1 00:00:00,030 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,830 Commons license. 3 00:00:03,830 --> 00:00:06,860 Your support will help MIT OpenCourseWare continue to 4 00:00:06,860 --> 00:00:10,520 offer high-quality educational resources for free. 5 00:00:10,520 --> 00:00:13,390 To make a donation or view additional materials from 6 00:00:13,390 --> 00:00:17,490 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:17,490 --> 00:00:18,740 ocw.mit.edu. 8 00:00:21,990 --> 00:00:23,680 PROFESSOR: Time to learn. 9 00:00:23,680 --> 00:00:26,980 Time to get back to business here in 3.091. 10 00:00:26,980 --> 00:00:32,500 So let's do the announcements first. Tomorrow quiz one, 11 00:00:32,500 --> 00:00:33,640 based on homework one. 12 00:00:33,640 --> 00:00:34,310 Ten minutes. 13 00:00:34,310 --> 00:00:37,130 Bring your Periodic Table, your table of constants, 14 00:00:37,130 --> 00:00:41,280 something to write with and a calculator. 15 00:00:41,280 --> 00:00:46,330 There's about a dozen or so copies of the text on reserve 16 00:00:46,330 --> 00:00:48,305 at the Hayden Library. 17 00:00:48,305 --> 00:00:51,740 I want you to be aware of that. 18 00:00:51,740 --> 00:00:55,350 Now some of you approached me last day and said is it true 19 00:00:55,350 --> 00:00:57,580 that we have to memorize the Periodic Table? 20 00:00:57,580 --> 00:00:58,830 Yes. 21 00:01:00,710 --> 00:01:02,400 But not the whole Periodic Table. 22 00:01:02,400 --> 00:01:04,340 I know some of you are going to say, well that's so 19th 23 00:01:04,340 --> 00:01:06,490 century, rote learning and so on. 24 00:01:06,490 --> 00:01:08,710 To which I say, you're wrong. 25 00:01:08,710 --> 00:01:11,950 Every educated person should know that potassium lies under 26 00:01:11,950 --> 00:01:14,290 sodium, which lies under lithium. 27 00:01:14,290 --> 00:01:16,180 And you are going to be educated whether 28 00:01:16,180 --> 00:01:18,550 you like it or not. 29 00:01:18,550 --> 00:01:21,840 But this is a lot to learn and so we're just going to look at 30 00:01:21,840 --> 00:01:24,280 the main block. 31 00:01:24,280 --> 00:01:27,816 We're not going to ask you to memorize the lanthanides, 32 00:01:27,816 --> 00:01:29,870 actinides and the super heavies. 33 00:01:29,870 --> 00:01:31,230 We'll leave that out. 34 00:01:31,230 --> 00:01:34,420 So it's quite straightforward. 35 00:01:34,420 --> 00:01:35,730 We've been doing this for many years. 36 00:01:35,730 --> 00:01:37,670 This is from 2004. 37 00:01:37,670 --> 00:01:38,870 And it's not that hard. 38 00:01:38,870 --> 00:01:40,420 I give you the blank here. 39 00:01:40,420 --> 00:01:42,570 And I even put the numbers on for you. 40 00:01:42,570 --> 00:01:44,620 And all you have to do is add the two-letter 41 00:01:44,620 --> 00:01:46,680 or one-letter symbol. 42 00:01:46,680 --> 00:01:48,840 You don't have to give me the full name of the element. 43 00:01:48,840 --> 00:01:50,805 You don't have to get me its density or 44 00:01:50,805 --> 00:01:52,080 its electron affinity. 45 00:01:52,080 --> 00:01:54,490 You've just got to put argon, in there. 46 00:01:54,490 --> 00:01:54,980 Ar. 47 00:01:54,980 --> 00:01:56,160 That's all you've got to put in there. 48 00:01:56,160 --> 00:01:57,420 OK? 49 00:01:57,420 --> 00:02:01,740 And every year people grouse when I announce this. 50 00:02:01,740 --> 00:02:05,930 But you'll find out that you'll breeze through it. 51 00:02:05,930 --> 00:02:07,080 You'll have 10 minutes. 52 00:02:07,080 --> 00:02:09,920 This will be on September 24. 53 00:02:09,920 --> 00:02:12,460 So next week there will be two minor celebrations. 54 00:02:12,460 --> 00:02:14,540 One on Tuesday and one on Thursday. 