1 00:00:00,500 --> 00:00:01,952 [SQUEAKING] 2 00:00:01,952 --> 00:00:03,904 [RUSTLING] 3 00:00:03,904 --> 00:00:07,808 [CLICKING] 4 00:00:16,129 --> 00:00:19,070 PROFESSOR: Today, we're moving on, 5 00:00:19,070 --> 00:00:21,590 and we're moving into what's really 6 00:00:21,590 --> 00:00:24,470 happening with those electrons. 7 00:00:24,470 --> 00:00:31,820 And I framed this on Monday by telling you that the Rutherford 8 00:00:31,820 --> 00:00:35,270 atom wasn't going to make it more than 10 9 00:00:35,270 --> 00:00:40,962 to the minus 11 seconds-ish because classical E&M would 10 00:00:40,962 --> 00:00:43,420 tell you that the electron, if it's going around like this, 11 00:00:43,420 --> 00:00:47,200 is radiating energy, and so it spirals down 12 00:00:47,200 --> 00:00:50,210 into that positively charged nucleus. 13 00:00:50,210 --> 00:00:52,790 So Rutherford got it right in the sense 14 00:00:52,790 --> 00:00:59,270 that you got all this positive charge concentrated in this one 15 00:00:59,270 --> 00:01:00,800 tiny little volume in the middle, 16 00:01:00,800 --> 00:01:02,300 and the electrons are way out there. 17 00:01:02,300 --> 00:01:03,890 That's the planetary model. 18 00:01:03,890 --> 00:01:06,460 But we needed some new theory to understand 19 00:01:06,460 --> 00:01:08,210 why the whole thing was stable, and that's 20 00:01:08,210 --> 00:01:11,930 where Bohr comes along, and that's what we're 21 00:01:11,930 --> 00:01:13,980 going to talk about today. 22 00:01:13,980 --> 00:01:21,580 Now, we need to feel our oneness with waves. 23 00:01:21,580 --> 00:01:26,220 Now, I think probably most of about waves, but since we're 24 00:01:26,220 --> 00:01:28,390 going to be talking about them a whole lot today 25 00:01:28,390 --> 00:01:30,515 and as we go forward, I want to make sure we're all 26 00:01:30,515 --> 00:01:31,510 on the same page. 27 00:01:31,510 --> 00:01:32,547 So here's a wave. 28 00:01:32,547 --> 00:01:33,880 Well, we know about water waves. 29 00:01:33,880 --> 00:01:35,005 They move a meter a second. 30 00:01:35,005 --> 00:01:36,880 Sound waves a little faster, right? 31 00:01:36,880 --> 00:01:39,070 And you've got these characteristics of a wave-- 32 00:01:39,070 --> 00:01:43,840 the frequency of the wave, the wavelength. 33 00:01:43,840 --> 00:01:46,330 And so I just want to make sure that we're all together 34 00:01:46,330 --> 00:01:51,710 on this because we're going to be talking 35 00:01:51,710 --> 00:01:53,300 about these variables a lot. 36 00:01:53,300 --> 00:01:58,640 So if you have a wavelength, that might be in meters. 37 00:01:58,640 --> 00:02:02,442 How many meters do you have per wave? 38 00:02:02,442 --> 00:02:03,650 We're getting somewhere here. 39 00:02:03,650 --> 00:02:06,830 If you have the frequency-- and I'll use this notation here. 40 00:02:06,830 --> 00:02:07,847 You can use f. 41 00:02:07,847 --> 00:02:08,930 You might see f sometimes. 42 00:02:08,930 --> 00:02:09,920 I like using nu. 43 00:02:09,920 --> 00:02:11,840 And if you have the frequency, well, that's 44 00:02:11,840 --> 00:02:18,140 going to be the number of waves per second, for example. 45 00:02:18,140 --> 00:02:24,090 And so the speed is going to be the two of them multiplied 46 00:02:24,090 --> 00:02:24,590 together. 47 00:02:24,590 --> 00:02:26,215 And I know a lot of you have seen this, 48 00:02:26,215 --> 00:02:28,110 but again, I want to get it up here. 49 00:02:28,110 --> 00:02:30,920 So it's going to be meters per second 50 00:02:30,920 --> 00:02:35,280 if these are the units that I'm using, seconds and meters. 51 00:02:35,280 --> 00:02:38,290 Now, if you're light-- 52 00:02:38,290 --> 00:02:39,970 light as in light-- 53 00:02:39,970 --> 00:02:43,400 then you have a speed that is a constant in vacuum, 54 00:02:43,400 --> 00:02:44,890 and we know that. 55 00:02:44,890 --> 00:02:46,930 So the speed of light-- 56 00:02:46,930 --> 00:02:49,710 so for light, let's put that right underneath. 57 00:02:49,710 --> 00:03:01,290 For light, the speed is c, which equals 3 times 10 58 00:03:01,290 --> 00:03:03,600 to the eighth meters per second. 59 00:03:03,600 --> 00:03:05,380 OK, just getting to some good stuff. 60 00:03:05,380 --> 00:03:10,320 So if I wanted to know, for example, how 61 00:03:10,320 --> 00:03:12,360 to go back and forth between frequency 62 00:03:12,360 --> 00:03:15,330 and wavelength for light, well, I 63 00:03:15,330 --> 00:03:18,000 can just use this relationship. 64 00:03:18,000 --> 00:03:19,530 So let's put an example up there. 65 00:03:26,610 --> 00:03:33,160 So for example, if you're red light, so if you're red light, 66 00:03:33,160 --> 00:03:38,920 then you might have a frequency of around, let's say, 450. 67 00:03:38,920 --> 00:03:45,420 There's a range, but 450 terahertz would be a frequency. 68 00:03:45,420 --> 00:03:47,100 And so now I can get the wavelength 69 00:03:47,100 --> 00:03:48,640 because I have that relationship. 70 00:03:48,640 --> 00:03:50,400 So the wavelength for red light is 71 00:03:50,400 --> 00:03:58,650 c over nu, which is going to be equal to 3 times 10 72 00:03:58,650 --> 00:04:07,500 to the eighth meters per second divided by 450 times 10 73 00:04:07,500 --> 00:04:09,990 to the 12th per second, right? 74 00:04:09,990 --> 00:04:13,590 That's the measurement of hertz is 1 over seconds, right? 75 00:04:13,590 --> 00:04:15,440 That's frequency, 1 over seconds. 76 00:04:18,180 --> 00:04:21,670 That gives me a number that seems like it's pretty small, 77 00:04:21,670 --> 00:04:30,300 0.000000667 meters. 78 00:04:30,300 --> 00:04:32,460 And so we could use a different unit 79 00:04:32,460 --> 00:04:36,840 like nanometers, which is just 10 to the minus ninth. 80 00:04:36,840 --> 00:04:42,450 So we could call that the wavelength of red light, 667 81 00:04:42,450 --> 00:04:42,990 nanometers. 82 00:04:42,990 --> 00:04:46,027 Now, I'm doing this all slowly and carefully because we're 83 00:04:46,027 --> 00:04:47,610 going to be doing this a lot, and so I 84 00:04:47,610 --> 00:04:50,220 want to make sure that you're comfortable with this. 85 00:04:50,220 --> 00:04:54,540 And we're going to add something to this in just a minute. 86 00:04:54,540 --> 00:04:56,628 If I was blue light-- 87 00:04:56,628 --> 00:04:57,420 where's blue light? 88 00:04:57,420 --> 00:04:58,337 Let's put blue light-- 89 00:04:58,337 --> 00:05:00,600 I'm going to leave red light here. 90 00:05:00,600 --> 00:05:04,680 And we'll put blue light right above it 91 00:05:04,680 --> 00:05:07,290 so that you can see them together. 92 00:05:07,290 --> 00:05:12,090 So blue might be something like, oh, 93 00:05:12,090 --> 00:05:17,310 a frequency of 650 terahertz, so higher frequency. 94 00:05:17,310 --> 00:05:20,340 And that would give you a wavelength of something 95 00:05:20,340 --> 00:05:23,923 like 460 nanometers. 96 00:05:23,923 --> 00:05:25,590 I'm putting these both here because I'll 97 00:05:25,590 --> 00:05:31,650 be comparing other aspects of these colors later. 98 00:05:31,650 --> 00:05:33,180 Now comes back-- no. 99 00:05:33,180 --> 00:05:35,580 That's our oneness moment with waves and light, 100 00:05:35,580 --> 00:05:37,530 and now we come back to our story, 101 00:05:37,530 --> 00:05:41,640 our detective story of what's happening inside of atoms, 102 00:05:41,640 --> 00:05:43,840 and it really requires us to go back. 103 00:05:43,840 --> 00:05:49,620 I said Bohr had some postulates about quantization. 104 00:05:49,620 --> 00:05:53,760 There was work going on at the time already related 105 00:05:53,760 --> 00:05:54,810 to quantization. 106 00:05:57,470 --> 00:05:59,880 So I want to share with you that work 107 00:05:59,880 --> 00:06:02,850 because it's what inspired Bohr, and then we'll 108 00:06:02,850 --> 00:06:03,870 do the Bohr model. 