hydrogen and then we look at some distant quasar, and that distant quasar emits light and it absorbs light, and there's absorption of light as it travels to us through the intergalactic medium, then we can trust that we can actually understand what's happening between us and the quasar and even at the quasar that emitted the light—say 10 billion years ago—and the light traveled for 10 billion years. So the universality of the laws of physics is what we trust because we've never been to the stars; we probably never will be to the stars. But the physics of light interacts with matter allows us to reach with our imagination out to the stars and learn about what is happening over there. And we'll see the effect of spectroscopy everywhere throughout all of these courses, and that's how we actually know what's going on over there.

Hello, this is Jason Kendall, and welcome to the next of my introductory astronomy lectures. Today we're going to be talking about the nature of matter itself. What is the matter with matter? Matter is that stuff that makes up the universe. In fact, let's even make a more interesting definition for matter: Matter has mass, and as mass, it must be pushed around by forces. So anything that can accelerate a mass through a force is how matter interacts with other matter—kind of a weird way of thinking about it, but that's old Newton's law. So we just go all the way back to Newton's laws and say there's some stuff that we'll call matter, and matter may be accelerated or decelerated, and the thing that does that accelerating or deceleration is called a force. And so there are four different ways the universe has of pushing things around, and they're called the four fundamental forces of nature. One of them is gravity, and gravity obviously attracts—every mass attracts every other mass and causes it to accelerate—that's the nature of gravity. Well, we also—we know by—by Einstein now—and just Newton's laws work very well—but we know Einstein's law—Einstein's version of gravity—says that matter curves space-time, and it falls inside of that curved space-time. But what we can think about—let's go back to Newton's laws—Newton's version of gravity—we have two pieces of matter that then gravitate to each other, and they accelerate towards each other—that's what we really care about is the acceleration of matter. Well, what's the other thing? Well, we could put a pair of charges on top of them; we could have a plus charge and a minus charge—an electric charge—and they could—if they're the same type of charge—they repel; if they have opposites, then they'll attract each other, and that will cause the matter to accelerate. The electromagnetic force causes the—cause and acceleration, and the thing that we call the electromagnetic force—that which transmits—transmits the force—in the case of gravity, it's the curvature of space-time, but with the electromagnetic force, it's the transmission of light—photo—photons—back and forth between the charged particles. As they move and vibrate, they change the electric field, and that vibrating—moving electric field then indicates how that thing should be pushed or pulled by the charges—that as the light is receiving them. All right. So the electromagnetic force is another way that matter can be accelerated or moved. And the next one is the strong and weak nuclear forces. The strong nuclear force holds—holds protons together inside of the nucleus of an atom and holds neutrons and protons all inside a nucleus as well as holding the constituent quarks of an atom, but we'll talk about that shortly. So the strong and weak nuclear forces only really come into play when we talk about nuclear particles or the centers of atoms. All right.

So what do we mean by matter? All right, so I just said it's the thing that gets pushed around when their force is acted upon it. All right, so you have to have some way of interacting. Well, gravity says that if it's got mass, it will—you have something to do with the gravitational force. If it also has charge, then the mass that has the charge will then be accelerated. If it has—if it interacts via the weak nuclear force by the exchange of W or Z bosons or it exchanges—or it interacts by the—by the strong nuclear force—the interchange of blue odds—then the matter then will accelerate because of these interactions. But what makes up matter? Well, matter in the universe is—comes in from very big things to very small things, and we'll start with the tiniest—like quarks and leptons, which are fundamental particles; you can't break them apart any further. And there's subatomic particles like protons and neutrons, which are composed of quarks, and then you think about electrons, which are fundamental particles themselves—uh—the fundamental particle called a lepton is an electron, and it can't be broken apart. And then you can take protons and neutrons and

Smash put them together, and that you get a nucleus of an atom. And if you put some electrons around it, you've got an atom. If you put atoms together next to each other, and you've got molecules. If you have multiple huge molecules, you can have a bucky ball, or a bucky chain, or a carbon nanotube, or you can have a crystal of iron, or a nice little quartz crystal of amethyst, or something, or you can have deoxyribonucleic acid, or just water, H2O—many of these things, complex molecules and simple molecules.

And then you can take all sorts of molecules and pump them together, make crystals out of them, or make conglomerations of them, put some over here and some over there, and pack them together, and you might get a person, or an elephant, or a giraffe, or a car, or a planet, or a star, or a galaxy. You know, all sorts of stuff you can make out of atoms. And just think of atoms as your building blocks of everything, and that's what you can make it out of. So the ordinary matter in the universe is what we call atoms, and it makes up all the stuff that we know.