55 00:02:14,540 --> 00:02:17,290 So it's going to be a very festive week. 56 00:02:17,290 --> 00:02:19,350 And people blast through it. 57 00:02:19,350 --> 00:02:22,220 It's one mark off for every error down to zero. 58 00:02:22,220 --> 00:02:23,960 We don't give negative scores. 59 00:02:23,960 --> 00:02:27,200 And people just go right through it. 60 00:02:27,200 --> 00:02:29,160 And then they urge me to make sure that in 61 00:02:29,160 --> 00:02:30,400 future years I victimi-- 62 00:02:30,400 --> 00:02:34,250 I mean I ask students to continue this. 63 00:02:34,250 --> 00:02:38,100 People are very proud of the fact they know the S, P, and D 64 00:02:38,100 --> 00:02:41,090 blocks of the Periodic Table by memory. 65 00:02:41,090 --> 00:02:44,580 But I don't want to neglect, disrespect the 66 00:02:44,580 --> 00:02:46,310 lanthanides and actinides. 67 00:02:46,310 --> 00:02:48,060 So we're going to have two contests. 68 00:02:48,060 --> 00:02:52,420 Mnemonics to help remember the names of the 69 00:02:52,420 --> 00:02:53,700 lanthanides and actinides. 70 00:02:53,700 --> 00:02:54,850 That's tricky to remember. 71 00:02:54,850 --> 00:03:03,590 So these are mnemonics contests. 72 00:03:03,590 --> 00:03:05,460 So here are some examples. 73 00:03:05,460 --> 00:03:08,650 Here's one, see lanthanum, cerium, praseodymium, 74 00:03:08,650 --> 00:03:10,440 neodymium and so on, all right? 75 00:03:10,440 --> 00:03:13,040 Obviously this one came from industry because of the slur 76 00:03:13,040 --> 00:03:14,430 against the Academy. 77 00:03:14,430 --> 00:03:16,910 Obviously, somebody in industry has no idea how hard 78 00:03:16,910 --> 00:03:17,770 we work here. 79 00:03:17,770 --> 00:03:20,560 And plus, look at this: "to dramatically help". 80 00:03:20,560 --> 00:03:23,010 This gigantic split infinitive. 81 00:03:23,010 --> 00:03:25,213 Clearly, clearly someone from industry. 82 00:03:28,410 --> 00:03:31,142 Here's another one that would help you memorize, I think. 83 00:03:35,664 --> 00:03:38,410 Now, this is obviously not referring to 3.091. 84 00:03:38,410 --> 00:03:39,730 It must be referring to some other 85 00:03:39,730 --> 00:03:41,636 chemistry professor here. 86 00:03:41,636 --> 00:03:43,490 I'll let that go unchallenged. 87 00:03:43,490 --> 00:03:46,570 Now, occasionally people ratchet up. 88 00:03:46,570 --> 00:03:50,020 And this was about six, seven years ago, a young man by the 89 00:03:50,020 --> 00:03:55,120 name of Blake Stacey, who was aware of the fact that there 90 00:03:55,120 --> 00:03:57,560 are 14 lanthanide elements because there 91 00:03:57,560 --> 00:03:59,750 are fourteen F electrons. 92 00:03:59,750 --> 00:04:03,570 And an Elizabethan sonnet has 14 lines. 93 00:04:03,570 --> 00:04:08,500 And so he took Sonnet 57 by Shakespeare in reference to 94 00:04:08,500 --> 00:04:11,250 the fact that lanthanum is element 57. 95 00:04:11,250 --> 00:04:18,120 And he wrote this in reference to Sonnet 57. 96 00:04:18,120 --> 00:04:21,690 And, of course, he knew he was going to win when he made 97 00:04:21,690 --> 00:04:24,520 samarium the word smelting, and being the chemical 98 00:04:24,520 --> 00:04:29,420 metallurgist I am, he had me at the fifth line. 99 00:04:29,420 --> 00:04:33,040 Actually, I showed this to Professor Sonenberg in 100 00:04:33,040 --> 00:04:37,760 Humanities, and she said, actually, this is pretty good. 101 00:04:37,760 --> 00:04:39,900 That's one of those times you look at and say, you wouldn't 102 00:04:39,900 --> 00:04:42,100 see this at Harvard. 103 00:04:42,100 --> 00:04:43,200 So now I'm going to show you one. 104 00:04:43,200 --> 00:04:44,360 Sometimes people ratchet up. 105 00:04:44,360 --> 00:04:46,980 A couple of years ago, there was a video. 