109 00:06:03,870 --> 00:06:06,420 But also just I want to get you thinking about what this 110 00:06:06,420 --> 00:06:07,980 all means. 111 00:06:07,980 --> 00:06:09,840 So if you think about music, you can think 112 00:06:09,840 --> 00:06:11,098 about these two instruments. 113 00:06:11,098 --> 00:06:13,140 This might feel like-- the violin might feel like 114 00:06:13,140 --> 00:06:15,750 something where you can just play continuous notes, 115 00:06:15,750 --> 00:06:18,670 whereas here you can't. 116 00:06:18,670 --> 00:06:20,410 It's discrete. 117 00:06:20,410 --> 00:06:23,380 I can't play any notes in between. 118 00:06:23,380 --> 00:06:24,780 Something is discrete. 119 00:06:24,780 --> 00:06:26,750 It's quantized. 120 00:06:26,750 --> 00:06:28,460 Well, that's pretty obvious. 121 00:06:28,460 --> 00:06:29,210 You look at those. 122 00:06:29,210 --> 00:06:31,000 You're like, OK, that makes sense. 123 00:06:31,000 --> 00:06:33,260 There's some things that aren't as obvious, like here. 124 00:06:33,260 --> 00:06:35,800 Oh, notice what's in the calendar. 125 00:06:35,800 --> 00:06:36,590 That's a screen. 126 00:06:36,590 --> 00:06:42,460 Now a screen from far enough away might not look quantized, 127 00:06:42,460 --> 00:06:47,470 but then when you look at it closely, it is. 128 00:06:47,470 --> 00:06:48,710 It's pixels. 129 00:06:48,710 --> 00:06:50,860 There's nothing in between. 130 00:06:50,860 --> 00:06:53,630 There's nothing in between. 131 00:06:53,630 --> 00:06:57,980 The thing is that at the time, people thought about the world 132 00:06:57,980 --> 00:07:00,500 in a certain way. 133 00:07:00,500 --> 00:07:02,780 There's some things where it's just obvious they're 134 00:07:02,780 --> 00:07:07,328 violins like light. 135 00:07:07,328 --> 00:07:08,870 And then they're like, wait a second. 136 00:07:08,870 --> 00:07:12,280 These things are acting like xylophones. 137 00:07:12,280 --> 00:07:14,980 What's going on? 138 00:07:14,980 --> 00:07:17,890 So Planck's contribution was really-- 139 00:07:17,890 --> 00:07:21,010 he was one of the first kind of deep thinkers 140 00:07:21,010 --> 00:07:27,140 to talk about quantization, and it was quantization of light. 141 00:07:27,140 --> 00:07:29,700 It was quantization of light. 142 00:07:29,700 --> 00:07:33,340 And so what he said-- and this is together with Einstein, 143 00:07:33,340 --> 00:07:35,340 and I'll show you what Einstein did in a minute. 144 00:07:35,340 --> 00:07:39,050 So it's called the Planck-Einstein relation. 145 00:07:39,050 --> 00:07:42,960 And what he said is that the energy of a photon-- 146 00:07:42,960 --> 00:07:47,430 so Planck-- why did I just go all caps? 147 00:07:47,430 --> 00:07:49,410 I don't know. 148 00:07:49,410 --> 00:07:51,360 I don't know. 149 00:07:51,360 --> 00:07:55,950 There's a reason, Planck-Einstein. 150 00:07:55,950 --> 00:08:02,100 They said that the energy for light-- the energy 151 00:08:02,100 --> 00:08:08,400 is related to the frequency through a constant. 152 00:08:08,400 --> 00:08:16,470 And so in particular, E equals h times the frequency. 153 00:08:16,470 --> 00:08:18,820 Now, this was revolutionary. 154 00:08:18,820 --> 00:08:20,980 It might just look like a simple relationship. 155 00:08:20,980 --> 00:08:24,520 Oh, and by the way, this is a constant 156 00:08:24,520 --> 00:08:28,650 named Planck's constant. 157 00:08:28,650 --> 00:08:30,790 I'm going lowercase-- 158 00:08:30,790 --> 00:08:32,049 Planck's constant. 159 00:08:32,049 --> 00:08:35,380 And, like other constants, it has 160 00:08:35,380 --> 00:08:38,320 a value that doesn't change. 161 00:08:38,320 --> 00:08:41,260 So that value for Planck's constant is in-- 162 00:08:41,260 --> 00:08:43,010 I'll give it to you in two different units 163 00:08:43,010 --> 00:08:46,090 so we have it up here, 6.26-- 164 00:08:46,090 --> 00:08:48,670 no-- 6.62-- sorry-- 165 00:08:48,670 --> 00:08:55,990 6.626 times 10 to the minus 34 joules-second. 166 00:08:58,620 --> 00:09:05,130 Or it's also equal to 4.136 times 10 167 00:09:05,130 --> 00:09:09,360 to the minus 15th electronvolt-seconds. 168 00:09:09,360 --> 00:09:14,310 Notice the units are in energy times time, Planck's constant. 169 00:09:17,610 --> 00:09:20,790 And you can see that it must be because this is energy 170 00:09:20,790 --> 00:09:24,210 and this is 1 over time, the frequency. 171 00:09:24,210 --> 00:09:27,810 So it's got to have those units for that to work. 172 00:09:27,810 --> 00:09:31,830 But this-- did I make a mistake? 173 00:09:31,830 --> 00:09:32,330 I'm worried. 174 00:09:32,330 --> 00:09:33,978 The dates are still hitting me hard. 175 00:09:33,978 --> 00:09:36,020 I'm still thinking about that, having nightmares. 176 00:09:36,020 --> 00:09:38,560 100 years off, 90 years off. 177 00:09:38,560 --> 00:09:40,160 I'm good. 178 00:09:40,160 --> 00:09:51,290 So what they saw is that light had a frequency, 179 00:09:51,290 --> 00:09:56,360 but it also had somehow this unit of energy, 180 00:09:56,360 --> 00:10:01,970 a unit, a discrete unit of energy 181 00:10:01,970 --> 00:10:04,715 that you can now calculate using Planck's constant. 182 00:10:07,250 --> 00:10:08,540 And that was revolutionary. 183 00:10:08,540 --> 00:10:10,850 That was not what people thought. 184 00:10:10,850 --> 00:10:14,550 And it really all came home in what Einstein did, 185 00:10:14,550 --> 00:10:17,210 which was the experiments that he 186 00:10:17,210 --> 00:10:19,400 won the Nobel Prize for-- his deeper thinking 187 00:10:19,400 --> 00:10:21,650 was in relativity, but he won the Nobel Prize for this 188 00:10:21,650 --> 00:10:27,880 because it was absolutely essential to further 189 00:10:27,880 --> 00:10:33,520 this idea of quantization and show it with an experiment. 190 00:10:33,520 --> 00:10:35,160 And because it was so important, I 191 00:10:35,160 --> 00:10:39,160 want to share that experiment because when Einstein did 192 00:10:39,160 --> 00:10:40,870 was really quite amazing. 193 00:10:40,870 --> 00:10:45,310 He shined light on a metal, and what he saw-- 194 00:10:45,310 --> 00:10:49,210 so this is called the photoelectric effect-- 195 00:10:49,210 --> 00:10:54,290 photoelectric effect. 196 00:10:54,290 --> 00:11:01,840 And this is where you take a piece of metal- 197 00:11:01,840 --> 00:11:05,800 and they knew there were electrons in there, right? 198 00:11:05,800 --> 00:11:07,397 That discovery had happened. 199 00:11:07,397 --> 00:11:08,980 So they knew there were electrons in-- 200 00:11:08,980 --> 00:11:11,188 and they also knew if you hit this metal with energy, 201 00:11:11,188 --> 00:11:12,970 the electrons could come off. 202 00:11:12,970 --> 00:11:17,410 I mean, after all, that's what the cathode ray tube was. 203 00:11:17,410 --> 00:11:21,990 It was electrons coming off of a piece of metal. 204 00:11:21,990 --> 00:11:24,250 And in that experiment, you hook up a voltage, 205 00:11:24,250 --> 00:11:26,630 but here he shined light. 206 00:11:26,630 --> 00:11:31,780 And so if you take, for example, different frequencies of light 207 00:11:31,780 --> 00:11:34,540 and you shine them on this same piece of metal-- so let's 208 00:11:34,540 --> 00:11:41,050 go red and then let's go green and then let's go blue. 209 00:11:45,800 --> 00:11:50,890 Now, if you shine red light on the metal, nothing happened. 210 00:11:50,890 --> 00:11:53,250 Nothing happened. 211 00:11:53,250 --> 00:11:55,107 But OK, we know if you just crank up 212 00:11:55,107 --> 00:11:57,440 the intensity of the light, something's got to come off. 213 00:11:57,440 --> 00:11:59,220 You're putting all this energy-- 214 00:11:59,220 --> 00:12:00,690 no. 215 00:12:00,690 --> 00:12:01,190 Why? 216 00:12:01,190 --> 00:12:06,260 Because the particles, the packets, the quantized amounts 217 00:12:06,260 --> 00:12:09,170 of energy that that kind of light can have 218 00:12:09,170 --> 00:12:12,330 is determined here. 219 00:12:12,330 --> 00:12:14,420 So what Einstein says is, well, OK, then these 220 00:12:14,420 --> 00:12:17,090 must be particles. 