1 00:00:02,820 --> 00:00:07,700 That was a long hard clip, we learned a lot. 2 00:00:07,700 --> 00:00:12,900 And there's more. One last addition of Physics. 3 00:00:12,900 --> 00:00:17,842 Before we turn our attention back to astronomy and we will be equipped for 4 00:00:17,842 --> 00:00:21,796 most of the class. Though we will have occasion to introduce 5 00:00:21,796 --> 00:00:26,937 more science, there is a lot to discover. so we're back to our understanding of 6 00:00:26,937 --> 00:00:31,814 light which as I said is extremely important to us and the first thing we 7 00:00:31,814 --> 00:00:37,086 want to consider are the possibilities for what happens when light meets matter. 8 00:00:37,086 --> 00:00:40,250 So we talked about dense objects like the earth. 9 00:00:40,250 --> 00:00:44,194 whence light hits the earth most of the light is absorbed. 10 00:00:44,194 --> 00:00:48,526 We know you shine a flashlight at the ground it doesn't go through. 11 00:00:48,526 --> 00:00:53,545 Objects as dense as Earth take up only a very small fraction of space. 12 00:00:53,545 --> 00:00:59,130 But there are, in fact, large cold clouds of dust and gas that absorb radiation, so 13 00:00:59,130 --> 00:01:03,197 they look very dark. So there is the possibility that dense 14 00:01:03,197 --> 00:01:06,713 enough and cold enough objects simply absorb light. 15 00:01:06,713 --> 00:01:12,228 Or some of the light might be reflected when you shine a flashlight beam on the 16 00:01:12,228 --> 00:01:14,228 ground. Some of it bounces up. 17 00:01:14,228 --> 00:01:19,500 If you put your hand above the beam, you will see light coming off your hand, so 18 00:01:19,500 --> 00:01:24,560 we can get some reflection off of dense objects, and that in fact is how we see 19 00:01:24,560 --> 00:01:27,830 the wold around us, sunlight bounces off dense things. 20 00:01:27,830 --> 00:01:30,030 And, we see them and don't walk into them. 21 00:01:30,030 --> 00:01:37,160 Now in general, how much is absorbed can depend on the wavelengths, so different 22 00:01:37,160 --> 00:01:42,981 materials reflect different amounts of the light in different wavelengths. 23 00:01:42,981 --> 00:01:48,706 This is how dyes and colors work. So the sweatshirt I am wearing is red 24 00:01:48,706 --> 00:01:55,282 because someone imbibed the fibers with a dye that absorbs, say, green light and 25 00:01:55,282 --> 00:02:01,548 that makes the light that it emits look this nice dark red color and other 26 00:02:01,548 --> 00:02:05,494 things. the walls behind me are painted with a, a 27 00:02:05,494 --> 00:02:10,910 paint that reflects mostly blue light, and therefore they look blue. 28 00:02:10,910 --> 00:02:14,961 And so, what that means is that as we look around the universe and we see 29 00:02:14,961 --> 00:02:19,178 colors of things, sometimes if you see the colors of reflected light, you can 30 00:02:19,178 --> 00:02:23,673 conclude something about the chemical composition of the thing you're looking 31 00:02:23,673 --> 00:02:26,348 at. There is another interaction of light 32 00:02:26,348 --> 00:02:31,365 with matter that will be of great importance to us, and as we will see we 33 00:02:31,365 --> 00:02:36,118 will explain interesting things. And that is the possibility that if you 34 00:02:36,118 --> 00:02:40,804 have matter that is not dense. That is tenuous enough to be transparent, 35 00:02:40,804 --> 00:02:46,085 so most of the light goes through [COUGH] light scatters off of molecules, atoms, 36 00:02:46,085 --> 00:02:50,559 dust grains, anything. Rayleigh and the mathematical formulation 37 00:02:50,559 --> 00:02:55,760 was given by Lord Rayleigh in 1871. So, it's called Rayleigh's scattering. 38 00:02:55,760 --> 00:03:01,395 And, what scattering means, means that a light being coming in will hit some 39 00:03:01,395 --> 00:03:07,246 particle and be deflected at some angle. What that means is that you looking here 40 00:03:07,246 --> 00:03:12,659 will see light Coming from over there that actually came from over there, you 41 00:03:12,659 --> 00:03:16,150 will see light coming from the wrong direction. 42 00:03:16,150 --> 00:03:18,513 Now, this phenomenon decreases with 43 00:03:18,513 --> 00:03:23,084 wavelength, long wavelengths scatter far less than short wavelengths. 44 00:03:23,084 --> 00:03:28,595 So blue lights scatters more than red if you recall this image of the Pleiades 45 00:03:28,595 --> 00:03:32,090 cluster N45, we saw this blue wispy light all around. 46 00:03:32,090 --> 00:03:37,198 This is scattered light, these are clouds of dust around these stars and the 47 00:03:37,198 --> 00:03:42,374 starlight is scattering off of them so that light from the star that was not 48 00:03:42,374 --> 00:03:46,340 suppose to hit us on earth that was heading somewhere else, 49 00:03:46,340 --> 00:03:52,240 got scattered by dust over here and so we are seeing light, 50 00:03:52,240 --> 00:03:57,362 starlight coming from the wrong direction, because it was scattered by 51 00:03:57,362 --> 00:04:00,801 the dust. this has lots of interesting 52 00:04:00,801 --> 00:04:05,420 consequences. And one of my favorite is the following. 53 00:04:05,420 --> 00:04:10,520 In this experiment, we're going to simulate the interaction of sunlight with 54 00:04:10,520 --> 00:04:13,455 the atmosphere and we'll learn somethings. 55 00:04:13,455 --> 00:04:16,460 On the left hand side we see the apparatus. 56 00:04:16,460 --> 00:04:20,512 We have a cup of water standing on an over head projector. 57 00:04:20,512 --> 00:04:24,285 The overhead projector has a round hole cut in a mask. 58 00:04:24,285 --> 00:04:29,945 And, so what we see is, we see the cup of water and we see the light going through 59 00:04:29,945 --> 00:04:33,160 the cup of water and projected on to the wall. 60 00:04:33,160 --> 00:04:37,486 Water is transparent and so looking through the cup and seeing the dark 61 00:04:37,486 --> 00:04:40,971 color, we're seeing the darkness of the curtains beyond it. 62 00:04:40,971 --> 00:04:45,357 Just as where the air completely transparent, you would look above us and 63 00:04:45,357 --> 00:04:50,175 see the darkness of space. Indeed, if our earth's atmosphere were 64 00:04:50,175 --> 00:04:55,393 completely clear then, looking at the sun, we would see the bright white color 65 00:04:55,393 --> 00:04:59,459 of a black body object with a peak somewhere in the visible. 