106 00:04:46,980 --> 00:04:49,150 So let's take a look at that one. 107 00:04:49,150 --> 00:04:50,400 [VIDEO PLAYBACK] 108 00:05:06,190 --> 00:05:08,720 PROFESSOR: And she goes through various poses as a 109 00:05:08,720 --> 00:05:11,040 superhero of different elemental value. 110 00:05:11,040 --> 00:05:11,140 [END OF VIDEO PLAYBACK] 111 00:05:11,140 --> 00:05:14,800 PROFESSOR: But we don't have that much time. 112 00:05:14,800 --> 00:05:18,680 So anyways, September 25, 5:00 p.m. 113 00:05:18,680 --> 00:05:20,340 Eastern Daylight Time. 114 00:05:20,340 --> 00:05:24,940 Submit your entry, whether it's the big canisters of the 115 00:05:24,940 --> 00:05:28,120 Hollywood footage or whether it's just a 116 00:05:28,120 --> 00:05:31,090 14-line mnemonic device. 117 00:05:31,090 --> 00:05:32,700 And the prizes-- 118 00:05:32,700 --> 00:05:34,090 it's a contest, there are prizes-- 119 00:05:34,090 --> 00:05:39,680 I have ties and scarves from the American Chemical Society. 120 00:05:39,680 --> 00:05:40,060 [LAUGHTER] 121 00:05:40,060 --> 00:05:40,810 PROFESSOR: What are you laughing at? 122 00:05:40,810 --> 00:05:41,170 These things! 123 00:05:41,170 --> 00:05:41,730 Now look at me! 124 00:05:41,730 --> 00:05:42,850 This is going to be stylish. 125 00:05:42,850 --> 00:05:43,490 They're black. 126 00:05:43,490 --> 00:05:47,540 They've got elements from the Periodic Table on them. 127 00:05:47,540 --> 00:05:48,410 Very hot. 128 00:05:48,410 --> 00:05:49,110 Very hot. 129 00:05:49,110 --> 00:05:50,030 They're black. 130 00:05:50,030 --> 00:05:51,540 They look great. 131 00:05:51,540 --> 00:05:55,390 And we're going to present them on the Friday of the 132 00:05:55,390 --> 00:05:57,700 parents' weekend because the parents eat this stuff up. 133 00:06:01,390 --> 00:06:04,010 So now I think it's time to get back to learning. 134 00:06:04,010 --> 00:06:08,280 So last day we ended with the stoichiometry, and I showed 135 00:06:08,280 --> 00:06:11,290 you the Kroll process, how to make titanium. 136 00:06:11,290 --> 00:06:16,220 So the question that we never got to was how do we tell that 137 00:06:16,220 --> 00:06:19,980 magnesium has a higher affinity for chlorine than 138 00:06:19,980 --> 00:06:21,010 titanium does? 139 00:06:21,010 --> 00:06:24,130 How do we know that magnesium is going to reduce titanium 140 00:06:24,130 --> 00:06:26,490 tetrachloride to a sponge? 141 00:06:26,490 --> 00:06:29,290 So for that we have to look inside the atom. 142 00:06:29,290 --> 00:06:30,590 We have to look inside the atom. 143 00:06:30,590 --> 00:06:32,510 So that's what we're going to start doing today. 144 00:06:32,510 --> 00:06:34,400 And we're going to begin, as often we will, 145 00:06:34,400 --> 00:06:35,390 with a history lesson. 146 00:06:35,390 --> 00:06:38,680 So let's go back for a status report around the end of the 147 00:06:38,680 --> 00:06:39,650 19th century. 148 00:06:39,650 --> 00:06:42,740 So what did we know towards the end of the 19th century? 149 00:06:42,740 --> 00:06:46,460 The atom is electrically neutral. 150 00:06:46,460 --> 00:06:51,802 The negative charge is carried by electrons. 151 00:06:51,802 --> 00:06:57,350 We knew that there was some carrier of negative charge. 152 00:06:57,350 --> 00:07:01,850 We knew further that this electron is very, very tiny. 153 00:07:01,850 --> 00:07:03,870 Small mass. 154 00:07:03,870 --> 00:07:07,580 And so if it has a very small mass, then by difference, then 155 00:07:07,580 --> 00:07:10,560 the bulk of the mass of atom must be contained in the 156 00:07:10,560 --> 00:07:13,330 positive charge. 