221 00:12:17,090 --> 00:12:19,370 They must have some energy associated 222 00:12:19,370 --> 00:12:23,990 with a particle that follows this relationship equals h nu. 223 00:12:23,990 --> 00:12:26,600 And notice that doesn't depend on intensity. 224 00:12:26,600 --> 00:12:28,960 It just depends on frequency. 225 00:12:28,960 --> 00:12:31,590 So I might be hitting this metal with more and more of them, 226 00:12:31,590 --> 00:12:34,550 but each one only has the same amount of energy 227 00:12:34,550 --> 00:12:37,350 limited by that relationship. 228 00:12:37,350 --> 00:12:40,690 So if I want to hit those electrons with more energy, 229 00:12:40,690 --> 00:12:43,720 I've got to change the frequency. 230 00:12:43,720 --> 00:12:45,740 And so what was found in this experiment 231 00:12:45,740 --> 00:12:48,810 is that, well, maybe here you get nothing. 232 00:12:48,810 --> 00:12:51,170 So here you get nothing. 233 00:12:51,170 --> 00:12:53,480 How am I going to write that? 234 00:12:53,480 --> 00:12:54,410 OK, nothing. 235 00:12:54,410 --> 00:12:55,970 I just won't write it. 236 00:12:55,970 --> 00:12:59,270 Here, maybe you get electrons. 237 00:12:59,270 --> 00:13:07,400 And here, maybe you get faster electrons 238 00:13:07,400 --> 00:13:12,530 because these fundamental particles of energy of light 239 00:13:12,530 --> 00:13:14,870 have different energies, right? 240 00:13:14,870 --> 00:13:17,360 So now we can calculate it. 241 00:13:17,360 --> 00:13:21,560 We can calculate the energy of that red light, 242 00:13:21,560 --> 00:13:23,600 and we calculate the energy of the blue light 243 00:13:23,600 --> 00:13:28,610 because I have now E equals h nu. 244 00:13:28,610 --> 00:13:31,010 And if I plug it in, which I won't do, 245 00:13:31,010 --> 00:13:34,490 you get something like 1.8 electronvolts. 246 00:13:34,490 --> 00:13:38,480 And if you do the same thing for blue, 247 00:13:38,480 --> 00:13:40,190 from the Planck-Einstein relation 248 00:13:40,190 --> 00:13:46,190 you get the energy is 2.7 electronvolts. 249 00:13:46,190 --> 00:13:51,140 So what Einstein did in this experiment which was so crucial 250 00:13:51,140 --> 00:13:54,170 is he measured. 251 00:13:54,170 --> 00:13:55,970 He changed the frequency of light 252 00:13:55,970 --> 00:13:58,550 that you shine on this metal, and what 253 00:13:58,550 --> 00:14:00,896 he saw is that there was nothing, nothing, nothing, 254 00:14:00,896 --> 00:14:01,640 nothing. 255 00:14:01,640 --> 00:14:04,340 And then all of a sudden you literally had, 256 00:14:04,340 --> 00:14:08,280 if you plot the kinetic energy of the-- 257 00:14:08,280 --> 00:14:09,590 I'll write it out here-- 258 00:14:09,590 --> 00:14:15,495 ejected electron-- so that's what's being plotted there. 259 00:14:18,110 --> 00:14:19,825 You plot that versus the-- 260 00:14:19,825 --> 00:14:21,200 I said it wasn't going to use f-- 261 00:14:21,200 --> 00:14:23,540 versus the frequency of the light, nothing, nothing, 262 00:14:23,540 --> 00:14:24,040 nothing. 263 00:14:24,040 --> 00:14:26,600 And then all of a sudden there's a linear relationship 264 00:14:26,600 --> 00:14:28,670 between them. 265 00:14:28,670 --> 00:14:31,190 That explains it because these things 266 00:14:31,190 --> 00:14:36,650 were made of these particles that were called photons. 267 00:14:36,650 --> 00:14:38,045 So photons. 268 00:14:42,260 --> 00:14:45,950 Now, while this was blowing their minds 269 00:14:45,950 --> 00:14:48,690 and winning prizes and all that, Bohr came along. 270 00:14:48,690 --> 00:14:51,380 Now remember, this is what I mean by dates. 271 00:14:51,380 --> 00:14:54,170 Apart from the dates, we know now 272 00:14:54,170 --> 00:14:58,610 there was a lot of time between those experiments, especially 273 00:14:58,610 --> 00:15:01,150 Dalton and Thompson. 274 00:15:01,150 --> 00:15:05,480 And that's where we were on Monday. 275 00:15:05,480 --> 00:15:08,060 So Bohr was looking at all this. 276 00:15:08,060 --> 00:15:09,620 Remember, he wrote the paper where 277 00:15:09,620 --> 00:15:15,200 he said it is with great interest the Rutherford atom, 278 00:15:15,200 --> 00:15:16,910 meaning it's wrong. 279 00:15:16,910 --> 00:15:17,942 It needs fixing. 280 00:15:17,942 --> 00:15:20,150 Meanwhile, Bohr's looking over at Einstein and Planck 281 00:15:20,150 --> 00:15:21,440 and he's like, wait a second. 282 00:15:21,440 --> 00:15:24,490 Let me get some of that quantization stuff 283 00:15:24,490 --> 00:15:28,420 because if it works for light, what if it also 284 00:15:28,420 --> 00:15:30,190 works for electrons? 285 00:15:30,190 --> 00:15:32,680 What if it also works for electrons? 286 00:15:32,680 --> 00:15:35,470 And so he's looking at this stuff going on 287 00:15:35,470 --> 00:15:38,740 with Planck and Einstein, and he applied it to the electron 288 00:15:38,740 --> 00:15:40,570 in Rutherford's atom. 289 00:15:40,570 --> 00:15:41,900 That's what he did. 290 00:15:41,900 --> 00:15:43,450 That's what Bohr did. 291 00:15:43,450 --> 00:15:46,000 He said, you guys got your light thing. 292 00:15:46,000 --> 00:15:48,750 I'm going after the atom. 293 00:15:48,750 --> 00:15:51,430 And what I'm going to do is I'm going to make just actually 294 00:15:51,430 --> 00:15:54,880 a fairly simple postulate. 295 00:15:54,880 --> 00:15:56,630 Why is that up there? 296 00:15:56,630 --> 00:15:58,110 Let's go. 297 00:15:58,110 --> 00:16:02,820 I'm going to say that for me, the quantization is 298 00:16:02,820 --> 00:16:05,110 going to happen with the angular momentum. 299 00:16:05,110 --> 00:16:10,530 So Bohr came along, and he said that the angular 300 00:16:10,530 --> 00:16:14,640 momentum of the electron-- so L equals mvr, right? 301 00:16:14,640 --> 00:16:17,640 Remember, we listed the Bohr postulates, and one of them 302 00:16:17,640 --> 00:16:22,300 was that Newtonian mechanics would hold. 303 00:16:22,300 --> 00:16:24,610 Angular momentum, mvr. 304 00:16:24,610 --> 00:16:27,070 But there's something added to it. 305 00:16:27,070 --> 00:16:29,770 He said that that angular momentum could only have 306 00:16:29,770 --> 00:16:33,940 discrete values, quantization. 307 00:16:33,940 --> 00:16:37,510 So he said that this is quantized, and he was specific. 308 00:16:40,720 --> 00:16:44,950 He said it could only be some number, some integer 309 00:16:44,950 --> 00:16:48,400 times Planck's constant divided by 2 pi. 310 00:16:48,400 --> 00:16:49,000 Why not? 311 00:16:49,000 --> 00:16:50,470 When in doubt, divide by 2 pi. 312 00:16:54,700 --> 00:16:59,140 As you all know, that has to do with just making math easier. 313 00:16:59,140 --> 00:17:01,130 Now, that's the angular momentum, 314 00:17:01,130 --> 00:17:02,380 and he said it's quantization. 315 00:17:02,380 --> 00:17:07,240 And n-- n is the key here because n is this thing that 316 00:17:07,240 --> 00:17:12,250 says that it must be some unit. 317 00:17:12,250 --> 00:17:13,540 This is like the unit. 318 00:17:13,540 --> 00:17:14,859 It's like that photon energy. 319 00:17:14,859 --> 00:17:20,089 It comes in units, but it comes in units of integers. 320 00:17:20,089 --> 00:17:26,920 So you could have 1 or you could have 2 or 3 but not 1.5. 321 00:17:26,920 --> 00:17:28,480 That's quantization. 322 00:17:28,480 --> 00:17:31,510 So n had to be 1, 2, 3. 323 00:17:31,510 --> 00:17:33,730 It had to be some integer. 324 00:17:33,730 --> 00:17:37,150 And oh, here we go. 325 00:17:37,150 --> 00:17:37,883 Watch this. 326 00:17:37,883 --> 00:17:39,550 We're going to call it a quantum number. 