66 00:04:59,459 --> 00:05:04,678 The peak is broad enough that there's distinguishable difference between the 67 00:05:04,678 --> 00:05:09,948 way our various receptors are excited. So any object with a black body spectrum 68 00:05:09,948 --> 00:05:13,687 of a few thousand degrees, like an incandescent light bulb, will appear 69 00:05:13,687 --> 00:05:17,903 bright white to us, as would the sun. The rest of the sky though when we're 70 00:05:17,903 --> 00:05:20,559 looking away from the sun would appear dark. 71 00:05:20,559 --> 00:05:25,449 And this famous Apollo image that we see of Earth rise over the lunar surface, is 72 00:05:25,449 --> 00:05:28,950 a great example of this. Clearly it is daytime on the moon. 73 00:05:28,950 --> 00:05:33,352 From the phase of the Earth, you can tell that the sun is directly overhead, as 74 00:05:33,352 --> 00:05:36,288 seen by, the astronauts on the moon, at this point. 75 00:05:36,288 --> 00:05:40,578 And you can see that the moon's surface is brightly lit, the sun is overhead. 76 00:05:40,578 --> 00:05:43,231 And yet, the sky on the moon is completely dark. 77 00:05:43,231 --> 00:05:46,448 Had we looked at the sun, we would see a bright white sun. 78 00:05:46,448 --> 00:05:48,819 Looking away from the sun, the sky is dark. 79 00:05:48,819 --> 00:05:51,360 And, in fact, you can see stars in the daytime. 80 00:05:51,360 --> 00:05:55,237 This is not the situation on Earth. And the difference between the moon and 81 00:05:55,237 --> 00:05:58,650 the Earth is our atmosphere. Dissimulate 100 miles of air overhead 82 00:05:58,650 --> 00:06:04,107 with its abundance of scattering opportunities for 83 00:06:04,107 --> 00:06:07,542 incoming light. What I've done is I've stirred some 84 00:06:07,542 --> 00:06:10,933 reagents into this cup. Over time, as they react, they will 85 00:06:10,933 --> 00:06:15,217 precipitate increasingly large concentrations of small crumps of sulfur 86 00:06:15,217 --> 00:06:18,371 into the water. These will service scattering centers, 87 00:06:18,371 --> 00:06:23,012 and will allow us to emulate a 100 miles of atmosphere in six inches and what 88 00:06:23,012 --> 00:06:27,831 we're going to do is as the concentration of sulphur increases we will follow on 89 00:06:27,831 --> 00:06:30,390 the left hand side what the cup looks like. 90 00:06:30,390 --> 00:06:34,800 this emulates what you'd see in the sky looking away from the sun, which right 91 00:06:34,800 --> 00:06:37,305 now is a dark sky and presumably star studded. 92 00:06:37,305 --> 00:06:41,444 And on the right, we'll see what happens when you look directly at the light 93 00:06:41,444 --> 00:06:43,895 source. This will simulate what you would see 94 00:06:43,895 --> 00:06:49,204 looking directly at the sun. You've now achieved a sufficient 95 00:06:49,204 --> 00:06:54,369 concentration of sulfur precipitate that there's a lot of scattering going on in 96 00:06:54,369 --> 00:06:57,430 that cup and the water is no longer transparent. 97 00:06:57,430 --> 00:07:02,468 In fact we don't see the dark curtains through it, we see that it's glowing and 98 00:07:02,468 --> 00:07:06,230 as predicted, blue light scatters more than any other color. 99 00:07:06,230 --> 00:07:11,332 So the color of this cup is glowing, is a bright sky blue and as the precipitate 100 00:07:11,332 --> 00:07:16,433 continues to increase in concentration, that glow will get brighter and brighter. 101 00:07:16,433 --> 00:07:19,750 What we are seeing is sunlight scattered off the 102 00:07:19,750 --> 00:07:24,277 scattering centers in the sky, water molecules, dust particles, air molecules 103 00:07:24,277 --> 00:07:28,985 themselves, causing the sky to glow blue when you're looking away from the sun, 104 00:07:28,985 --> 00:07:33,150 and this is a very dramatic demonstration of what it is we're seeing. 105 00:07:33,150 --> 00:07:37,711 Looking on the right, we see that what has happened to the transmitted sunlight. 106 00:07:37,711 --> 00:07:41,406 This is, remember, what you see when you look straight at the sun. 107 00:07:41,406 --> 00:07:45,621 Some of the blue light that would have reached your eyes had it not been 108 00:07:45,621 --> 00:07:50,067 scattered, has been scattered in other directions in interactions with the 109 00:07:50,067 --> 00:07:53,300 atmosphere. This leave the sunlight that reaches your 110 00:07:53,300 --> 00:07:57,515 eyes, blue depleted and blue depleted white light, you recall, looks to our 111 00:07:57,515 --> 00:08:00,575 eyes yellow. It's a combination of green and red with 112 00:08:00,575 --> 00:08:04,790 less smaller amounts of blue. What we perceive that is as yellow light. 113 00:08:04,790 --> 00:08:08,979 This is the reason the sun looks yellow. We've now achieved a high enough 114 00:08:08,979 --> 00:08:13,306 concentration of scatterers, and in fact when we look at the cup, it not only 115 00:08:13,306 --> 00:08:16,096 glows very brightly, pretty in fact appears white. 116 00:08:16,096 --> 00:08:19,399 We see all colors of the light scattered towards our eyes. 117 00:08:19,399 --> 00:08:22,872 This is some what the color of bright white cloud in the sky. 118 00:08:22,872 --> 00:08:27,370 A cloud contains many ice crystals, light is reflected and scattered off of the 119 00:08:27,370 --> 00:08:31,868 ice, we see all colors reflected from a white cloud, so that's the reason we are 120 00:08:31,868 --> 00:08:35,129 seeing this. But, we still have as you can see at the 121 00:08:35,129 --> 00:08:39,950 edges where the camera is less saturated, there is still a preponderance of blue 122 00:08:39,950 --> 00:08:44,167 light in the scattered light. And this is very dramatically evident on 123 00:08:44,167 --> 00:08:48,566 the right when we see that the transmitted sunlight is now really a dark 124 00:08:48,566 --> 00:08:52,993 yellow as the light loses blue components to scattering, what's left is yellow, 125 00:08:52,993 --> 00:08:56,465 that is some reminiscent of the color of the Sun as we see it. 126 00:08:56,465 --> 00:09:00,888 We also see that as more and more light get scattered, the observed sunlight is 127 00:09:00,888 --> 00:09:03,408 dimmer. Indeed, the atmosphere dims the Sun by 128 00:09:03,408 --> 00:09:07,607 distributing some of its light in all kinds of other directions, the Sun is 129 00:09:07,607 --> 00:09:10,687 much brighter on the moon where there is no atmosphere. 