157 00:07:13,330 --> 00:07:16,860 So now the question is, what is the spatial distribution of 158 00:07:16,860 --> 00:07:17,930 charge inside an atom? 159 00:07:17,930 --> 00:07:19,440 You might say, well why do we want to know that? 160 00:07:19,440 --> 00:07:22,930 Well, we're trying to get a physical model of the atom so 161 00:07:22,930 --> 00:07:24,980 that then we can start to address the question of 162 00:07:24,980 --> 00:07:26,410 chemical reactivity. 163 00:07:26,410 --> 00:07:29,130 So we have got to know where all the players are before we 164 00:07:29,130 --> 00:07:31,370 can attribute action to them. 165 00:07:31,370 --> 00:07:34,720 So let's now take a look at models of the atom. 166 00:07:34,720 --> 00:07:40,330 For the first modern model of the atom we go to J. 167 00:07:40,330 --> 00:07:40,570 J. 168 00:07:40,570 --> 00:07:41,820 Thompson. 169 00:07:44,430 --> 00:07:44,710 J. 170 00:07:44,710 --> 00:07:44,940 J. 171 00:07:44,940 --> 00:07:48,590 Thompson, he was a professor of physics and director of the 172 00:07:48,590 --> 00:07:51,566 Cavendish lab at Cambridge University. 173 00:08:11,530 --> 00:08:13,170 The other Cambridge. 174 00:08:13,170 --> 00:08:15,480 Cambridge University. 175 00:08:15,480 --> 00:08:19,620 And this Cavendish Lab was named after Henry Cavendish. 176 00:08:19,620 --> 00:08:21,640 The same one who is credited with the discovery 177 00:08:21,640 --> 00:08:24,060 of hydrogen in 1766. 178 00:08:24,060 --> 00:08:27,500 He never married, and when he died he bequeathed this 179 00:08:27,500 --> 00:08:30,920 fortune to Cambridge University, and they took that 180 00:08:30,920 --> 00:08:34,060 money and established a physics laboratory, which is 181 00:08:34,060 --> 00:08:36,110 still in operation to this day. 182 00:08:36,110 --> 00:08:39,380 So what did J. 183 00:08:39,380 --> 00:08:39,570 J. 184 00:08:39,570 --> 00:08:40,430 Thompson tell us? 185 00:08:40,430 --> 00:08:44,580 He said the electrons were distributed throughout a 186 00:08:44,580 --> 00:08:48,360 uniformly charged positive sphere of atomic dimensions. 187 00:09:17,240 --> 00:09:18,410 So that's the text. 188 00:09:18,410 --> 00:09:22,500 Now let's make this cartoon, because that makes more sense. 189 00:09:22,500 --> 00:09:23,920 Visualize it a little bit better. 190 00:09:23,920 --> 00:09:26,320 So it looks a little bit like this. 191 00:09:26,320 --> 00:09:32,350 So here's a sphere of atomic dimension. 192 00:09:32,350 --> 00:09:37,570 Electrons are these tiny little things distributed 193 00:09:37,570 --> 00:09:41,130 throughout the positive sphere. 194 00:09:44,350 --> 00:09:47,570 And this is massive because the electrons have 195 00:09:47,570 --> 00:09:49,940 very, very low mass. 196 00:09:49,940 --> 00:09:53,530 And just to be clear, there are no protons. 197 00:09:53,530 --> 00:09:54,660 No protons. 198 00:09:54,660 --> 00:09:55,740 So this isn't positive. 199 00:09:55,740 --> 00:09:57,440 It's a positive chargeness. 200 00:09:57,440 --> 00:10:00,240 It's just a big positive blur. 201 00:10:00,240 --> 00:10:02,140 And then the little electrons inside. 202 00:10:02,140 --> 00:10:12,010 So the electrons are negative, and they're tiny and low-mass, 203 00:10:12,010 --> 00:10:13,260 and they're mobile. 204 00:10:15,200 --> 00:10:17,450 He didn't say much about how they move, but you can imagine 205 00:10:17,450 --> 00:10:19,870 that they move, and maybe they even spin. 206 00:10:19,870 --> 00:10:20,540 And so on. 207 00:10:20,540 --> 00:10:22,820 And this was known as the Plum Pudding Model. 208 00:10:27,555 --> 00:10:30,550 There's a big cultural bias here. 209 00:10:30,550 --> 00:10:33,610 So even though I grew up in British Canada, I never had 210 00:10:33,610 --> 00:10:34,950 this stuff. 