327 00:17:43,090 --> 00:17:45,986 I should have written that in all caps. 328 00:17:45,986 --> 00:17:47,620 [LAUGHTER] 329 00:17:47,620 --> 00:17:50,860 Thank you for that. 330 00:17:50,860 --> 00:17:53,560 It's our first quantum number, and we've only 331 00:17:53,560 --> 00:17:56,320 known each other for a week-- 332 00:17:56,320 --> 00:17:57,190 a week. 333 00:17:57,190 --> 00:17:58,240 Here we are. 334 00:17:58,240 --> 00:18:00,890 We're quantization things. 335 00:18:00,890 --> 00:18:06,230 Quantum number because it's a number that counts quantumness, 336 00:18:06,230 --> 00:18:08,090 quantization. 337 00:18:08,090 --> 00:18:10,910 This is how you get the quantization from this. 338 00:18:10,910 --> 00:18:12,510 So it's a quantum number. 339 00:18:12,510 --> 00:18:14,330 Now here's the thing. 340 00:18:14,330 --> 00:18:17,570 I will not derive Bohr's model for you. 341 00:18:17,570 --> 00:18:20,700 I will tell you what it is. 342 00:18:20,700 --> 00:18:25,580 And if you want, you can look up the derivation. 343 00:18:25,580 --> 00:18:28,850 It's actually really fairly straightforward. 344 00:18:28,850 --> 00:18:32,690 It basically has to do with this one assumption, 345 00:18:32,690 --> 00:18:35,750 quantization of the angular momentum 346 00:18:35,750 --> 00:18:39,320 of that electron, combined with F equals ma 347 00:18:39,320 --> 00:18:41,450 and the electron is stable. 348 00:18:41,450 --> 00:18:43,260 It's not accelerating in. 349 00:18:43,260 --> 00:18:45,690 And when you do that, what you get-- 350 00:18:45,690 --> 00:18:49,400 let's put this-- no. 351 00:18:49,400 --> 00:18:51,390 Let's put that back up. 352 00:18:51,390 --> 00:18:57,110 So what you get with Bohr's model is the following. 353 00:18:59,890 --> 00:19:06,320 You get three extremely important outcomes. 354 00:19:06,320 --> 00:19:13,120 First, you get that the radius of that electron is quantized. 355 00:19:17,290 --> 00:19:22,390 Then you get that it's energy. 356 00:19:22,390 --> 00:19:27,940 The energy that it's allowed to have is also quantized. 357 00:19:27,940 --> 00:19:35,530 And finally, you get that its transitions are-- 358 00:19:38,190 --> 00:19:38,830 you got it. 359 00:19:38,830 --> 00:19:40,920 Thank you-- quantized. 360 00:19:43,590 --> 00:19:47,220 So if you plug stuff in and you do the Bohr derivation 361 00:19:47,220 --> 00:19:49,530 for the hydrogen atom, what you get 362 00:19:49,530 --> 00:19:53,370 is that the radius of that electron 363 00:19:53,370 --> 00:19:58,020 is equal to n squared times a constant divided 364 00:19:58,020 --> 00:20:00,000 by the atomic number. 365 00:20:00,000 --> 00:20:05,010 And this constant is called the Bohr radius. 366 00:20:05,010 --> 00:20:13,170 It's got a value of 0.0529 nanometers, 367 00:20:13,170 --> 00:20:17,120 and it's also called the Bohr radius if you want. 368 00:20:17,120 --> 00:20:18,780 But that's its value. 369 00:20:18,780 --> 00:20:22,890 And then if do the same-- now if you look at energy-- 370 00:20:22,890 --> 00:20:28,040 so energy, the equation for that comes out to be minus 13.6 371 00:20:28,040 --> 00:20:31,460 times the atomic number squared divided 372 00:20:31,460 --> 00:20:36,890 by n squared in units of eV. 373 00:20:36,890 --> 00:20:39,530 Those are the two key results that 374 00:20:39,530 --> 00:20:44,360 come from Bohr's postulates and from Bohr doing this-- 375 00:20:44,360 --> 00:20:44,930 doing that. 376 00:20:47,710 --> 00:20:49,850 And we're going to talk about each one of these. 377 00:20:49,850 --> 00:20:51,100 All right, so if I-- 378 00:20:51,100 --> 00:20:51,600 OK. 379 00:20:56,960 --> 00:20:59,370 So let's go one at a time. 380 00:20:59,370 --> 00:20:59,870 No. 381 00:21:03,107 --> 00:21:04,940 So let's talk about the radius for a minute. 382 00:21:08,783 --> 00:21:09,950 Let's talk about the radius. 383 00:21:09,950 --> 00:21:14,160 So if I look at the radius and I'm a nucleus here-- 384 00:21:14,160 --> 00:21:16,040 so I've got like some positive charge 385 00:21:16,040 --> 00:21:19,790 in the middle and some nucleons and stuff, what I'm saying-- 386 00:21:19,790 --> 00:21:22,550 I'm sorry, some nuclei neutrons-- 387 00:21:22,550 --> 00:21:29,825 is that the electron can only be at certain values. 388 00:21:32,580 --> 00:21:38,660 This distance r can only be at these values, 389 00:21:38,660 --> 00:21:42,560 and that's dictated by the quantization 390 00:21:42,560 --> 00:21:43,910 number, the quantum number. 391 00:21:43,910 --> 00:21:45,988 n equals 1 would be the closest. 392 00:21:45,988 --> 00:21:47,405 You can see that from the formula. 393 00:21:49,980 --> 00:21:55,420 And n equals 2, and so on. 394 00:21:55,420 --> 00:21:59,470 And this is not necessarily drawn to scale. 395 00:21:59,470 --> 00:22:04,420 You can see that for n equals 1 and z equals 1, 396 00:22:04,420 --> 00:22:09,220 the electron is simply at the distance of the constant, 397 00:22:09,220 --> 00:22:15,700 0.5-ish angstroms, 0.05 nanometers, right? 398 00:22:15,700 --> 00:22:18,580 At n equals 2, it's 4 times that. 399 00:22:18,580 --> 00:22:19,270 Oh, yeah? 400 00:22:19,270 --> 00:22:20,537 STUDENT: What's the z? 401 00:22:20,537 --> 00:22:22,120 PROFESSOR: The z is the atomic number. 402 00:22:25,010 --> 00:22:27,680 And that comes in-- 403 00:22:27,680 --> 00:22:28,520 let's put that here. 404 00:22:34,010 --> 00:22:36,140 And that comes in because it tells us 405 00:22:36,140 --> 00:22:38,390 how many positive charges there are, 406 00:22:38,390 --> 00:22:42,740 how many protons there are in the nucleus. 407 00:22:42,740 --> 00:22:44,900 And that comes in when you do F equals ma. 408 00:22:44,900 --> 00:22:47,300 That's how it comes into the Bohr equations. 409 00:22:51,170 --> 00:22:53,570 And r is a distance, and n is the quantum number, 410 00:22:53,570 --> 00:22:54,860 and a0 is a constant. 411 00:22:54,860 --> 00:22:56,600 z is the atomic number in both cases. 412 00:23:02,330 --> 00:23:07,340 This is mind-blowing because it tells you 413 00:23:07,340 --> 00:23:11,090 that that's where the electrons are in the atom orbit, 414 00:23:11,090 --> 00:23:14,040 in the atom, but they're only those distances. 415 00:23:14,040 --> 00:23:16,940 Remember, quantization means nothing else. 416 00:23:16,940 --> 00:23:18,230 Think about that. 417 00:23:18,230 --> 00:23:20,450 I'm saying that that electron can't be anywhere else. 418 00:23:20,450 --> 00:23:25,170 It must be this distance, or it must be this distance. 419 00:23:25,170 --> 00:23:26,790 So this was a big deal. 420 00:23:26,790 --> 00:23:29,410 People were like, what? 421 00:23:29,410 --> 00:23:30,940 It didn't compute. 422 00:23:30,940 --> 00:23:31,940 It didn't make sense. 423 00:23:31,940 --> 00:23:33,850 But this is what they were starting 424 00:23:33,850 --> 00:23:38,350 to see, that this was the only way to explain what they saw, 425 00:23:38,350 --> 00:23:41,330 which we'll come to when we talk about transitions. 426 00:23:41,330 --> 00:23:43,030 So this would be the radius. 427 00:23:43,030 --> 00:23:47,170 And when you look at the energy, it's just as-- 428 00:23:47,170 --> 00:23:48,690 I'm going to use-- 429 00:23:48,690 --> 00:23:50,920 yeah, I'll put it here. 430 00:23:50,920 --> 00:23:53,650 So you take that equation for the energy 431 00:23:53,650 --> 00:23:59,110 of an electron in an atom, and you take z equals 1. 432 00:23:59,110 --> 00:24:04,980 If z equals 1, then the energy is quantized, 433 00:24:04,980 --> 00:24:11,710 and it's minus 13.6 divided by n squared electronvolts. 434 00:24:11,710 --> 00:24:17,645 And if I just draw this as energy going up-- 435 00:24:17,645 --> 00:24:19,020 so if I just draw this, then what 436 00:24:19,020 --> 00:24:23,520 that means is that I've got one line down here showing 437 00:24:23,520 --> 00:24:24,700 kind of the energy level. 