130 00:09:10,687 --> 00:09:14,550 Finally, having waited for the concentration of scattered rays in the 131 00:09:14,550 --> 00:09:18,974 cup to increase to the point where as you see in the left, the cup glows bright 132 00:09:18,974 --> 00:09:21,988 white. you can see that what's going on is that 133 00:09:21,988 --> 00:09:26,615 not only have the blue hues of the incoming white light been scattered away 134 00:09:26,615 --> 00:09:30,938 but in fact its lost much of it's green. And the remaining color of the 135 00:09:30,938 --> 00:09:35,748 transmitted light as we see on the right is darker than yellow in fact it's an 136 00:09:35,748 --> 00:09:38,731 orange. As scattering continues to increase we 137 00:09:38,731 --> 00:09:43,724 will lose more and more of the green and eventually the transmitted sunlight will 138 00:09:43,724 --> 00:09:46,889 appear almost red. This might remind you that there are 139 00:09:46,889 --> 00:09:50,470 circumstances under which indeed, the sun in the sky appears red. 140 00:09:50,470 --> 00:09:54,703 I hope you found that demo as fascinating as I always do. 141 00:09:54,703 --> 00:09:58,725 What did we see? We saw that the atmosphere scatters blue 142 00:09:58,725 --> 00:10:03,170 light in preference over other colors making the sky glow blue. 143 00:10:03,170 --> 00:10:08,981 And because of depletion of blue light the sun appears yellow so light of all 144 00:10:08,981 --> 00:10:14,585 colors impinges on the atmosphere and the blue light scatters so that if we look 145 00:10:14,585 --> 00:10:20,050 away from the sun over here we see blue light scattered in our direction among 146 00:10:20,050 --> 00:10:25,585 others from the sunlight that hit over here but the rays that penetrate are the 147 00:10:25,585 --> 00:10:30,774 greens and the reds together blue depleted white light appears to us to be 148 00:10:30,774 --> 00:10:33,143 blue. And then, as we increase the 149 00:10:33,143 --> 00:10:38,564 concentration of scatterers, effectively making the atmosphere contain more 150 00:10:38,564 --> 00:10:42,720 impurities. Or be thicker, we saw, 151 00:10:42,720 --> 00:10:46,919 when we got more scattering, we lost the green as well as the blue, 152 00:10:46,919 --> 00:10:49,583 and that left the sun looking distinctly red. 153 00:10:49,583 --> 00:10:54,378 And of course the sun looks red to us at sun rise and sunset when its low in the 154 00:10:54,378 --> 00:10:56,924 sky. The reason for this is both because at 155 00:10:56,924 --> 00:11:01,482 sun rise and sunset we're looking not through a 100 kilometers of atmosphere, 156 00:11:01,482 --> 00:11:04,087 but through a 1000 kilometers of atmosphere. 157 00:11:04,087 --> 00:11:08,823 And more over most of the impurities in the atmosphere, the bigger scatteres are 158 00:11:08,823 --> 00:11:12,020 at low altitudes. And the grazing rays of the rising or 159 00:11:12,020 --> 00:11:15,018 setting sun have more opportunity to encounter them. 160 00:11:15,018 --> 00:11:19,399 And scatter and so the blue scatters early than the greens than the yellows 161 00:11:19,399 --> 00:11:22,339 and so on. And only at the end of the day, red light 162 00:11:22,339 --> 00:11:24,818 penetrates all the way through to our rise. 163 00:11:24,818 --> 00:11:29,430 So that same demo shows us why the sky is blue, why the sun looks yellow, and why 164 00:11:29,430 --> 00:11:33,079 sun sets are red. Now, I can't resist the few other 165 00:11:33,079 --> 00:11:36,720 brilliant examples of scattering on Earth. 166 00:11:36,720 --> 00:11:41,871 One is crystals of ice, because of their geometry, tend to scatter like 167 00:11:41,871 --> 00:11:47,464 preferentially at particular angles. There is, are many forms of ice crystals, 168 00:11:47,464 --> 00:11:53,462 one hexagonal form that forms in high altitude clouds tends to scatter light at 169 00:11:53,462 --> 00:11:58,147 an angle of 22 degrees and so very often you see at night the moon with a 22 170 00:11:58,147 --> 00:12:02,103 degree ring around it. So again this is moonlight that was not 171 00:12:02,103 --> 00:12:07,153 aimed at you but someone 22 degrees away from you was deflected and is hitting you 172 00:12:07,153 --> 00:12:10,257 and so you see this beautiful ring around the moon. 173 00:12:10,257 --> 00:12:14,030 You can get a ring around the sun but the sun is to brilliant. 174 00:12:14,030 --> 00:12:19,691 On the other hand, the geometry of water droplets in the, optical properties of 175 00:12:19,691 --> 00:12:22,791 water. Say that water droplets like to scatter 176 00:12:22,791 --> 00:12:26,296 light through an angle of 140 degrees, approximately. 177 00:12:26,296 --> 00:12:31,620 What this means is that the light is returning in the direction of the Sun and 178 00:12:31,620 --> 00:12:36,405 it forms a big circle with a radius of 40 degrees around the direction 179 00:12:36,405 --> 00:12:41,131 diametrically opposed to the Sun. And so, if the sun is high in the sky 180 00:12:41,131 --> 00:12:44,570 this is typically below you, and you don't see anything. 181 00:12:44,570 --> 00:12:49,098 But if the Sun is low you can see parts of a big circle in the sky in the 182 00:12:49,098 --> 00:12:51,790 direction, opposite the direction of the Sun. 183 00:12:51,790 --> 00:12:56,747 And because the light has gone through water and the optical properties of water 184 00:12:56,747 --> 00:13:01,642 depend on the wavelength different colors of light get deflected by slightly 185 00:13:01,642 --> 00:13:05,803 different angles and we get the brilliant phenomenon of the rainbow. 