So what's an atom? All right, so an atom has a nucleus, and a nucleus has some electrons swarming around it. And the cartoon thing that we always see, and always I've seen for a long time, uh, that's a really helpful visualization, but it really doesn't look like that. We'll talk about what we mean by that next time, but we'll look at it, but we'll kind of go with this cartoon for a little bit. And the cartoon says that in the center of the atom there is a nucleus, and the nucleus is composed of protons and neutrons. And the neutrons are uncharged and electrically neutral; they don't do anything. They're a little bit more massive than the proton; but the neutron itself, just a tiny bit more massive than the proton. But the proton has a positive charge, so the proton's positive charge is part of the nucleus, and the neutron's positive charge can be in the nucleus, and they're surrounded by a cloud of electrons. And there is, if it's a neutral atom, then there's one electron for every proton that exists in the atom. So you got one and one. Uh, if it's ionized, then there will be fewer electrons than there are protons. And you can also have ions where there are more electrons; that's kind of weird. You'd have to have a very strange arrangement. So the electrons don't fully screen the protons, or it might be a dense environment where the electrons are being forced upon the atom. But in general, we can think of that electrons and protons come one to one with respect to each other, and when they go one to one, we see a cloud of electrons, and we have a neutral atom.

What's funny is also that we talked about fundamental particles. So an electron is a fundamental particle, and a proton is not; it is a subatomic particle; it's composed of quarks. But a proton is about 1800 times the mass of an electron. And if we think about how much mass that is, a typical person, college student say here at William Paterson, the typical student is about—hey, if they're eating ramen on a Saturday night as they're studying for their finals, then they'll be like 140, 150 pounds because they're losing weight, they're all stressed out. So, but now you take 1800 of those, and that's approximately 100 tons. So an electron—let's say a normal person is the mass of an electron—then the mass of the proton would be 100 tons. I'm just trying to think of what exactly would be a hundred tons. I mean, dump trucks, huge dump trucks. Well, we'd have to look at earthmover dump trucks, those enormous things that are in mining operations or strip mining operations; those are hundreds of tons. So there's some big things that are hundreds of tons, and we can think about, wow, me compared to 100 tons, and what is—okay, so some pickup trucks or some large trucks that you might go by are about a ton. So a hundred pickup trucks, or a hundred SUVs, or a hundred large cars, compare and compact them together and call that one object, is equivalent is the mass of one thing, the best the proton compared to say you, if you are an electron—kind of interesting.

All right, so now how are they distributed in space? According to this cartoon, it makes it look like, oh, everybody's all happy and joyful, and the electrons are really big, and the protons are really big, and neutral neutrons are really big, but they're not; they're incredibly tiny. The typical size scale of an atom is on the order of 10 to the minus 10th meter, so about an angstrom or so, and most of the atom itself is empty space. In fact, only one part in 10 to the 15th of an atom is actually taken up by the matter of the atom; the rest is the fields of electromagnetism between the electron and the proton, the disturbed field that actually keeps the electron in place and the protons where it tells the electrons where they are. In any event, this is really interesting because we think, well, how empty is it? If we were to say take a relatively decent-sized building or a house, and a typical house might be say 30 meters across, specifically if we go to the Museum of Natural History, we see the Hayden Sphere is exactly 30 meters across—that big glassed-in ball at the Hayden Planetarium in New York City. So at the Museum of Natural History, in fact, there's a really fun exhibit in there that shows the size of a proton compared to the atom, and in fact, the 30-meter wide, which is a hundred feet wide, 100-foot-wide ball compared is say the size of an atom somewhere in the surface of that ball is where the electron is for hydrogen—it's called just plain old hydrogen, hydrogen atom, which only has one proton and one electron. So if we're looking at that, a typical atom of hydrogen will have one proton and one electron; the electron is somewhere on the surface of that ball, and the proton is at the center of that ball. How big's the proton? It's about a six-point font of a print, a six-point printed font, so it's the size of a mote of dust. So that's how small the proton is; it is a mote of dust compared to something a hundred feet in diameter—that's amazing. So most of the atoms is completely empty space; electrons are really tiny, so, and the electrons are about a hundred times smaller than a proton in terms of size, which is fascinating. So an electron is a tiny, tiny, tiny, tiny thing, and even still the mote of dust compared to where the electron is on the surface of an atom, anyway.