211 00:10:34,950 --> 00:10:38,540 But my understanding is plum pudding is this dish that's 212 00:10:38,540 --> 00:10:41,620 served at holidays and Christmas-time. 213 00:10:41,620 --> 00:10:45,660 So the custard is the charge, the positive charge. 214 00:10:45,660 --> 00:10:50,010 And these little bits of fruit are the electrons. 215 00:10:50,010 --> 00:10:50,650 And they're throughout. 216 00:10:50,650 --> 00:10:51,970 At Christmas-time, they might even put 217 00:10:51,970 --> 00:10:52,930 little charms in here. 218 00:10:52,930 --> 00:10:55,910 Like a little wishbone or something for good luck. 219 00:10:55,910 --> 00:10:58,510 And you pull it out and all that kind of stuff. 220 00:10:58,510 --> 00:11:02,080 Yeah that's merry, old England. 221 00:11:02,080 --> 00:11:04,370 So this is the Plum Pudding Model. 222 00:11:04,370 --> 00:11:06,080 And that's what was in place. 223 00:11:06,080 --> 00:11:09,150 By the way, we've been using the term electron, but J. 224 00:11:09,150 --> 00:11:09,880 J. 225 00:11:09,880 --> 00:11:11,630 did not like the term electron. 226 00:11:11,630 --> 00:11:15,090 Actually, he won his Nobel Prize for the-- quote, 227 00:11:15,090 --> 00:11:17,160 unquote-- the discovery of the electron. 228 00:11:17,160 --> 00:11:19,800 Just as Cavendish didn't discover hydrogen, he 229 00:11:19,800 --> 00:11:21,020 characterized it. 230 00:11:21,020 --> 00:11:21,270 J. 231 00:11:21,270 --> 00:11:21,460 J. 232 00:11:21,460 --> 00:11:23,560 Thompson characterized the electron. 233 00:11:23,560 --> 00:11:25,630 What did he in particular characterize? 234 00:11:25,630 --> 00:11:27,890 He characterized the charge-to-mass ratio. 235 00:11:27,890 --> 00:11:30,930 He made the first quantitative measure of the charge-to-mass 236 00:11:30,930 --> 00:11:32,180 ratio of the electron. 237 00:11:32,180 --> 00:11:34,210 But he never used the term, electron. 238 00:11:34,210 --> 00:11:35,550 He called it the corpuscle. 239 00:11:48,260 --> 00:11:53,190 He called it the corpuscle of electrical charge, whereas 240 00:11:53,190 --> 00:11:57,700 this is really sort of an elementary charge. 241 00:11:57,700 --> 00:11:58,970 The corpuscle. 242 00:11:58,970 --> 00:12:05,500 And fortunately there was another British chemist. In 243 00:12:05,500 --> 00:12:08,070 fact, he was an electrochemist. His name was 244 00:12:08,070 --> 00:12:13,230 John Stoney, who, while I think that Thompson was a 245 00:12:13,230 --> 00:12:17,420 brilliant man, I wasn't crazy about his literary choices. 246 00:12:17,420 --> 00:12:21,420 And it was Stoney who said, let's call the term electron, 247 00:12:21,420 --> 00:12:25,050 coming from the Greek term, elektra, which is the Greek 248 00:12:25,050 --> 00:12:26,040 word for amber. 249 00:12:26,040 --> 00:12:28,810 And you know if you rub amber, you'll build up static 250 00:12:28,810 --> 00:12:31,880 charge, and so on. 251 00:12:31,880 --> 00:12:34,730 That's where we got the electron from. 252 00:12:34,730 --> 00:12:38,000 So that looks pretty good. 253 00:12:38,000 --> 00:12:41,450 So that's our theory. 254 00:12:41,450 --> 00:12:43,670 And what happens next? 255 00:12:43,670 --> 00:12:47,130 Well, what happens next is that we've got to put this 256 00:12:47,130 --> 00:12:49,530 theory to the test. And the person who puts the theory to 257 00:12:49,530 --> 00:12:52,285 the test is a man by the name of Ernest Rutherford. 258 00:12:56,680 --> 00:12:58,350 Rutherford was an interesting character. 259 00:12:58,350 --> 00:13:02,530 He came from New Zealand and he was born on a farm. 260 00:13:02,530 --> 00:13:04,990 It was a family with 12 children. 