186 00:13:05,803 --> 00:13:10,576 And as I said the best rainbows are always early in the morning or late in 187 00:13:10,576 --> 00:13:13,941 the afternoon. The Sun is low and the rainbow therefore 188 00:13:13,941 --> 00:13:16,774 high. If you want to see a rainbow at, midday, 189 00:13:16,774 --> 00:13:21,078 with the sun overhead. You have to be able to be looking down at 190 00:13:21,078 --> 00:13:24,104 the clouds. As this paraglider pilot is doing. 191 00:13:24,104 --> 00:13:29,417 the round rainbow, in this case double with the shadow of your glider in the 192 00:13:29,417 --> 00:13:33,520 middle is called the glory. And it is, indeed, a glorious sight. 193 00:13:33,520 --> 00:13:36,439 The sun as we know, has a black body spectrum. 194 00:13:36,439 --> 00:13:39,942 It's a black body with a temperature of 6,000 degrees. 195 00:13:39,942 --> 00:13:44,483 And it looks white in general. The black body spectrum is sufficiently 196 00:13:44,483 --> 00:13:47,532 broad. And anything with a temperature of a few 197 00:13:47,532 --> 00:13:50,581 thousand degrees. The sun and incandescent lamp. 198 00:13:50,581 --> 00:13:55,836 Such that the maximum is anywhere near the visible will not create sufficient 199 00:13:55,836 --> 00:14:01,155 differences between the way it activates our green, blue and red receptors to give 200 00:14:01,155 --> 00:14:05,659 us a great sensation of color, so the sun appears to us white, remember its 201 00:14:05,659 --> 00:14:10,201 wavelength of maximum emission is right smack in the middle of the visible 202 00:14:10,201 --> 00:14:13,230 spectrum of the green, and it makes a beautiful 203 00:14:13,230 --> 00:14:16,757 rainbow of colors. And here, someone has laid out the solar 204 00:14:16,757 --> 00:14:20,649 spectrum line by line by line. So this is to be read like a book. 205 00:14:20,649 --> 00:14:25,636 It's a very detailed spectrum of the sun. And indeed, there's a black body spectrum 206 00:14:25,636 --> 00:14:28,798 here centered on the green. But there are these gaps. 207 00:14:28,798 --> 00:14:32,265 There are holes. There are specific wavelengths along the 208 00:14:32,265 --> 00:14:37,079 spectrum in which there are holes. Something is eating the black body 209 00:14:37,079 --> 00:14:41,381 spectrum is continuous. Something is absorbing the light at 210 00:14:41,381 --> 00:14:46,194 particular wavelengths. And this was a discovery by Fraunhofer in 211 00:14:46,194 --> 00:14:48,163 1814. And a few years later, Kirchoff and 212 00:14:48,163 --> 00:14:54,070 Bunsen discovered that if you heat a tenuous gas, a gas under low pressure and 213 00:14:54,070 --> 00:14:57,685 very low density, then the la, glass will glow if you 214 00:14:57,685 --> 00:15:01,782 either. Heated by burning or ionize it by passing 215 00:15:01,782 --> 00:15:06,773 a current through it. When the gas is sufficiently tenuous, the 216 00:15:06,773 --> 00:15:13,133 light that it glows with is actually not black body spectrum but only discrete 217 00:15:13,133 --> 00:15:17,426 spectral lines. And Kirchhoff is the one who figured out 218 00:15:17,426 --> 00:15:22,896 the regularity that relates these two pictures, and let's see how that works. 219 00:15:22,896 --> 00:15:28,797 We have a incandescent light here, or if you want any black body, say a star, and, 220 00:15:28,797 --> 00:15:32,612 like the Sun. If you are looking at the star, then you 221 00:15:32,612 --> 00:15:37,793 will see in your spectrometer a continuous black body spectrum with the 222 00:15:37,793 --> 00:15:42,040 maximum emission determined by the temperature of the star. 223 00:15:42,040 --> 00:15:48,163 To the left, is a cloud of tenuous gas. So low pressure, low density. 224 00:15:48,163 --> 00:15:54,997 And if you observe the emissions from that cloud of tenuous gas, you get this 225 00:15:54,997 --> 00:15:58,929 line spectrum that Kirchhoff and Bunsen discovered. 226 00:15:58,929 --> 00:16:02,083 There will be discrete wavelengths, discrete places. 227 00:16:02,083 --> 00:16:06,474 It's called the line spectrum for the obvious reason of its appearance. 228 00:16:06,474 --> 00:16:10,990 There will be discrete places in the spectrum where this cloud will emit. 229 00:16:10,990 --> 00:16:16,610 On the other hand, if you observe the continuous emitter, the black body, 230 00:16:16,610 --> 00:16:22,467 through the cloud, you will see the rainbow the full continuous black body 231 00:16:22,467 --> 00:16:28,721 spectrum of the black body that's behind. And at precisely the same wavelengths 232 00:16:28,721 --> 00:16:32,441 where you saw emission you will see absorption. 233 00:16:32,441 --> 00:16:38,378 In other words, an atom or a molecule is characterized by a specific set of 234 00:16:38,378 --> 00:16:43,460 wavelengths at which it can either emit light or absorb. 235 00:16:43,460 --> 00:16:48,869 Now when you bunch a whole collection of atoms densely together, then these lines 236 00:16:48,869 --> 00:16:52,342 are broadened gradually as you increase the density. 237 00:16:52,342 --> 00:16:57,418 And eventually when the density becomes large enough they merge into the 238 00:16:57,418 --> 00:17:02,426 continuous spectrum of a black body spectrum that absorbs all light at any 239 00:17:02,426 --> 00:17:06,233 wavelength and emits in a continuous black body spectrum. 240 00:17:06,233 --> 00:17:10,975 But if the density is low and the pressure is low enough then you find 241 00:17:10,975 --> 00:17:14,247 discreet emission as well as discreet absorption. 242 00:17:14,247 --> 00:17:17,320 So these wavelengths are properties of the 243 00:17:17,320 --> 00:17:21,160 Gases in the cloud, that we're talking about. 244 00:17:21,160 --> 00:17:25,725 Naturally, this discovery was a huge boon to chemistry. 245 00:17:25,725 --> 00:17:32,490 Because what it allowed, Kirchhoff and Bunsen to do was to heat various gases. 