438 00:24:24,700 --> 00:24:30,690 So this would be minus 13.6 eV. 439 00:24:30,690 --> 00:24:33,030 And then I've got another line here, 440 00:24:33,030 --> 00:24:36,690 and this would be minus 3.4 eV. 441 00:24:36,690 --> 00:24:40,230 And then I've got another one here, minus-- 442 00:24:40,230 --> 00:24:43,400 let's see-- 1.5-ish eV. 443 00:24:43,400 --> 00:24:45,510 And I'm going to start to get crowded. 444 00:24:45,510 --> 00:24:49,230 As you can see, they're going to get closer and closer until you 445 00:24:49,230 --> 00:24:52,800 get to some level here, which would 446 00:24:52,800 --> 00:24:54,652 be like n equals infinity. 447 00:24:58,430 --> 00:25:02,230 And then above that, zero. 448 00:25:02,230 --> 00:25:04,430 Above that is free. 449 00:25:04,430 --> 00:25:06,160 The electron is free. 450 00:25:06,160 --> 00:25:08,020 When its n is infinity, when it's 451 00:25:08,020 --> 00:25:11,720 gone through all the quantum numbers up to infinity, 452 00:25:11,720 --> 00:25:12,980 it's free. 453 00:25:12,980 --> 00:25:16,580 And that is called ionization, taking it out of the atom 454 00:25:16,580 --> 00:25:19,460 and making it not part of an atom anymore but just out 455 00:25:19,460 --> 00:25:22,520 there free able to do what it wants. 456 00:25:22,520 --> 00:25:23,407 You've ionized it. 457 00:25:23,407 --> 00:25:24,240 You've taken it out. 458 00:25:24,240 --> 00:25:28,700 We'll come back to this concept multiple times. 459 00:25:28,700 --> 00:25:31,280 These are the energy levels for an electron, 460 00:25:31,280 --> 00:25:33,320 and they are also quantized. 461 00:25:33,320 --> 00:25:35,190 They could only be this value or only 462 00:25:35,190 --> 00:25:36,440 that value or only that value. 463 00:25:36,440 --> 00:25:38,270 They cannot be anything else in between. 464 00:25:38,270 --> 00:25:42,470 That was revolutionary at the time. 465 00:25:42,470 --> 00:25:44,910 So this would be like n equals 1. 466 00:25:44,910 --> 00:25:45,410 Sorry. 467 00:25:45,410 --> 00:25:47,750 That's not E. That's eV. 468 00:25:47,750 --> 00:25:53,040 n equals 1, n equals 2, and so on. 469 00:25:53,040 --> 00:25:55,970 Now the third point that I made is that it also 470 00:25:55,970 --> 00:25:57,620 tells us about transitions. 471 00:26:03,560 --> 00:26:06,380 This was also absolutely essential, 472 00:26:06,380 --> 00:26:11,900 and this was the key piece to understanding what they saw. 473 00:26:11,900 --> 00:26:14,780 And so we'll get to that in a few minutes. 474 00:26:14,780 --> 00:26:16,130 What do I mean by a transition? 475 00:26:16,130 --> 00:26:20,510 I mean that an electron is in an atom at some level, 476 00:26:20,510 --> 00:26:21,860 and it moves to another level. 477 00:26:25,010 --> 00:26:27,220 But now the point is that if it can only 478 00:26:27,220 --> 00:26:29,230 be in these discrete quantized levels, 479 00:26:29,230 --> 00:26:31,240 then when it moves from one to another, 480 00:26:31,240 --> 00:26:35,320 those changes in energy are also discrete values. 481 00:26:35,320 --> 00:26:37,930 There are only certain changes in energy 482 00:26:37,930 --> 00:26:40,800 that that electron can experience. 483 00:26:40,800 --> 00:26:43,110 And there's even more which is that 484 00:26:43,110 --> 00:26:44,850 what can cause those changes or what 485 00:26:44,850 --> 00:26:47,220 happens as a result of those changes 486 00:26:47,220 --> 00:26:49,350 is the interaction with light. 487 00:26:49,350 --> 00:26:53,900 And we're all the way back to here, photons. 488 00:26:53,900 --> 00:26:55,660 Think about it this way. 489 00:26:55,660 --> 00:26:58,150 If I take a ball and I have it up here, 490 00:26:58,150 --> 00:26:59,980 it's got some mgh in it, right? 491 00:26:59,980 --> 00:27:01,950 And I drop it, and now it's got some KE. 492 00:27:04,930 --> 00:27:07,930 More energy was in gravitation, was 493 00:27:07,930 --> 00:27:10,745 stored in mgh, gravitational potential energy, 494 00:27:10,745 --> 00:27:11,620 and then I let it go. 495 00:27:11,620 --> 00:27:15,450 Well, for an electron, this is its ground state. 496 00:27:15,450 --> 00:27:18,190 This is the kind of happy place. 497 00:27:18,190 --> 00:27:22,470 So this would be like a ground state, 498 00:27:22,470 --> 00:27:29,560 and these would be all excited states. 499 00:27:29,560 --> 00:27:33,370 It would be like excited states. 500 00:27:33,370 --> 00:27:38,490 So that would be like lifting the electron up and letting go. 501 00:27:38,490 --> 00:27:41,890 But when you let it go, it's not kinetic energy 502 00:27:41,890 --> 00:27:43,500 that that transfers into. 503 00:27:43,500 --> 00:27:44,680 It's photon energy. 504 00:27:49,160 --> 00:27:54,500 Photon energy gets emitted from electrons changing their levels 505 00:27:54,500 --> 00:27:55,850 in an atom. 506 00:27:55,850 --> 00:28:01,290 Light is an absolutely intricate part of this system. 507 00:28:01,290 --> 00:28:03,660 And not only that, but everything is quantized. 508 00:28:07,120 --> 00:28:09,730 I almost need a moment, but I'm OK. 509 00:28:09,730 --> 00:28:10,990 I'm going to keep going. 510 00:28:10,990 --> 00:28:17,840 This was our big deal, a really big deal 511 00:28:17,840 --> 00:28:20,720 because now I can tell you-- 512 00:28:25,630 --> 00:28:27,910 OK, there we go-- 513 00:28:27,910 --> 00:28:31,000 because now I could tell you, for example, that if that's 514 00:28:31,000 --> 00:28:34,930 the second orbit in hydrogen and that's the first orbit, 515 00:28:34,930 --> 00:28:36,730 I can tell you what frequency light 516 00:28:36,730 --> 00:28:39,820 is emitted if you go from n equals 2 to n 517 00:28:39,820 --> 00:28:47,590 equals 1 because the change in energy from n equals 2 to n 518 00:28:47,590 --> 00:28:55,390 equals 1 is nothing more than minus 13.6 eV times-- 519 00:28:55,390 --> 00:28:58,450 well, it's the final state minus the initial state, right? 520 00:28:58,450 --> 00:29:02,830 The final state is 1 over 1 squared, 521 00:29:02,830 --> 00:29:05,740 and the initial state is 1 over 2 squared. 522 00:29:05,740 --> 00:29:11,290 All I've done is pull out the 13.6, but these are just-- 523 00:29:11,290 --> 00:29:13,540 these are just the Bohr-model energies, 524 00:29:13,540 --> 00:29:15,140 and I'm just taking the difference. 525 00:29:15,140 --> 00:29:19,990 This is equal to Ef minus Ei. 526 00:29:19,990 --> 00:29:21,700 It's the change in energy. 527 00:29:21,700 --> 00:29:25,820 So in this case, it's minus 10.2 electronvolts 528 00:29:25,820 --> 00:29:28,600 and going from the second orbit, quantized orbit, 529 00:29:28,600 --> 00:29:30,250 down to the first. 530 00:29:30,250 --> 00:29:33,190 And I can now tell you because of what we did in the beginning 531 00:29:33,190 --> 00:29:44,790 that that would emit a photon of frequency 2.5 times 10 532 00:29:44,790 --> 00:29:46,500 to the 15th hertz. 533 00:29:49,280 --> 00:29:51,590 That's the energy difference, and that energy 534 00:29:51,590 --> 00:29:53,868 goes into producing a photon-- 535 00:29:53,868 --> 00:29:55,910 goes into producing a photon, and we can tell you 536 00:29:55,910 --> 00:29:58,670 exactly what that frequency is. 537 00:29:58,670 --> 00:30:00,830 So these are the kinds of transitions 538 00:30:00,830 --> 00:30:02,540 that the Bohr model explains, and it 539 00:30:02,540 --> 00:30:06,090 explains energy changing from electron transitions 540 00:30:06,090 --> 00:30:06,590 to photons. 541 00:30:09,290 --> 00:30:11,030 So what are the implications of this? 542 00:30:11,030 --> 00:30:14,810 Oh, there's the question that I just answered. 543 00:30:14,810 --> 00:30:17,120 If this is hydrogen, z equals 1. 