261 00:13:04,990 --> 00:13:07,580 You notice Mendeleyev came from a family of 14, this guy 262 00:13:07,580 --> 00:13:09,750 comes from a family of 12. 263 00:13:09,750 --> 00:13:12,680 So you learn how to survive. 264 00:13:12,680 --> 00:13:16,170 He worked on a farm so he was very handy, and that came in 265 00:13:16,170 --> 00:13:20,010 to play as his career progressed. 266 00:13:20,010 --> 00:13:22,080 He was a brilliant experimentalist. He was able 267 00:13:22,080 --> 00:13:24,870 to do experiments where others failed. 268 00:13:24,870 --> 00:13:32,400 And he did this experiment where he was a professor of 269 00:13:32,400 --> 00:13:42,840 physics at Victoria University in Manchester in the UK. 270 00:13:47,670 --> 00:13:52,570 Now, he came out of New Zealand, got a scholarship to 271 00:13:52,570 --> 00:13:54,920 study at Cambridge University. 272 00:13:54,920 --> 00:13:57,340 And he was actually a research student for J. 273 00:13:57,340 --> 00:13:57,540 J. 274 00:13:57,540 --> 00:13:58,530 Thompson. 275 00:13:58,530 --> 00:14:01,720 And he conducted his thesis research under J. 276 00:14:01,720 --> 00:14:02,500 J. 277 00:14:02,500 --> 00:14:07,250 and during that time his thesis research was about the 278 00:14:07,250 --> 00:14:09,125 properties of charged particles. 279 00:14:19,270 --> 00:14:24,200 And they were very interested in gases and radioactive 280 00:14:24,200 --> 00:14:26,500 elements, ionizing radiation, the whole thing. 281 00:14:26,500 --> 00:14:30,070 The Cavendish lab was a beehive of activity. 282 00:14:30,070 --> 00:14:34,670 And what he did under his PhD was he understood both the 283 00:14:34,670 --> 00:14:37,080 alpha particle and the beta particle. 284 00:14:37,080 --> 00:14:39,100 First, he identified what they are. 285 00:14:39,100 --> 00:14:41,040 The alpha particle was determined to 286 00:14:41,040 --> 00:14:42,780 be the helium nucleus. 287 00:14:42,780 --> 00:14:45,700 So this is helium that's lost both of its electrons. 288 00:14:45,700 --> 00:14:49,000 So it's just protons and neutrons in the nucleus. 289 00:14:49,000 --> 00:14:49,930 Completely naked. 290 00:14:49,930 --> 00:14:51,050 No electrons. 291 00:14:51,050 --> 00:14:54,380 And then the beta particle, which other people in physics 292 00:14:54,380 --> 00:14:57,240 had been referring to this mysterious beta particle, he 293 00:14:57,240 --> 00:14:58,850 made the connection between the beta 294 00:14:58,850 --> 00:15:00,080 particle and the electron. 295 00:15:00,080 --> 00:15:03,220 So the same electron that's over here and attributed to 296 00:15:03,220 --> 00:15:06,580 the negative charge within the nucleus is also a free 297 00:15:06,580 --> 00:15:08,060 particle that can go through space. 298 00:15:08,060 --> 00:15:10,190 And these are taken from your reading. 299 00:15:10,190 --> 00:15:15,360 And you can see that if you send the particle beam through 300 00:15:15,360 --> 00:15:19,120 a charged plate, the negative plate here being the lower 301 00:15:19,120 --> 00:15:21,830 plate, the positive particle, which in this case is the 302 00:15:21,830 --> 00:15:25,940 alpha particle, will bend down towards the negative plate. 303 00:15:25,940 --> 00:15:28,740 And the negative particle, being the free electron, is 304 00:15:28,740 --> 00:15:30,680 bent in the opposite direction. 305 00:15:30,680 --> 00:15:32,710 So these are the kinds of experiments they would do. 306 00:15:32,710 --> 00:15:34,730 And they also looked at their ability to 307 00:15:34,730 --> 00:15:37,600 penetrate different media. 308 00:15:37,600 --> 00:15:46,905 So when it comes to their ability to penetrate solids, 309 00:15:46,905 --> 00:15:48,500 they differentiate themselves. 