So how do we distinguish atoms? Well, we can have multiple protons in the nucleus. So let's say we have multiple protons, and these protons tend to be—well, they're always at the nucleus, but if you have one proton, we call it hydrogen; we have two, we call it helium; three, we call it lithium; four, we call it beryllium; and then nitrogen, carbon, oxygen, and so on. The name of the element tells you how many protons it has in it, and so the atomic number is the number of protons. And every single atom, every single atom, every single element, which is chemically distinct and operates, and each of the chemi—the chemistry is different between each one. So right now we know that there are 118 elements that have been made; about 24 of them have to actually be made in laboratories, and they only live for like microseconds or nanoseconds before they fall apart. About 87 of them are metals, meaning they have the capacity to allow electrons to flow off of them into—in the valence electrons, so they can easily be stripped off. Eleven of them, in, in, in naturally—well, like normal human circumstances, not too hot, not too cold, good enough for a human, not too high in the atmosphere, not too far below the ground—that 11 of them come as gases. Um, two of them occur like as liquids, like mercury is one of them, and bromine is another. A bunch of them are radioactive, about 25 or so, and these are the chemical elements, and only the most—the most massive ones are only formed in, in, in particle accelerators.

So when we look at the na—we look at that, we've seen periodic tables in the past. So let's look at how we read the name of the elements. Always the number of protons, the atomic number, describes the name of the element. And so if it's got one proton, it's always hydrogen; if it's got 23 protons, it's always vanadium; if it's got 19 protons, it's always potassium; if it's got 11, it's always sodium; if it's got two, it's always helium; if it's got six, it's always carbon; that's the name of it. And so all of the names require are exactly what the atomic number is. Now the funny thing is is that the names themselves then become abbreviated. So hydrogen is H, beryllium is Be, lithium is Li, sodium of course is Na, gold is of course Au. Oh my goodness, potassium is K; what's going on here? So basically, most of them are abbreviations, but some of them derive from Greek and Latin, so we don't necessarily have a one-to-one with their with their abbreviations and the names that are common in say English, but they would be common in other languages. So, but the name is always, no matter what language they're spoken in, the name of the thing describes the total number of protons. And so there's a whole slog of them, and the periodic table of elements is broken up into similar chemical behavior, such as hydrogen and lithium and sodium readily, readily, readily give away their electron, and fluorine, chlorine, bromine, and iodine readily grab an electron, and so they're under—they're not filled electron shell, so they will take an electron. So the most reactive elements come on both sides of the periodic table, so that's kind of how they go. And the farthest right ones are the noble gases, and they hardly react to anything because they're like their electron shells are filled. So when the—the most abundant elements out of all of the elements in the universe—almost 75% of all the matter, all the elements of the universe, all the matter of the universe is hydrogen, and 25% of the matter in the universe is helium. And then oxygen, carbon, neon, nitrogen, silicon, iron, magnesium, and sulfur come next. And so all of the things beyond hydrogen and helium make up only about 1% of all the matter in the universe. So if we want to say what is the matter of the universe, it's hydrogen and it's helium; that's pretty much it. All the other stuff, the things that we're made out of, the things that everything else that we encounter that's made out of, that's just really rare stuff, and some of it's really rare compared to the rarity of it is—so hydrogen and helium is everything in the universe. And where's the helium on Earth? Well, it's embedded inside of natural gas deposits, and it comes to us as a result of emissions by the sun.