544 00:30:21,220 --> 00:30:24,370 The implications of this are groundbreaking, 545 00:30:24,370 --> 00:30:26,020 and it explained what people were 546 00:30:26,020 --> 00:30:28,030 seeing because you could be talking 547 00:30:28,030 --> 00:30:29,170 about angstroms already. 548 00:30:29,170 --> 00:30:31,630 Angstrom looked up, and he's like, well, you guys think 549 00:30:31,630 --> 00:30:33,640 it's a rainbow, but I'm not seeing that. 550 00:30:33,640 --> 00:30:36,728 I'm seeing discrete lines all over the place. 551 00:30:36,728 --> 00:30:38,770 And that's what he saw when he looked at the sun. 552 00:30:38,770 --> 00:30:40,060 Don't look at the sun. 553 00:30:40,060 --> 00:30:44,040 It's not a good idea, but Angstrom did. 554 00:30:44,040 --> 00:30:46,830 And now he said, well, but there are all these lines, 555 00:30:46,830 --> 00:30:50,740 and the wavelengths that he tabulated 556 00:30:50,740 --> 00:30:52,810 happened to come on this sort of thousands 557 00:30:52,810 --> 00:30:56,370 of angstrom kind of scale. 558 00:30:56,370 --> 00:30:58,770 And so he liked that, and chemists love it, 559 00:30:58,770 --> 00:31:00,770 and that's why the angstrom is named what it is, 560 00:31:00,770 --> 00:31:01,937 10 to the minus 10th meters. 561 00:31:05,260 --> 00:31:09,700 Chemists love it because a bond is a few angstroms. 562 00:31:09,700 --> 00:31:11,710 Spectroscopists like nanometers. 563 00:31:11,710 --> 00:31:13,860 They're like, thousands are too big. 564 00:31:13,860 --> 00:31:14,860 We don't like thousands. 565 00:31:14,860 --> 00:31:16,510 We want to work with hundreds. 566 00:31:16,510 --> 00:31:18,833 So spectroscopists use nanometers. 567 00:31:18,833 --> 00:31:20,500 Other people, chemists, whose angstroms. 568 00:31:20,500 --> 00:31:23,730 I say can't we all just really get along? 569 00:31:23,730 --> 00:31:24,640 And it's fine. 570 00:31:24,640 --> 00:31:28,150 Don't make spectroscopists angry, really. 571 00:31:28,150 --> 00:31:30,160 I did it once. 572 00:31:30,160 --> 00:31:35,370 Now on Friday, you are going to get 573 00:31:35,370 --> 00:31:37,410 the most accurate spectroscope that 574 00:31:37,410 --> 00:31:42,350 has been made by humans in your goodie bag, 575 00:31:42,350 --> 00:31:44,540 and you'll be able to look at the fact 576 00:31:44,540 --> 00:31:46,350 that the world is not continuous. 577 00:31:46,350 --> 00:31:51,180 These frequencies, wavelengths that are coming out 578 00:31:51,180 --> 00:31:52,830 are not continuous. 579 00:31:52,830 --> 00:31:57,210 If you take a tube of H2 gas and you apply an enormous voltage 580 00:31:57,210 --> 00:32:04,260 to it, you will excite electrons in the H2 molecules. 581 00:32:04,260 --> 00:32:06,660 As they go back down, they will emit photons, 582 00:32:06,660 --> 00:32:07,620 and what will you see? 583 00:32:07,620 --> 00:32:09,300 Only certain values. 584 00:32:09,300 --> 00:32:11,390 Well, this is what people were doing. 585 00:32:11,390 --> 00:32:13,890 They were looking out into the universe-- which, by the way, 586 00:32:13,890 --> 00:32:21,760 is 75% hydrogen. And they're like, really? 587 00:32:21,760 --> 00:32:23,419 The hydrogen economy. 588 00:32:23,419 --> 00:32:26,353 [LAUGHTER] 589 00:32:28,800 --> 00:32:34,810 We-- we-- they were looking now and seeing discrete lines 590 00:32:34,810 --> 00:32:37,340 all over the place. 591 00:32:37,340 --> 00:32:38,800 How to explain it? 592 00:32:38,800 --> 00:32:41,560 The Bohr model is what explained it. 593 00:32:41,560 --> 00:32:43,990 You will be able to see these discrete lines yourselves 594 00:32:43,990 --> 00:32:45,790 with the goodie bag on Friday. 595 00:32:45,790 --> 00:32:51,760 But if you do this, this is what you might see from hydrogen. 596 00:32:51,760 --> 00:32:53,620 And there were a lot of people trying 597 00:32:53,620 --> 00:32:56,563 to understand this at the time, Balmer and Rydberg. 598 00:32:56,563 --> 00:32:58,480 And I'm not going to go through-- they came up 599 00:32:58,480 --> 00:33:00,130 with sort of partial formula. 600 00:33:00,130 --> 00:33:02,680 They were empirically based. 601 00:33:02,680 --> 00:33:05,500 But Bohr-- it was only the Bohr model 602 00:33:05,500 --> 00:33:07,030 that could explain it all. 603 00:33:07,030 --> 00:33:08,410 It was only the Bohr model. 604 00:33:08,410 --> 00:33:14,800 And the reason is that all the transitions were out there, 605 00:33:14,800 --> 00:33:18,760 and you need the complete picture of these changes 606 00:33:18,760 --> 00:33:21,250 in energy between these levels. 607 00:33:21,250 --> 00:33:23,590 You need to know about that to understand 608 00:33:23,590 --> 00:33:24,778 all those transitions. 609 00:33:24,778 --> 00:33:26,320 And at the time, it was a real thing. 610 00:33:26,320 --> 00:33:28,278 If you were like, I want to get something named 611 00:33:28,278 --> 00:33:30,670 after myself in science, you'd be like 612 00:33:30,670 --> 00:33:34,030 let me go and find a new set of transitions, which are just 613 00:33:34,030 --> 00:33:35,498 basically lines, right? 614 00:33:35,498 --> 00:33:37,540 It's that you're not seeing a continuous spectrum 615 00:33:37,540 --> 00:33:39,538 in some part of space. 616 00:33:39,538 --> 00:33:41,080 You're instead seeing discrete lines. 617 00:33:41,080 --> 00:33:42,340 And look at this, right? 618 00:33:42,340 --> 00:33:45,160 So like Lyman-- you could go down 619 00:33:45,160 --> 00:33:50,350 to n equals 1 like we did there, 2 to 1, so from here to here. 620 00:33:50,350 --> 00:33:53,580 But you could also go from 3 down to 1. 621 00:33:53,580 --> 00:33:56,860 You could also go from 4, and that's a series. 622 00:33:56,860 --> 00:34:00,123 Then you could also transition not from to 1 but to 2 or to 3, 623 00:34:00,123 --> 00:34:01,540 and each one of those is a series. 624 00:34:01,540 --> 00:34:04,440 And then I think finally they're like, OK, no more names. 625 00:34:04,440 --> 00:34:08,188 After Pfund, we're done with naming. 626 00:34:08,188 --> 00:34:09,730 But all those series are still there. 627 00:34:09,730 --> 00:34:12,280 Those are the allowed transitions. 628 00:34:12,280 --> 00:34:16,929 So you can also imagine that it's not just emission. 629 00:34:16,929 --> 00:34:18,550 So we've been talking about emission. 630 00:34:18,550 --> 00:34:22,360 You get these lines when an electron goes down in energy. 631 00:34:22,360 --> 00:34:24,639 Remember, like the ball, the mgh goes down. 632 00:34:24,639 --> 00:34:29,409 It gives off photons in these quantized energies, 633 00:34:29,409 --> 00:34:30,880 but it can be the opposite. 634 00:34:30,880 --> 00:34:32,050 You could shine light. 635 00:34:32,050 --> 00:34:35,020 So I could get a continuous spectrum here and shine it 636 00:34:35,020 --> 00:34:40,230 on an atom, and that atom absorbs light literally 637 00:34:40,230 --> 00:34:42,679 by exciting electrons. 638 00:34:42,679 --> 00:34:45,960 An electron is in some state, maybe the ground state, 639 00:34:45,960 --> 00:34:50,040 and some energy comes along that exactly takes it up 640 00:34:50,040 --> 00:34:53,190 to one of these states. 641 00:34:53,190 --> 00:34:58,440 But it can't sort of take you up there. 642 00:34:58,440 --> 00:35:00,330 It's got to take you there-- 643 00:35:00,330 --> 00:35:01,200 quantization. 644 00:35:01,200 --> 00:35:04,770 That's why you see these lines here. 645 00:35:04,770 --> 00:35:09,890 These are the places where that atom can absorb a photon 646 00:35:09,890 --> 00:35:12,620 because it exactly corresponds to a transition 647 00:35:12,620 --> 00:35:16,100 from one discrete level to another. 648 00:35:16,100 --> 00:35:18,950 So it works both ways, absorbing photon energy, 649 00:35:18,950 --> 00:35:20,510 promoting electrons up. 650 00:35:23,260 --> 00:35:26,670 And when we do X-rays, we just ionize everything. 