246 00:17:32,490 --> 00:17:38,587 Observe the emission line spectrum. And conclude, identify the wavelengths of 247 00:17:38,587 --> 00:17:43,695 emission with those from known atoms, known elements and they could find the 248 00:17:43,695 --> 00:17:48,870 element, the elementary composition, the chemical composition of the substance 249 00:17:48,870 --> 00:17:53,239 that they were observing. Thus was born the field of spectroscopy. 250 00:17:53,239 --> 00:17:58,751 And, so as we see, as we seen, observing the line spectrum allows you to identify. 251 00:17:58,751 --> 00:18:03,926 So, you can go over, an expert can go over the spectrum, and identify that this 252 00:18:03,926 --> 00:18:09,532 line and that line corresponds to the wavelengths at which we know Thrice 253 00:18:09,532 --> 00:18:12,680 ionized Iron. Atoms. 254 00:18:12,680 --> 00:18:16,286 Absorb radiation. So, the, degree, the darkness of these 255 00:18:16,286 --> 00:18:20,438 lines, the amount of, absorption, indicates something about the 256 00:18:20,438 --> 00:18:24,521 concentration of, thrice-ionized iron. And so on and so forth. 257 00:18:24,521 --> 00:18:29,761 You can go through the solar spectrum, and identify, all the elements that are 258 00:18:29,761 --> 00:18:32,780 there. And then in 1868 an interesting discovery 259 00:18:32,780 --> 00:18:37,256 is made by Jansen ad Lockyer. independently they look at the spectrum 260 00:18:37,256 --> 00:18:42,228 of sunlight during an eclipse and they discover a line in the yellow, right over 261 00:18:42,228 --> 00:18:46,952 here in this region of the spectrum. And it does not correspond to any known 262 00:18:46,952 --> 00:18:50,449 element. and so after some further checks they did 263 00:18:50,449 --> 00:18:54,136 decide that they've discovered a brand new unknown element. 264 00:18:54,136 --> 00:18:58,385 And since it was discovered in the spectrum of the sun they name it 265 00:18:58,385 --> 00:19:02,446 appropriately helium. yeah, the helium you put in your birthday 266 00:19:02,446 --> 00:19:06,570 balloons was first discovered to exist in the spectrum of the sun. 267 00:19:06,570 --> 00:19:10,570 We'll talk later about why it's so hard to find helium on earth. 268 00:19:10,570 --> 00:19:16,213 But the first indications of the existence of such a substance were in the 269 00:19:16,213 --> 00:19:20,094 spectrum of the Sun. So, observing the line spectrum of an 270 00:19:20,094 --> 00:19:24,372 astronomical object will tell us about it's chemical composition. 271 00:19:24,372 --> 00:19:29,834 And as we shall see a whole lot more. So spectra will be with for a good part 272 00:19:29,834 --> 00:19:33,046 of the class. Understanding why particular atoms 273 00:19:33,046 --> 00:19:38,030 emitted particular wavelengths was an interesting problem, but before that 274 00:19:38,030 --> 00:19:43,215 could be solved a revolution in our understanding of the structure of the 275 00:19:43,215 --> 00:19:46,930 atom had emerged. By this time G.G.Thompson had discovered 276 00:19:46,930 --> 00:19:51,506 that one of the constituents of matter was something he called electrons. 277 00:19:51,506 --> 00:19:55,769 They were responsible for the conduction of electricity in metal. 278 00:19:55,769 --> 00:19:58,778 Hence the name. And they were negatively charged. 279 00:19:58,778 --> 00:20:03,605 And one suspected that an atom being electrically neutral would have some 280 00:20:03,605 --> 00:20:08,620 positive charge and some electrons. And indeed Rutherford in 1909 sets out to 281 00:20:08,620 --> 00:20:12,444 discover this structure with his students Geiger and Marsden. 282 00:20:12,444 --> 00:20:17,396 And what he discovers is astonishing. He discovers that most of the mass of the 283 00:20:17,396 --> 00:20:20,819 atom. Is contained in a positive nucleus whose 284 00:20:20,819 --> 00:20:24,565 size is of the order of ten the minus fifteen meters. 285 00:20:24,565 --> 00:20:30,007 For the sake of comparison, the size of an atom is on the order of ten to the 286 00:20:30,007 --> 00:20:32,127 minus ten meters. So angstrums. 287 00:20:32,127 --> 00:20:37,983 So o, only one hundred thousandth of the radius of an atom, a number you have to 288 00:20:37,983 --> 00:20:42,296 cube list to get the volume, is taken up by most of the mass. 289 00:20:42,296 --> 00:20:46,251 So there's a very tiny, very heavy, very compact nucleus. 290 00:20:46,251 --> 00:20:50,962 And it's surrounded Rutherford understands, by electrons. 291 00:20:50,962 --> 00:20:56,870 The charge of the nucleus is the atomic, is the atomic number of the element 292 00:20:56,870 --> 00:21:01,356 depending on the atom. And there are corresponding number of 293 00:21:01,356 --> 00:21:05,993 negatively charged electrons, so the whole thing is neutral. 294 00:21:05,993 --> 00:21:11,901 And with Rutherford concludes is it the electrons are essentially orbiting the 295 00:21:11,901 --> 00:21:17,734 nucleus in keplerian orbits, which is what gives this large size with the mass 296 00:21:17,734 --> 00:21:23,373 concentrated very tightly in the middle. This is a beautiful example of 297 00:21:23,373 --> 00:21:26,508 universality. The force law between electrons and 298 00:21:26,508 --> 00:21:29,067 protons is Coulomb's law. It's quadratic. 299 00:21:29,067 --> 00:21:33,930 You get exactly the same elliptical orbits that you see in the solar system. 300 00:21:33,930 --> 00:21:37,424 And so, this is the picture of the atom that 301 00:21:37,424 --> 00:21:40,238 we're so familiar with. And then we understand, 302 00:21:40,238 --> 00:21:44,028 once we understand this that atoms can bind chemically by trading, 303 00:21:44,028 --> 00:21:48,219 sharing electrons or deforming the distribution of their electron orbits. 304 00:21:48,219 --> 00:21:51,607 The development of chemistry from this point is very quick. 305 00:21:51,607 --> 00:21:54,880 And chemistry is the science of electronic rearrangement. 306 00:21:54,880 --> 00:21:58,555 What we understand now is why it is that elements are immutable. 