All right, so remember we talked about the total number of protons did give with the atomic number, but remember we also said that neutrons can be in the core, in, in the nucleus of an atom. So when neutrons are in the nucleus of an atom, if they're differing numbers, we call them isotopes. So the isotope, meaning isotopic, meaning the topos is the number of protons, and so the number of protons is always the same. So hydrogen, plain old hydrogen, has none, no neutrons, but if it has a neutron, it's called deuterium, and there's deuterium; it has two objects in the core; it's called tritium if it is hydrogen with two neutrons attached to it in the nucleus. So tritium, though, is radioactive and will readily decay; that neutron will readily decay away. But in every case, there's all—to make an atom with deuterium, it only takes, even though there's two things in the nucleus, there's only one electron because the proton has one charge and the neutron has no charge. So if we look at something a little bit bigger, say carbon, carbon-12 has six neutrons and six protons; uh, carbon-13 has six protons and seven neutrons; carbon-14 has six protons and eight neutrons. And once you get too many neutrons, it tends to fall apart. So isotopes with lots and lots and lots of neutrons tend to fall apart; if they have far, and if they happen to have fewer neutrons than protons, they'll also fall apart, fall apart too. So radioactive carbon is very familiar; we call it radioactive carbon dating, and carbon falls apart. And what does falling apart mean? We mean that it's radioactive, and radioactivity is a decay of a subatomic particle from one type of thing to another. So tritium, as I said, was radioactive; tritium will spontaneously decay at some random interval, a random atom, a random nucleus of tritium will spontaneously—one of the neutrons will go, I don't think I want to be a neutron anymore, and turn into a proton, and in so doing, the nucleus will spit out an electron and also spit out a neutrino, and those things will go away, but now it's helium because there's two protons and one neutron, so it's light helium. So that's—we call light helium, or see it's got one neutron less than the number of protons; that's light helium. And likewise, carbon-14 decays to nitrogen-14 by one of the neutrons transforming itself into a proton. And so carbon then, which has six protons, becomes nitrogen, which has seven. So now we have seven and seven, and the nitrogen is happy, and then so decaying and switching from a proton from a neutron to a proton, an electron gets spent, sput out, and a neutrino gets sput out, and that, and if a neutron is also all by itself, it'll spontaneously decay in about 11 minutes or so. So these neutrons really don't know how to stay together because the electron, the proton and electron really want to fly apart, and the thing that's holding them together is the weak nuclear force, and that's the reaction; if you have a neutrino coming out, you've got the weak nuclear forces, which we've talked about in earlier parts. So these things are all called beta decays. You can also have an alpha decay where a full helium nucleus of two protons and two neutrons gets spat out by a very massive, very massive nucleus like uranium or something like that. Uh, you can also have gamma decay where the nucleus itself is in an energized state and emits a very high-energy light particle, a very high-energy photon in the form of a gamma ray. So wait a second, that's where we get the gamma ray idea from, is gamma rays are high-energy light. So we have alpha, beta, and gammas; alpha particles are heavy nuclei, beta particles are electrons, and gamma particles are photons of very high energy. And these things were given their names during the early years of studying radioactivity, uh, back in the turn of the 19th century, right around the turn of the 20th century in that area. I was so people named them that way, and sometimes you'll always be hearing alpha particles or alpha decay or alpha this, that; always means a helium nucleus, and we can sort of beta decay or beta particles, and those are always electrons, and the gamma rays, what we know about gamma rays, they're like, and that's where that comes from.

So why we care about all this is because when we're looking at astronomy, we can't actually reach out to the stars and take a bucket of a distant star and bring it home and see what's cooking in there; we can't do that. So we want to learn what is going on in those distant stars, and what's happening to the matter over there; we wish to identify what kind of matter it is, and that's where we get Kirchhoff's laws of spectroscopy, because every single element on the periodic table has its own spectrum when it gets excited or gets collided into and emits light; if it will absorb specific light, light energy, and it'll emit those things, exactly those wavelengths. So every single chemical element in existence has its own individual spectrum, and those spectra are always the same, no matter what, because every hydrogen atom is exactly the same in the entire universe; every carbon atom is the same in the entire universe, different isotopes, but they're the same; they're always the same because they're just—because protons are the same everywhere in the universe, and neutrons are the same everywhere in the universe, and electrons are the same everywhere in the universe. So every atom is just like any other atom if it's the same isotope, and even if they're different isotopes, they're almost the same because they just differ by the total number of neutrons. So there's no difference between them other than the number of neutrons. But what's a neutron? What's a proton? What's an electron? They're the same things everywhere in the universe, and you stack them together to make atoms, and each individual atom and all the molecules associated with them—well, let's stick with atoms because we're talking about elements for a second—the atomic elements, each one of them has their own individual spectral signature, and that can be discovered; in fact, it was first discovered that these things existed as objects spectroscopically because we'd have to say, oh, what do we have in this gas? If we have some rarified gas that we cannot see, but yet it glows because of the energy we're putting into it, if it glows with that characteristic pink, it must be hydrogen; if it glows in a particular different way, it's helium. And we break apart the spectrum, and we look at the spectrum of the thing as it's glowing, or maybe it's cool, and we've got something behind it that's hot that passes through the cool gas; the absorption lines are exactly the same as the emission lines, and that's what we talked about with Kirchhoff's laws of spectroscopy. So every single element, every single atom is the same in the cosmos in terms of what they are, meaning one carbon-12 atom is exactly the same as every other carbon-12 atom in the universe, and they all have exactly the same spectral fingerprint. That fundamental statement, that the spectra of all of these are identical, says that the light interacts with the matter, interacts with carbon-12, no matter how it interacts, every—all light interacts with everything, and that is part of an incredibly important idea called the Copernican principle, which means the cosmological principle says that there is no special place in the cosmos, and that all laws of physics are the same everywhere, and we will rely on that idea to get us out to the stars and enjo—and what is out there. But what's funny is is that not this whole thing that I discussed about the nature of these things, it's not been known forever. So let's see next time how the history of the atom developed through time.