651 00:35:26,670 --> 00:35:29,340 But right now, we're staying within the potential 652 00:35:29,340 --> 00:35:30,340 of the atom. 653 00:35:30,340 --> 00:35:35,850 So we're staying within these levels, 654 00:35:35,850 --> 00:35:37,770 absorbing or emitting energy. 655 00:35:37,770 --> 00:35:39,408 So I could answer questions like this. 656 00:35:39,408 --> 00:35:40,950 If you look at a question like this-- 657 00:35:40,950 --> 00:35:41,610 I forget. 658 00:35:41,610 --> 00:35:45,180 I think this might be from a couple of years ago quiz, 659 00:35:45,180 --> 00:35:47,760 so you might get something like this tomorrow. 660 00:35:47,760 --> 00:35:48,870 No, you won't. 661 00:35:48,870 --> 00:35:50,760 I just looked at a few faces, and no 662 00:35:50,760 --> 00:35:52,900 because we're talking about it today. 663 00:35:52,900 --> 00:35:55,350 So you wouldn't get it tomorrow because, remember, 664 00:35:55,350 --> 00:35:59,300 you only get quizzed on things that we did ending on Monday. 665 00:35:59,300 --> 00:36:00,660 It wouldn't be fair otherwise. 666 00:36:00,660 --> 00:36:04,050 But next week, OK. 667 00:36:04,050 --> 00:36:06,080 What's the lowest-energy photon shown? 668 00:36:10,220 --> 00:36:11,210 Which one is it? 669 00:36:11,210 --> 00:36:12,200 These are photons now. 670 00:36:12,200 --> 00:36:13,408 We think of these as photons. 671 00:36:15,660 --> 00:36:16,620 Red. 672 00:36:16,620 --> 00:36:21,390 High wavelength, lower energy. 673 00:36:21,390 --> 00:36:22,080 OK, good. 674 00:36:22,080 --> 00:36:24,390 That was over here. 675 00:36:24,390 --> 00:36:26,310 Now what about what transition give us 676 00:36:26,310 --> 00:36:29,640 the line at 639 nanometers? 677 00:36:29,640 --> 00:36:34,470 Hello, [? Humana. ?] 639 nanometers. 678 00:36:34,470 --> 00:36:37,740 So I want to know what electron transition did that. 679 00:36:37,740 --> 00:36:40,260 Well, to solve that problem-- 680 00:36:40,260 --> 00:36:42,900 to solve that problem, I need to do some erasing. 681 00:36:42,900 --> 00:36:49,660 Maybe I'll just draw it in here because what 682 00:36:49,660 --> 00:36:58,170 you have is minus 13.6 eV times-- 683 00:36:58,170 --> 00:37:03,000 I'm assuming z equals 1 because did I say it was hydrogen? 684 00:37:03,000 --> 00:37:06,430 I did, hydrogen. z equals 1. 685 00:37:06,430 --> 00:37:08,520 So z goes away, 1 squared. 686 00:37:08,520 --> 00:37:15,270 So minus 13.6 eV times 1 over the final state squared minus 1 687 00:37:15,270 --> 00:37:18,975 over the initial quantum state squared quantum number squared. 688 00:37:21,820 --> 00:37:26,760 So that's going to equal 639 nanometers, which we now 689 00:37:26,760 --> 00:37:30,030 know we can convert, thanks to Planck and Einstein, 690 00:37:30,030 --> 00:37:31,770 into an energy. 691 00:37:31,770 --> 00:37:33,630 We now know that, a photon energy. 692 00:37:33,630 --> 00:37:38,970 It's that photon, that unit, that discrete unit that 693 00:37:38,970 --> 00:37:45,360 does it, and this is 1.94 eV because it 694 00:37:45,360 --> 00:37:47,218 comes from 639 nanometers. 695 00:37:47,218 --> 00:37:48,510 Back and forth, back and forth. 696 00:37:48,510 --> 00:37:51,870 We've got to get into that mode and into that mood. 697 00:37:51,870 --> 00:37:56,230 Back and forth, energy, frequency, wavelength. 698 00:37:56,230 --> 00:37:58,200 And so I won't do the math here, but the answer 699 00:37:58,200 --> 00:38:04,590 comes into something like it's the 4 to 3. 700 00:38:04,590 --> 00:38:12,050 4 to 3 is the transition that gives you that. 701 00:38:12,050 --> 00:38:13,630 We're not going to go-- 702 00:38:13,630 --> 00:38:15,110 some day. 703 00:38:15,110 --> 00:38:16,805 We're not going to go kind of all-- 704 00:38:16,805 --> 00:38:18,380 this is a fairly simple one to see. 705 00:38:18,380 --> 00:38:23,720 We're not going to go like n equals 528 to n equals 7,000, 706 00:38:23,720 --> 00:38:25,770 but some simple kind of back and forth. 707 00:38:25,770 --> 00:38:29,900 Just get into that mode of looking at these transitions 708 00:38:29,900 --> 00:38:32,270 as changes in energy, which means the emission 709 00:38:32,270 --> 00:38:33,980 or absorption of a photon. 710 00:38:33,980 --> 00:38:36,480 That's what I want you to get out of this. 711 00:38:36,480 --> 00:38:38,780 And you can go further than that and answer questions 712 00:38:38,780 --> 00:38:41,300 like power questions. 713 00:38:41,300 --> 00:38:42,800 So here's a question. 714 00:38:42,800 --> 00:38:44,780 If your favorite radio station broadcasts 715 00:38:44,780 --> 00:38:47,450 at a frequency of 107.9-- 716 00:38:47,450 --> 00:38:51,470 I'm not saying that's mine, but you got to groove out-- 717 00:38:51,470 --> 00:38:53,870 and a power output of 50 kilowatts, 718 00:38:53,870 --> 00:38:58,732 how many photons are emitted by the transmitter each second? 719 00:38:58,732 --> 00:39:01,190 I just want to give you this as another example of thinking 720 00:39:01,190 --> 00:39:01,910 about this. 721 00:39:01,910 --> 00:39:07,120 Light, energy-- light to energy, photons, particles. 722 00:39:07,120 --> 00:39:16,400 And here, you can get that by simply knowing what power is. 723 00:39:16,400 --> 00:39:20,690 And if you know what power is, it's watts per second. 724 00:39:20,690 --> 00:39:23,310 Sorry, watts is joules per second. 725 00:39:23,310 --> 00:39:26,250 And so the energy here is h nu. 726 00:39:26,250 --> 00:39:27,750 And I won't go through all the math, 727 00:39:27,750 --> 00:39:29,540 but I'll leave the answer here. 728 00:39:29,540 --> 00:39:38,711 You get 7.12 times 10 to the minus 26 joules per photon. 729 00:39:38,711 --> 00:39:40,040 Now, how did I get that? 730 00:39:40,040 --> 00:39:43,550 I got that because I know the frequency. 731 00:39:43,550 --> 00:39:44,810 Why am I using joules? 732 00:39:44,810 --> 00:39:47,600 Remember, I put them both up there-- joules, eV. 733 00:39:47,600 --> 00:39:53,840 Ah, because I know my power, which is 50 kilowatts, which 734 00:39:53,840 --> 00:39:59,620 is 50,000 joules per second. 735 00:39:59,620 --> 00:40:01,210 And so I've got joules in the power. 736 00:40:01,210 --> 00:40:03,070 I just decided to stick with joules. 737 00:40:03,070 --> 00:40:05,350 Joules, eV, joules, eV, back and forth. 738 00:40:05,350 --> 00:40:08,200 They're just units. 739 00:40:08,200 --> 00:40:10,420 If you're not familiar with changing back and forth, 740 00:40:10,420 --> 00:40:12,430 you should do a little practice. 741 00:40:12,430 --> 00:40:16,090 And this gives you something like 7 times 10 742 00:40:16,090 --> 00:40:23,150 to the 29th photons per second. 743 00:40:23,150 --> 00:40:26,720 So you can think about power, photons, light, energy. 744 00:40:26,720 --> 00:40:29,000 If I shine that many-- 745 00:40:29,000 --> 00:40:34,470 if I shine that many on Einstein's medal, 746 00:40:34,470 --> 00:40:36,270 will the electrons come off? 747 00:40:36,270 --> 00:40:38,570 That seems like a lot. 748 00:40:38,570 --> 00:40:41,300 We don't know because we need to know how much energy it takes 749 00:40:41,300 --> 00:40:42,717 to liberate the electron, and then 750 00:40:42,717 --> 00:40:46,660 that ties into the frequency. 751 00:40:46,660 --> 00:40:48,490 Radio waves are much lower energy, 752 00:40:48,490 --> 00:40:50,920 much, much lower energy. 753 00:40:50,920 --> 00:40:52,720 Now, this gets me to why this matters, 754 00:40:52,720 --> 00:40:54,685 and that's how I want to end today's lecture 755 00:40:54,685 --> 00:41:01,060 in the last five minutes because we talked about emission, 756 00:41:01,060 --> 00:41:05,410 electrons transitioning from their discrete orbitals 757 00:41:05,410 --> 00:41:07,990 as a way of emitting or absorbing. 