307 00:21:58,555 --> 00:22:03,493 The number of carbon atoms that goes into a reaction is always equal to the number 308 00:22:03,493 --> 00:22:08,250 of carbon atoms that emerge. And that is because the nucleus is not 309 00:22:08,250 --> 00:22:11,930 effected. carbon nucleus specifies that this is 310 00:22:11,930 --> 00:22:16,970 going to be a carbon atom, because it has the right the charge, set it out some 311 00:22:16,970 --> 00:22:22,268 where and it will acquire electrons until it is neutral, so nucleus identifies the 312 00:22:22,268 --> 00:22:26,598 chemical structure of the element. And, because the nucleus does not 313 00:22:26,598 --> 00:22:30,927 participate and these electronic rearrangement issues, elements are 314 00:22:30,927 --> 00:22:35,902 immutable and the project of alchemy of converting the element gold into the 315 00:22:35,902 --> 00:22:40,300 element lead or the other way around is completely hopeless. 316 00:22:40,300 --> 00:22:47,422 this is a brilliant and successful picture of the world and Newton's 317 00:22:47,422 --> 00:22:54,070 universe is becoming richer and at the same time better understood. 318 00:22:54,070 --> 00:22:58,930 And there are those who speculate at the end of the nineteenth century that 319 00:22:58,930 --> 00:23:02,782 physics is all about resolved, but there are few negling problems. 320 00:23:02,782 --> 00:23:06,220 One of them that we can understand is this issue of atoms. 321 00:23:06,220 --> 00:23:10,665 So imagine the simplest of all atoms, a hydrogen atom, it has a nucleus with 322 00:23:10,665 --> 00:23:15,347 charge one and one electron orbiting it. This electron is in motion, and in fact 323 00:23:15,347 --> 00:23:17,718 is accelerating. It's moving in a circle. 324 00:23:17,718 --> 00:23:22,460 And an accelerating charge will create changing electric and magnetic fields. 325 00:23:22,460 --> 00:23:26,973 This means it will create radiation. The radiation will carry off energy. 326 00:23:26,973 --> 00:23:31,362 The electron will lose energy. And as we know, you have some particular 327 00:23:31,362 --> 00:23:34,183 ener-, amount of energy determines your orbit. 328 00:23:34,183 --> 00:23:37,568 As you lose energy, you fall to lower and lower orbits. 329 00:23:37,568 --> 00:23:42,520 So, what you expect the, electron to do is just spiral in towards the nucleus 330 00:23:42,520 --> 00:23:47,097 while continuously emitting radiation. Atoms obviously are observed to be 331 00:23:47,097 --> 00:23:49,981 stable. And the stability of the atom is a big 332 00:23:49,981 --> 00:23:53,216 riddle. Similarly, why is it that atoms only emit 333 00:23:53,216 --> 00:23:57,582 at discrete frequencies? You can easily imagine that an electron 334 00:23:57,582 --> 00:24:01,401 revolving around an atom would radiate at the frequency. 335 00:24:01,401 --> 00:24:06,653 The periodic nature of the radiation would be related to the periodic nature 336 00:24:06,653 --> 00:24:10,064 of the motion. But Keplerian orbit as we know, exist at 337 00:24:10,064 --> 00:24:13,406 any radius. And given a radius, you can figure out 338 00:24:13,406 --> 00:24:19,068 the frequency from P^2 = KA^3. And so, since you can orbit at any 339 00:24:19,068 --> 00:24:24,307 radius, you can orbit at any frequency. And therefore you will atoms to be able 340 00:24:24,307 --> 00:24:28,874 to emit radiation at all wavelengths. What is this, this discrete line 341 00:24:28,874 --> 00:24:31,735 spectrum? And then there is some experimental 342 00:24:31,735 --> 00:24:34,629 puzzles. These are sort of theoretical thought 343 00:24:34,629 --> 00:24:37,587 puzzles. Their experimental situations in which 344 00:24:37,587 --> 00:24:40,292 light is observed a particle like behavior. 345 00:24:40,292 --> 00:24:44,634 Remember Newton said light was a particle, and it was one of the rare 346 00:24:44,634 --> 00:24:48,410 times he was wrong, but not quite. And so this is first 347 00:24:48,410 --> 00:24:53,951 conjectured by Plack in 1900 to explain some details of the shape of a black body 348 00:24:53,951 --> 00:24:57,262 spectrum. And then by Einstein in 1905, to explain 349 00:24:57,262 --> 00:25:01,655 the photo electric effect. And the picture that emerges is that a 350 00:25:01,655 --> 00:25:06,520 beam of light can be thought of under some circumstances as a stream of 351 00:25:06,520 --> 00:25:10,170 particles and if the light wave has frequency f, 352 00:25:10,170 --> 00:25:15,030 then, each of those particles carries an energy which is proportional to the 353 00:25:15,030 --> 00:25:19,762 frequency f and the constant of proportionality this object h is known as 354 00:25:19,762 --> 00:25:24,750 Planck's constant, and it has units of course of energy per frequency or energy 355 00:25:24,750 --> 00:25:28,650 times time and it's a very small amount of energy times time. 356 00:25:28,650 --> 00:25:33,811 So, h is a very small number means that a beam with a Nontrivial flux of energy 357 00:25:33,811 --> 00:25:38,923 contains huge numbers of these photons, as these light particles are called. 358 00:25:38,923 --> 00:25:43,966 And, because there are so many of them, the fact that at any given moment a 359 00:25:43,966 --> 00:25:48,191 particle is or isn't impinging on the detector doesn't happen. 360 00:25:48,191 --> 00:25:53,371 But, if you have a beam of very low power, then this quantization as Einstein 361 00:25:53,371 --> 00:25:58,959 calls it, the fact that the energy of beam is carried in discrete packets might 362 00:25:58,959 --> 00:26:01,760 become apparent. And to complicate things. 363 00:26:01,760 --> 00:26:06,753 So we have this object that has been observed to be a, li, wave, because 364 00:26:06,753 --> 00:26:11,561 [INAUDIBLE] that light undergoes interference exhibiting some particle 365 00:26:11,561 --> 00:26:14,885 properties. And then in 1927, Davison and Germer in 366 00:26:14,885 --> 00:26:20,136 the US, do an experiment in which they basically observe that electrons exhibit 367 00:26:20,136 --> 00:26:23,726 interference. Electrons manifest the particles, exhibit 368 00:26:23,726 --> 00:26:28,246 some of the properties that we set with a hallmark of wave behavior. 