Hello, this is Jason Kendall, and welcome to the next of my introductory astronomy lectures. Today we're continuing on the history of the atom. Well, we talked last time about what an atom is, what elements are, how they have protons and electrons and neutrons, and how they're arranged in these orbits around them, and there's isotopes and so forth, but where did this concept of the idea of the atom ever really come from? So that's what we're going to talk about right now. So the history of the atom is an interesting one because it develops out of natural philosophy. Natural philosophy is basically a way of talking about the world, philosophizing about the world in a way that is consistent with how you perceive the world. And so natural philosophy is a way of conducting science without having the tools to actually be able to gather the evidence or analyze it, but you do it as rigorously as you can. So let's take a couple of ideas about the nature of what we mean by matter, because stuff is in existence, and so stuff does things to other stuff, so you might want to say what exactly is matter. And some of the earliest recorded ideas about what the nature of matter are come from Democritus, which was who was a pre-Socratic philosopher in ancient Greece, and his goals around 400 BC or so, there abouts, he came up with the concept of an indivisible unit of matter, meaning you can cut something and keep cutting things, and it doesn't divide, and that's where the word atom comes from, a-tomos, meaning not division, divisible, not cuttable, not sliceable; that's what tomos, meaning to cut or divide, a meaning not. So the atom is that which cannot be cut. Democritus himself was, was is referenced throughout much of antiquities literature; however, a lot of his works did not survive because he was kind of on the outs with respect to medieval theology, and he disagreed with Plato and Aristotle and some key ideas, so his work was excluded throughout

History, but we know that he came up with the cut; we know that he alluded to the concept of the atom. We also know that he alluded to the idea that the Milky Way is a series of stars that are incredibly distant; so they're so distant that they actually look like one thing, and that kind of is it. It goes along with this concept of the atom, uh, and let's see what that is right now. The concept of the atom that Democritus had is that imagine you had a block of clay, or anything, but let's just use clay for this instance. Um, actually, I'm going to diverge away from—I'm going to say clay; I'm going to start with a tree. And if we start with a tree and you cut the tree, say, in half, well, which half of the tree is it? Well, you know you're going to get some half, whatever it happens to be. Let's say we cut it vertically, and so you've got a half of the tree that's vertically cut, and so that still has a big chunk of the branches, a big chunk of the of the root, um, a big chunk of the leaves and so forth. But at some point, as you keep cutting this tree in half, depending on how you cut it, eventually you're going to have to get to a point where you're going to cut the tree and you're going to divide the bark or the or the wood of the tree from the leaves of the tree. So therefore, the tree was one thing, and now you're cutting into two things, and each of those things is different from the other. All right, so now you're parrying away the thing that is not the same as it; so we get rid of the the leaf, and so we're left with the wood. And so now we cut the wood away, and we say, "Oh, there's the meat of the wood, the wood that's below the bark," and we have the wood that's above the bark, the bark wood. And so we cut away the bark, and now we're left with the with the wood, with the grains, and it's that nice yellow, nice yellow tone. As we cut further, we find that there's water inside of the bark; we find that they're inside of the wood; we find that there's sap inside of the wood; we find that there's dark and light little striations of the wood. So we keep cutting those things, eliminating the bark, eliminating the sap, eliminating the water, trying to get down to the essence of what is wood. And so at some point, you can philosophize that you would get down to the point where you say, "Ah, I've cut away everything that is not wood, and I found the tiniest element of something that is wood," and if I cut it, I will no longer have wood; I might have something else, but but then I just keep cutting until I get down to the thing that I say that this is the element of wood.

So the concept of the atomos then says there must be some fundamental building block out of which you can no longer cut, because how can you cut anything infinitely? Opposed Democritus, and so this is an interesting concept. Night likewise, that's his—that's where his concept of matter comes from. It doesn't matter whether it's clay or water or anything; there will eventually be some point at which you cannot cut any further, because that is the atomos, the indivisible unit. Well, this has some ramifications, and there was no real evidence for it, because like I said, in 400 BC, it's philosophy; it's not science yet. So the thing is is that other philosophers disagree, notably Plato and Aristotle, who disagreed with him entirely and thought that matter, like space, is continuous. So you'll notice that there is no gap in space or gap in matter between, say, the tree and the air that surrounds it, or when the tree is submerged in water; the water goes right up to the trees. There must be a transition between tree and water; that's a very sharp transition, but we notice that there's water in the tree, that the sap is made from tree and water, that when you burn a tree, the fire comes out of the tree, and so it's very interesting to think that maybe a tree is made up of fire; maybe it's made out of some sort of earthy element; maybe it's made out of some sort of airy element, because the fire lifts—the smoke is lifted out of there; maybe it's made out of some sort of water. Well, we know that—so all of these things can combine together, and if you combine them in just the right way, alchemically—an alchemist would do this—then you would get tree. So the proper combinations of fire, earth, water, and air, according to Plato and Aristotle, give you tree, or gold, or iron, or what have you. All of the various things that exist, according to Plato and Aristotle, were continuous matter, and this continuous matter, it can never be subdivided, and you can't find a boundary to it, so it's kind of innately important, neatly linked to the concept of space as well.