758 00:41:07,990 --> 00:41:10,150 And so you if you have different atoms, 759 00:41:10,150 --> 00:41:13,540 there's hydrogen. These are the absorption lines-- 760 00:41:13,540 --> 00:41:15,370 absorption lines. 761 00:41:15,370 --> 00:41:16,900 Carbon has absorption lines. 762 00:41:16,900 --> 00:41:19,330 Oxygen, nitrogen, sulfur, so lots of things 763 00:41:19,330 --> 00:41:20,620 have absorption lines. 764 00:41:20,620 --> 00:41:22,010 Why does this matter? 765 00:41:22,010 --> 00:41:24,320 Well, of course, because of the refrigerator. 766 00:41:27,300 --> 00:41:28,170 I love this plot. 767 00:41:28,170 --> 00:41:31,440 This is a plot of the refrigerator. 768 00:41:31,440 --> 00:41:34,500 This is the size of the refrigerator 769 00:41:34,500 --> 00:41:35,640 as a function of year. 770 00:41:35,640 --> 00:41:38,345 The date only goes to 2002, but it's roughly stable now. 771 00:41:38,345 --> 00:41:39,720 Does anybody know what's limiting 772 00:41:39,720 --> 00:41:41,796 the size of the refrigerator? 773 00:41:41,796 --> 00:41:45,272 It was going up and up and up a lot, and then it stopped. 774 00:41:45,272 --> 00:41:46,730 Does anybody know what limits that? 775 00:41:46,730 --> 00:41:49,090 STUDENT: The average height [INAUDIBLE].. 776 00:41:49,090 --> 00:41:51,520 PROFESSOR: It's the width of the doorway. 777 00:41:51,520 --> 00:41:52,900 It's the width of the doorway. 778 00:41:52,900 --> 00:41:55,067 That's why we don't-- that's why people get a second 779 00:41:55,067 --> 00:41:55,620 refrigerator. 780 00:41:58,800 --> 00:42:00,850 And there's energy use. 781 00:42:00,850 --> 00:42:03,010 Energy Star program, big deal. 782 00:42:03,010 --> 00:42:04,420 Big deal. 783 00:42:04,420 --> 00:42:06,220 But I'm talking about refrigerators 784 00:42:06,220 --> 00:42:07,840 for a different reason. 785 00:42:07,840 --> 00:42:11,170 I'm talking about refrigerators because until the 1980s, 786 00:42:11,170 --> 00:42:15,190 the way we did cooling was with a chemical called 787 00:42:15,190 --> 00:42:16,810 chlorofluorocarbon. 788 00:42:16,810 --> 00:42:18,310 This is a chemistry class, and we're 789 00:42:18,310 --> 00:42:19,990 going to be talking about-- 790 00:42:19,990 --> 00:42:21,520 when we talk about why this matters, 791 00:42:21,520 --> 00:42:23,440 we connect to the chemistry. 792 00:42:23,440 --> 00:42:25,270 Well, the chemistry there was critical. 793 00:42:25,270 --> 00:42:28,750 There was a molecule there called chlorofluorocarbon 794 00:42:28,750 --> 00:42:30,280 or CFC. 795 00:42:30,280 --> 00:42:33,250 And the thing about that molecule 796 00:42:33,250 --> 00:42:40,120 is that its absorption, the chlorofluorocarbon-- 797 00:42:40,120 --> 00:42:41,860 so let's write it down here, CCl3F. 798 00:42:47,500 --> 00:42:52,420 There's a gas phase, so we put the little lower script g. 799 00:42:52,420 --> 00:42:57,550 That molecule has its own absorption. 800 00:42:57,550 --> 00:43:00,050 It has its own absorption, and it has its own reaction, 801 00:43:00,050 --> 00:43:01,610 and so do other things. 802 00:43:01,610 --> 00:43:04,270 But it has a really important reaction 803 00:43:04,270 --> 00:43:09,510 because when it absorbs UV rays, then 804 00:43:09,510 --> 00:43:12,790 it doesn't just like then like electrons get pumped up. 805 00:43:12,790 --> 00:43:14,920 No, the whole thing reacts. 806 00:43:14,920 --> 00:43:23,860 And so this thing degrades into CCl2F plus chlorine gas, 807 00:43:23,860 --> 00:43:28,330 and that's once it's up maybe in the atmosphere, which 808 00:43:28,330 --> 00:43:30,220 it was getting released all the time because 809 00:43:30,220 --> 00:43:31,095 of the refrigerators. 810 00:43:31,095 --> 00:43:35,080 And the thing is that the chlorine gas would then 811 00:43:35,080 --> 00:43:43,570 react with ozone, and this would go to ClO plus O2, 812 00:43:43,570 --> 00:43:44,782 and here's the problem. 813 00:43:44,782 --> 00:43:46,240 I mean, we're already at a problem, 814 00:43:46,240 --> 00:43:48,035 but now it's a big problem because-- 815 00:43:48,035 --> 00:43:48,910 you can already tell. 816 00:43:48,910 --> 00:43:52,210 But I've got ClO, and that's really reactive. 817 00:43:52,210 --> 00:43:56,010 So what happens is ClO, which was a gas-- 818 00:43:56,010 --> 00:43:58,630 I'm just being careful here with my subjects-- 819 00:43:58,630 --> 00:44:01,830 would react with atomic oxygen to give you 820 00:44:01,830 --> 00:44:05,920 O2 and the chlorine atom back. 821 00:44:05,920 --> 00:44:08,020 And here's the thing. 822 00:44:08,020 --> 00:44:09,520 Now I've got my chlorine atom again. 823 00:44:09,520 --> 00:44:11,520 These are very reactive atoms in the atmosphere. 824 00:44:11,520 --> 00:44:14,460 They love ozone. 825 00:44:14,460 --> 00:44:19,540 And so this cycle for one CFC molecule 826 00:44:19,540 --> 00:44:22,720 would happen 100,000 times, roughly, 827 00:44:22,720 --> 00:44:24,440 before that chlorine kind of goes 828 00:44:24,440 --> 00:44:25,690 away and does something else-- 829 00:44:25,690 --> 00:44:28,905 100,000 ozone molecules per CFC. 830 00:44:28,905 --> 00:44:29,780 Why does that matter? 831 00:44:29,780 --> 00:44:31,600 Well, it matters because-- 832 00:44:31,600 --> 00:44:33,520 I love this plot. 833 00:44:33,520 --> 00:44:39,200 This is the energy of light from the sun hitting our planet. 834 00:44:39,200 --> 00:44:44,280 So this is the energy that you get, and look at this. 835 00:44:44,280 --> 00:44:46,540 This is the sun at the top of the atmosphere. 836 00:44:46,540 --> 00:44:48,337 Here it is on Earth, the red. 837 00:44:48,337 --> 00:44:49,420 Look at these things here. 838 00:44:53,090 --> 00:44:55,280 If you could only see in this spectrum, 839 00:44:55,280 --> 00:44:58,880 the world would be dark because there's no light on the planet. 840 00:44:58,880 --> 00:44:59,380 Why? 841 00:44:59,380 --> 00:45:02,120 Because it's all absorbed in the upper atmosphere by water. 842 00:45:02,120 --> 00:45:06,900 Absorption-- it's the same principle, Bohr. 843 00:45:06,900 --> 00:45:09,720 Bohr's idea of electrons getting promoted 844 00:45:09,720 --> 00:45:12,660 when they absorb light is happening, 845 00:45:12,660 --> 00:45:16,530 and it's protecting us because right here, see, that's the UV. 846 00:45:16,530 --> 00:45:19,140 Low wavelength, high energy. 847 00:45:19,140 --> 00:45:20,640 UV, O3. 848 00:45:20,640 --> 00:45:21,442 Look at that. 849 00:45:21,442 --> 00:45:22,650 Look at what it's taking out. 850 00:45:22,650 --> 00:45:26,820 That little sliver of yellow is critical. 851 00:45:26,820 --> 00:45:31,380 And ozone was doing the job, and it still is. 852 00:45:31,380 --> 00:45:34,410 But if we tear all that ozone out with these CFCs, 853 00:45:34,410 --> 00:45:35,860 we have a crisis. 854 00:45:35,860 --> 00:45:40,500 And that led to what is one of the greatest policy decisions 855 00:45:40,500 --> 00:45:44,220 which was made in 1987-- it's called the Montreal Protocol-- 856 00:45:44,220 --> 00:45:47,850 to essentially globally ban-- the US led this. 857 00:45:47,850 --> 00:45:51,420 This is a great example of how policy is so critical. 858 00:45:51,420 --> 00:45:54,300 The US led this effort to ban CFCs, 859 00:45:54,300 --> 00:45:57,780 and we're almost back to normal ozone levels, 860 00:45:57,780 --> 00:45:58,610 and we avoid this. 861 00:45:58,610 --> 00:46:01,770 And by the way, if this had happened, 862 00:46:01,770 --> 00:46:04,350 the prediction at the time was roughly 280 million 863 00:46:04,350 --> 00:46:09,010 additional cases of skin cancer over this generation. 864 00:46:09,010 --> 00:46:11,130 This is a very big deal, and it all 865 00:46:11,130 --> 00:46:16,740 comes back to absorption of electrons 866 00:46:16,740 --> 00:46:18,480 by atoms and molecules. 867 00:46:18,480 --> 00:46:20,540 See you guys on Friday.