369 00:26:28,246 --> 00:26:32,700 So there's this weird duality emerging between waves and particles. 370 00:26:32,700 --> 00:26:38,084 What is a particle sometimes.behaves like a wave, a wave sometimes behaves like a 371 00:26:38,084 --> 00:26:42,139 collection of particles. And all of this is resolved over the 372 00:26:42,139 --> 00:26:48,275 course of the teens and twenties of the twentieth Century, by a beautiful and to 373 00:26:48,275 --> 00:26:53,540 this day somewhat puzzling theory called Quantum Mechanics, 374 00:26:53,540 --> 00:26:58,190 Which leads to a complete revolution in our understanding of nature. 375 00:26:58,190 --> 00:27:02,841 This is the first time that we go way beyond anything Newton could have 376 00:27:02,841 --> 00:27:06,730 imagined, let alone written down. and this is, 377 00:27:06,730 --> 00:27:11,579 modern physics, as we call it, twentieth century physics, and in quantum mechanic 378 00:27:11,579 --> 00:27:16,073 particles, all the states of a particle, rather than being described by their 379 00:27:16,073 --> 00:27:20,450 positions at velocities, are described by something called a wave function. 380 00:27:20,450 --> 00:27:25,121 and this wave function has the, the property that its value at any position 381 00:27:25,121 --> 00:27:29,912 in space at any given time predicts the probability of finding the particle the 382 00:27:29,912 --> 00:27:34,463 probability density technically of finding the particle at that point of in 383 00:27:34,463 --> 00:27:39,254 space at that particular time and notice I said probability and I said state so 384 00:27:39,254 --> 00:27:43,866 the full state of the universe only predicts the probabilities for particles 385 00:27:43,866 --> 00:27:48,597 to be here there or anywhere else, there are not definitive predictions its not 386 00:27:48,597 --> 00:27:52,670 that our ignorance prevents us from knowing it in quantum mechanics. 387 00:27:52,670 --> 00:27:57,760 The Universe does not know where a particle is, and yet the 388 00:27:57,760 --> 00:28:03,726 deterministic evolution, that was so, satisfactory, about Newtonian mechanics, 389 00:28:03,726 --> 00:28:09,619 is in some, deep sense retained here, in the sense that the evolution of the wave 390 00:28:09,619 --> 00:28:12,860 function itself, is, completely deterministic. 391 00:28:12,860 --> 00:28:17,787 the results of measurements however, can only be predicted with probability. 392 00:28:17,787 --> 00:28:22,840 Again, when the numbers of particles are on the order of a boule, then the law of 393 00:28:22,840 --> 00:28:27,325 large numbers guarantees that these distributions will be very sharply 394 00:28:27,325 --> 00:28:30,357 peaked. And the probability that, I am not here 395 00:28:30,357 --> 00:28:34,842 right now but some where else, is exceeding the low and I don't need to 396 00:28:34,842 --> 00:28:38,780 worry about it. Now associated to this, a particle as a, 397 00:28:38,780 --> 00:28:43,480 to a particle is associated to a wave, this wave has a wave length. 398 00:28:43,480 --> 00:28:47,468 The wave length is determined by the particles momentum. 399 00:28:47,468 --> 00:28:51,100 And again that Planck's Constant thing shows up 400 00:28:51,100 --> 00:28:56,601 The wavelength is related to the momentum by this relation lambda h / p. 401 00:28:56,601 --> 00:29:02,396 So again h is a very microscopic number, macroscopic values of momentum lead to 402 00:29:02,396 --> 00:29:08,558 negligible wavelength and therefore the wave behavior of a macroscopic object is 403 00:29:08,558 --> 00:29:14,500 completely negligible and you won't see it only microsco macroscopic distance 404 00:29:14,500 --> 00:29:17,801 scales can you observe real quantum behavior. 405 00:29:17,801 --> 00:29:23,449 Now, we won't have time to discuss either the nature of this beautiful theory, 406 00:29:23,449 --> 00:29:25,849 sadly. Or all of its consequences. 407 00:29:25,849 --> 00:29:31,800 But a few that are important to us, first I said this resolves the issue of the 408 00:29:31,800 --> 00:29:36,172 Discreet spectrum. Indeed solving the equation for this wave 409 00:29:36,172 --> 00:29:41,929 function for electrons in an atom, you find that electrons can only occupy a 410 00:29:41,929 --> 00:29:46,957 discreet set of energy levels. The energy of an electron can be, in an 411 00:29:46,957 --> 00:29:49,945 atom, can be one of a few discreet values. 412 00:29:49,945 --> 00:29:55,775 And in a hydrogen atom, for example, this is the form that these energy levels 413 00:29:55,775 --> 00:30:00,512 take, K is constant, and the energies are of course negative. 414 00:30:00,512 --> 00:30:05,528 These are all bound states, and The energy levels are some constant 415 00:30:05,528 --> 00:30:08,913 divided by n^2 where n can be one, two etc. 416 00:30:08,913 --> 00:30:13,638 So, one is the lowest energy. And as n gets bigger, you get states of 417 00:30:13,638 --> 00:30:18,010 larger and larger energies tending to zero as n becomes large. 418 00:30:18,010 --> 00:30:23,511 Then, the point is that the dominant interaction between an atom and radiation 419 00:30:23,511 --> 00:30:26,966 is the emission or absorption of a single photon. 420 00:30:26,966 --> 00:30:30,197 One atom emits one photon. One light particle. 421 00:30:30,197 --> 00:30:35,565 And at the same time the electron jumps. Undergoes what we call a quantum 422 00:30:35,565 --> 00:30:40,933 transition between energy levels. And then energy conservation guarantees 423 00:30:40,933 --> 00:30:46,889 that for example if a photon is emitted while jumping from level N to level M in 424 00:30:46,889 --> 00:30:50,272 which case the energy N must be bigger than M. 425 00:30:50,272 --> 00:30:52,806 Then. Energy conservation says, the energy 426 00:30:52,806 --> 00:30:57,560 taken away by the photon, which is HF, is the difference between the initial and 427 00:30:57,560 --> 00:31:00,749 final energy. The energy lost by the atom is equal to 428 00:31:00,749 --> 00:31:04,480 the energy takem away by the photon and plugging in our value. 