So why did Aristotle disagree, and what happened, and where did the concept of this continuous matter, and how did Aristotle blast Democritus' idea? Well, he appealed to religion and repealed to divinity, and divinity is definitely a part of natural philosophy, and you can actually add it in by saying, imagine that there's a spiritual plane, a spiritual divine plane, and this—this was okay in that time because they've divided the physics of the earth, the material versus the physics of this—of the heavens, the celestial, and the two really did not behave the same, according to each—according to anybody's observations. So the celestial realm is the divine realm; it's the unchanging realm; it's the—it's the permanent realm; the material world is ever changing and ever and ever fluid. And so there is a concept which arises from the four elements, and the fifth element is then spirituality or divinity. And Aristotle said the following: "So, Mr. Democritus, you're saying that the god Zeus, who is all-powerful, who took the eight-legged beast and ripped it apart to make man and woman, you're saying that he cannot rip apart the tiniest, tiniest dust mote, the thing that you say is the smallest possible thing. How can a god not break that apart?" That's kind of a valid philosophical argument if you posit the the existence of deities. So it really is a big thing, and so most of Christian thought and most of Western thought gravitated towards the concept of the continuous matter and Aristotle's thinking, because it is—because of the heightened element of the divin—the divine in natural philosophy. All right, so it took some time before people would take uh Democritus' idea seriously, and John Dalton, in about 1803 or so—2000 years after Democritus came up with this concept—2,000 years, and even 200 years after Galileo first put some—first put some dents in the armor of Aristotle with his—with—with all of his work—uh—so that we have Dalton coming along and proposed, "Well, hmm, we've got some interesting things that we see; we see that if you have—if you have water, water is always—not roughly 98—roughly 88 or 80—88.9 mass oxygen, and the rest is hydrogen. So we can always have that the same—or the percentages of oxygen and hydrogen are always the same, where they're cut—where mass is conserved, and mass doesn't disappear or reappear. You can say, 'Well, imagine that there's little tiny building blocks that have certain amounts of mass, and these things then—matter then is the arrangement of these little tiny building blocks, and perhaps some of the those little tiny building blocks are hydrogen, some of them are oxygen,' then it's a process of discovering which they are."

And so the atomic theory that Dalton revived—they used the word atom—atomic theory, he said that atoms can neither be created nor they can be destroyed; they are just there; there are pieces of matter that are permanent in existence, and all chemistry can be defined by adding and putting together various atoms in various arrangements. So Dalton's theory of the atom, which is—which is a highly simplified version of chemistry today, is that basically—well, even when you do elementary first-semester chemistry, you're going to be looking at Dalton's version of the atom; we're not going to look at quantum mechanics just yet. But when you look at Dalton's version, you say, "Well, if you want to make water, well, you take one atom of oxygen and two atoms of hydrogen, and that is water," and if you want to make carbon dioxide, it's one carbon and two oxygens; if you wish to make uh methane, it's a CH4; and if you want to make ammonia, it's NH3. So you got all these things where they combine together, and the combination thereof becomes the molecule. So Dalton's theory of the atom worked out pretty good; every element has its own particular properties; they all have the same properties, and atoms simply combine in whole numbers; you can't break atoms apart in order to say, "Oh, there's no half water," which is like a half an oxygen and one and one hydrogen; that's not half water; there's no such thing as half water. So Dalton's idea of the atom held sway for about a hundred years, and about 1903—uh, roughly—actually more like 1897—J.J. Thomson's—or J.J. Thomson discovered the electron, the first fundamental particle—when we—this is the discovery of the concept that yes, there can actually be fundamental particles, meaning things that cannot be divided anymore, the literal atomos of Democritus back in 400 BC. Um, so what he discovered was the electron, which had a positive—it was a negative charge, and it must reside—he discovered it by using cathode ray to—and just understanding what the nature of a cathode ray is. And so what he said is that, "Well, wait a second; we know these electrons must exist," and so he posited that that perhaps Dalton's concept of the atom can be modified; instead of being this smooth distribution of Lego bops or just little things, little balls like billiard balls that are smooth, perhaps inside the billiard ball of Dalton there are electrons, and they're moving around. And so therefore, if there's an electron which is a negative charge, there must be some positive charged object, a proton, that's also in there, because every atom is electrically neutral; if it wasn't, it would be quickly—therefore it would quickly neutralize itself by either acquiring electron or losing an electron. So Thompson's concept was is that inside of each of these little billiard balls, Dalton's billiard balls, there were a plum pudding of electrons and protons in a mash that neutralized themselves out. So this is a good little model of the—of the—of the atom, and the thing is is that it's—it took the concept of the electron, said, "Oh, it's a piece of the atom," and inside the atom there's this thing. All right, so this also led him to learn that electrons were about 2,000 times smaller mass than the proton, whatever it was; these tiny, tiny, tiny things were there anyway. So it didn't take long for people to say, "Well, okay, got it; what Thompson is saying is that the electrons and protons are arranged inside the atom. All right, how exactly are they arranged? That's a really key question; it's like, 'Okay, fine; are they moving randomly? Do they have structure? Are they set up like little bricks? How are they set up inside of Dalton's little atom?'" And into—how is the plum pudding mixed? Are the plums evenly distributed in the pudding, or are the plums tiny little bits going through?

So what Sir Ernest—that's right—Ernest Rutherford, in 1911, sought to understand this, the—the interior of Thompson's plum pudding model, and what he decided to do is to say, "I'm going to take a very, very, very heavy atom that I can make into a very, very, very flat sheet, an extraordinarily thin flat sheet," and the goal of this extraordinarily thin flat sheet is that if I throw something at a thin flat sheet, things should go through it or bounce off of it, and you know that if you take an object that is not flat and you throw something at it, things can reflect off of it in all sorts of ways. So if you take a flat surface, then you bounce a ball off of the flat surface, the angle of incidence equals the angle of reflection off a flat surface. However, if the surface is all jagged or irregular in some way, then if you throw balls at that surface at different angles, the angle of incidence at the moment—at the location where the ball hit the surface—let's say the basketball—let's say you do this off a basketball court which is flat, and now you play a game where it's on a curved surface like this—maybe it's got humps—and so as it reflects, you can actually see where it reflects from and where it goes to after it reflects, and that gives you a map—by looking back where the things came from—is to the shape of the object. And now that's one way of looking at things, but Tom—but—but Sir Ernest Rutherford—why do I keep saying Sir? I'm—I forget if he is a Sir—in any event, Ernest Rutherford, in 1911, said, "I'm going to take gold, which I can hammer down and make into gold foil, and this gold foil can be literally only a few atoms thick, just—just the thinnest thing," and this is an amazing property of gold, by the way, and gold itself can be—can be made into very, very thin foils, and it's so thin that if a gold atom is one of Thompson's plum pudding models, then the electrons in there have to be distributed in some way, and if I throw something at it and it goes through the atom, it might deflect it as it goes through. So if you throw something through something—if you throw ghosts—go through something and you interact with it gently, it'll diverge the path of the thing that you threw through it. So it assumes that Thompson's plum pudding model is—is porous or at least maybe not necessarily porous, but at least kind of some material, something, and we don't know exactly how it's structured, but let's take a helium nucleus called an alpha particle, and we'll take that alpha particle and send it through the gold nucleus.