429 00:31:04,480 --> 00:31:08,819 We get this answer. And indeed these frequencies, you can 430 00:31:08,819 --> 00:31:14,190 convert them to wavelengths, are observed in the spectrum of the hydrogen atom, for 431 00:31:14,190 --> 00:31:17,202 example. And so the, the discreet energy levels 432 00:31:17,202 --> 00:31:21,983 are very nicely explained by this and many other phenomena are explained. 433 00:31:21,983 --> 00:31:26,502 As, one outcome of this that is very crucially important to us, is the Pauli 434 00:31:26,502 --> 00:31:30,534 exclusion principle. Pauli exclusion principle states that 435 00:31:30,534 --> 00:31:34,190 electrons are a kind of particle later termed fermions. 436 00:31:34,190 --> 00:31:38,916 And it tells us that at most two electrons can occupy a given energy level 437 00:31:38,916 --> 00:31:42,572 or a given state. And for those who like to think about 438 00:31:42,572 --> 00:31:47,235 these things, electrons have spin, they can have two different spins states. 439 00:31:47,235 --> 00:31:52,466 One electron can actually occupy a given state but that state information includes 440 00:31:52,466 --> 00:31:57,760 which of the two spin states it's in. the fact that electrons cannot be 441 00:31:57,760 --> 00:32:02,794 compressed and you can not have more than one electron in a given state explains 442 00:32:02,794 --> 00:32:06,151 many things. It explains the structure of the periodic 443 00:32:06,151 --> 00:32:11,061 table, and all the regularities that Mendeleev had found in the chemistry of 444 00:32:11,061 --> 00:32:15,412 elements in similar positions in the period table are explained by 445 00:32:15,412 --> 00:32:20,136 understanding the structure of energy levels, and pairing it with this Pauli 446 00:32:20,136 --> 00:32:23,679 exclusion principle. It also explains why when I slam the 447 00:32:23,679 --> 00:32:27,039 table with my hand. My hand doesn't go through the table. 448 00:32:27,039 --> 00:32:29,807 remember that my hand is mostly empty space. 449 00:32:29,807 --> 00:32:32,339 Each atom of my hand is mostly empty space. 450 00:32:32,339 --> 00:32:35,932 So it's not that there's literally a collision between atoms. 451 00:32:35,932 --> 00:32:40,644 Now, what's really going on, is that both in my hand and in the table, all the low 452 00:32:40,644 --> 00:32:45,156 lying energy levels are filled. In order to take a mole of electrons from 453 00:32:45,156 --> 00:32:50,080 my hand and mix them into a mole of electrons that are the local part of the 454 00:32:50,080 --> 00:32:54,621 table, you need to excite a mole of electrons to slightly higher energy 455 00:32:54,621 --> 00:32:59,162 levels that are not yet occupied. Per electron that's not lot of energy, 456 00:32:59,162 --> 00:33:04,127 but a mole is ten to the 23 electrons, is a lot of electrons It takes a lot of 457 00:33:04,127 --> 00:33:09,516 energy to excite so many electrons to the next energy level and if I hit the table 458 00:33:09,516 --> 00:33:14,279 hard enough, it generates enough energy to excite a mole of electrons to the 459 00:33:14,279 --> 00:33:18,101 requisite energy level. Then I've exerted so much energy that 460 00:33:18,101 --> 00:33:23,052 either the chemical bonds in my hand or in the table will break and one of the 461 00:33:23,052 --> 00:33:26,060 two objects will just fall apart rather than 462 00:33:26,060 --> 00:33:30,187 moving right through each other. So this Pauli exclusion principle 463 00:33:30,187 --> 00:33:33,236 explains many, much of our day to day experience. 464 00:33:33,236 --> 00:33:37,554 It'll also become very important in understanding some phenomena in 465 00:33:37,554 --> 00:33:40,780 astrophysics. Whew. 466 00:33:40,780 --> 00:33:47,360 That was a busy week. we have found a ton of new science and we 467 00:33:47,360 --> 00:33:51,469 have come a long way since Newton not to mention Aristotle. 468 00:33:51,469 --> 00:33:57,250 There are many phenomenon's both on earth and off of it that we understand and the 469 00:33:57,250 --> 00:34:01,637 main tool that allows us to be so insightful is that atoms are 470 00:34:01,637 --> 00:34:07,209 fundamentally the same wherever you go. The behavior of a hydrogen atom on earth 471 00:34:07,209 --> 00:34:12,780 right here is indistinguishable from the behavior of a hydrogen atom out in the 472 00:34:12,780 --> 00:34:17,355 crab nebula or inside the sun. There may be physical circumstances that 473 00:34:17,355 --> 00:34:21,417 are different in the Sun. But if we can emulate those circumstances 474 00:34:21,417 --> 00:34:25,175 hydrogen atoms or hydrogen atoms, helium atoms or helium atoms. 475 00:34:25,175 --> 00:34:29,843 The laws of Physics are the same here, there and everywhere and so these laws 476 00:34:29,843 --> 00:34:34,495 that we have discovered by measuring things in labs on Earth can be and are 477 00:34:34,495 --> 00:34:37,449 applied to the way things behave in the heavens. 478 00:34:37,449 --> 00:34:42,433 Remember we said that we are going to do our Aristotle one better by looking for 479 00:34:42,433 --> 00:34:45,633 laws that are valid on heavens as they are on Earth. 480 00:34:45,633 --> 00:34:49,480 And indeed, these are the laws that we are going to find. 481 00:34:49,480 --> 00:34:52,436 There's a satisfaction in understanding all these things. 482 00:34:52,436 --> 00:34:56,585 And I hope that you will take away from this discussion a new way of looking at 483 00:34:56,585 --> 00:35:00,268 things you see here on Earth. But the purpose of this class was to talk 484 00:35:00,268 --> 00:35:03,017 about things away from Earth, and we're finally ready. 485 00:35:03,017 --> 00:35:06,699 When we come back next week, we will start to take all this amazing new 486 00:35:06,699 --> 00:35:10,278 arsenal of tools we've developed, and apply it to actual astronomical 487 00:35:10,278 --> 00:35:12,612 phenomena. In the meantime, get some good rest. 488 00:35:12,612 --> 00:35:14,272 You've have certainly earned it.