Now, here was the expectation; the expectation was that as the gold—as the helium nuclei went through, they would be gently redirected by the distribution of electrons inside of there, because it's been known that by cathode ray—by—with the interactions of cathode rays and again alpha particles that they actually interact, and they can redirect each other's paths. So what happens is that you send the elect—send the alpha particle through the gold foil and see how it gets bent around, and that gives you the structure of the electrons inside there, because the gold must be—the gold, right? It just must be whatever it is, and nicely enough gold does not do much reaction; it's very—not heavily reactive, and it's very, very thin. So here's what—what Rutherford found; he found that most of the—of the alpha particles went straight through the gold foil and were detected on a silver iodide screen on the far side, but just to be careful, Rutherford put a screen all the way around it, and he found out that a significant number—and a non-apprecia—significant number—actually bounced back. So that's kind of weird; so you throw something at something very, very thin that's supposed to allow things to pass through, but instead it bounces off of something. So that meant that if—if with Rutherford's concept, then he had to reconfigure what he meant by the atom, and he said, "Wait, there must be some dense heavy thing that the alpha particle's knocking off of," because if you then say—let's say you have the protons or the alpha particles are part of the gold nucleus; if you send one alpha particle into the other, they're going to hit off of each other, but they won't necessarily bounce straight off of each other; they have to be a perfect alignment for them to do that. But what happened is is that the gold foil reflected off of the—the alpha particles reflected off of the gold foil coming back towards the detail—towards the emitter—and that, as Rutherford said, was like taking a 15-inch shell, an artillery shell such as might have been used in, say, the First World War, right around 1911—which we're talking about 1911—I—and the 15-inch shell going through a piece of tissue paper, and the tissue paper bounces the artillery shell off of it. Now, that would be surprising, and that's a surprise; in fact, that the energetics of that are about as surprising as what Rutherford discovered with this experiment, which meant that there must be some massive object in the atom that can reflect off of it—can reflect something—can push something back that's coming into it at high speed that has some data—some decent mass to it. So he reconfigured the concept to say that at the center of the atom was this—was a positively charged nucleus, and that positively charged nucleus has mass—as most of the mass of the atom—and the electrons are somehow spiraling around it. So these—that is the difference between—between the plum pudding model and Rutherford's—a swarm of electrons around a nucleus, and this was—it put to bed Thompson's model of the—of—of the—of the plum pudding. So now we have this concept that there must be a dense nucleus. This led to some problems, though, because the—if it's smoothly distributed, then it can be electrically neutral, but if Rutherford's concept is right, now you've got this positive charge thing, and you've got these negative charge things flying around it, and observationally—experimentally—they exist; they—there is some large positive charge thing, and the electrons are negatively charged, and they're clearly not on top of it; they're near it, but not on top of it. So the question then becomes, why doesn't the electron spiral down from its orbit around this nucleus and fall into the nucleus and become Thompson's plum pudding? What is the thing that makes the plum pudding not true, meaning it should just spiral together so it's all neutral and everybody's on top of each other? Why do the electrons stay away from the nucleus, which is positively charged? We get why it should be near, because there's an attractive force, but why should all of a sudden it stop? And nobody—nobody knew why that would go—why that would be so. No matter what, when you did this experiment, you found that the nucleus had to be there, separate from the electrons, and this became the—the topic for an enormous amount of research, and it spurred the entire idea, because Rutherford's atom has a very difficult time explaining the spectra of light, because now we have—disabled—Rutherford's atom says if you have an electron spiraling around, as it spirals, it should emit a continuous spectrum of light, not a discrete spectrum. So Rutherford's atom cannot predict the spectrum; however, it does predict the—the event of colli—collisions into it, and it does disprove the plum pudding model. So there's a bit of a problem, and that problem is—one experiment shows one thing, but other experiments demand that that's not the full story, and the full story of what happens to Rutherford's atom comes up next time when we talk about the Bohr model of the atom.

Hello, this is Jason Kendall. Welcome to the next of my introductory astronomy lectures. Today we're going to be talk—finishing out the nature of what the hydrogen atom is and the models of the atom through history. So let's take a step back. Last time we looked at Rutherford's version of the atom, which is kind of like little stars orbiting a little planet—a little planet orbiting a little star—that's the kind of basic assumption that Rutherford came about when he—when he did his gold foil experiment. But if we go back just a little bit further back in time, we find that there's a very interesting hint to things to come. The Swedish physicist Johannes Rydberg, in 1888, looked at the nature of the hydrogen spectrum and tried to create an empirical formula. This empirical formula had a goal, and the goal was to actually simply model the actual lines that are seen, the transitions that are seen, or at least the spectral lines that are seen in the hydrogen spectrum. So what he did is he found a periodic pattern to them, and he was able to determine that the reciprocal of the wavelength is equal to some constant, some full constant, and then multiply it by the reciprocal of two—the inverse of two squared integers. Now, this is really interesting because it highlights a concept that what you sometimes do in science is you just try to create some sort of empirical formula for what you're observing in nature, and after you do that empirical formula, you then try to see if you can understand the underlying science below it. Well, that's—so that's what Rydberg did; he made an empirical formula that is only based off of the data, but he had no under—underlying reason as to—

Friend, being downtown at the same time. In any event, quantum mechanics is how we actually discuss the nature of the world. But we talk astronomically; we tend to use the Bohr model of the atom because it's really simple to understand, and that kind of gives a really good visualization. It's very hard to visualize all these other things. Um, so we do is we we try to think that we know that there's that that basically electrons must live in fixed orbital radii away from their nuclei of their atoms.

And that concept that leads us to the nature of what spectroscopy does and helps us to understand how Kirchhoff's laws arise. And so when we look at we look at distant astronomical objects, as we will in the future, then we will see that we can model an atomic process to the light that gets emitted to what happens when it arrives at our telescope and our detector.

So next time we'll talk about telescopes and how they work.