310 00:15:48,500 --> 00:15:51,760 So they alpha particle is quite poor 311 00:15:51,760 --> 00:15:53,020 at penetrating solids. 312 00:15:53,020 --> 00:15:55,230 So you see in the cartoon there, the alpha particle is 313 00:15:55,230 --> 00:15:58,600 stopped even by that little sheet of paper. 314 00:15:58,600 --> 00:16:02,610 So it doesn't do so well here, whereas the beta particle, the 315 00:16:02,610 --> 00:16:05,760 electron, can go zooming right through the paper and is 316 00:16:05,760 --> 00:16:08,040 stopped by the lead. 317 00:16:08,040 --> 00:16:10,860 And then over here they were also studying their ability to 318 00:16:10,860 --> 00:16:12,690 ionize gases. 319 00:16:12,690 --> 00:16:15,190 So if you take a gas and you bombard it with alpha 320 00:16:15,190 --> 00:16:17,230 particles, will you get a lot of ionization? 321 00:16:17,230 --> 00:16:19,150 Yes or no, et cetera. 322 00:16:19,150 --> 00:16:22,830 And what they found was that it was a complementary, that 323 00:16:22,830 --> 00:16:26,150 the alpha particle is pretty good at ionizing gases, 324 00:16:26,150 --> 00:16:29,900 whereas the beta particle is poor at ionizing gases, and in 325 00:16:29,900 --> 00:16:30,680 fact, is stopped. 326 00:16:30,680 --> 00:16:32,220 This is why, if you have an electron 327 00:16:32,220 --> 00:16:33,320 beam you need a vacuum. 328 00:16:33,320 --> 00:16:36,380 Otherwise, the electron will be dissipated in very, very 329 00:16:36,380 --> 00:16:37,440 short order. 330 00:16:37,440 --> 00:16:39,130 So after doing this work with J. 331 00:16:39,130 --> 00:16:42,660 J., he got a teaching job in Canada at McGill 332 00:16:42,660 --> 00:16:44,770 University up north. 333 00:16:44,770 --> 00:16:48,530 And while he was there he continued to do work on the 334 00:16:48,530 --> 00:16:52,510 origin of alpha particles and won the Nobel Prize for his 335 00:16:52,510 --> 00:16:54,800 work while he was at McGill. 336 00:16:54,800 --> 00:17:01,380 And so when he determined that the alpha particle origin in 337 00:17:01,380 --> 00:17:13,720 the decomposition, the disintegration of elements. 338 00:17:13,720 --> 00:17:19,300 And believe it or not, in this work back in 1906, 1907, he 339 00:17:19,300 --> 00:17:23,530 was already anticipating nuclear fission because he was 340 00:17:23,530 --> 00:17:28,080 saying that if you put thorium or polonium into a tube, you 341 00:17:28,080 --> 00:17:30,610 can expect that it will emit alpha particles. 342 00:17:30,610 --> 00:17:33,150 Well, conservation of mass says they have got to be 343 00:17:33,150 --> 00:17:34,080 coming from somewhere. 344 00:17:34,080 --> 00:17:36,450 And if they're not coming from out here, they have got to be 345 00:17:36,450 --> 00:17:37,620 coming from inside. 346 00:17:37,620 --> 00:17:38,670 This was brilliant work. 347 00:17:38,670 --> 00:17:42,930 This is Rutherford, young man in Montreal, gets the Nobel 348 00:17:42,930 --> 00:17:44,730 Prize in 1908. 349 00:17:44,730 --> 00:17:49,930 And then he goes to Victoria University, and he sets up 350 00:17:49,930 --> 00:17:51,640 this experiment. 351 00:17:51,640 --> 00:17:53,760 Critical experiment. 352 00:17:53,760 --> 00:17:54,940 I mean, imagine this guy. 353 00:17:54,940 --> 00:17:56,550 I mean, he's already got the Nobel Prize. 354 00:17:56,550 --> 00:17:58,670 He could just put his feet up. 355 00:17:58,670 --> 00:17:59,590 No, he keeps going. 356 00:17:59,590 --> 00:18:00,610 So this is the experiment. 357 00:18:00,610 --> 00:18:02,740 It's called the Rutherford-Geiger-Marsden 358 00:18:02,740 --> 00:18:03,650 experiment. 359 00:18:03,650 --> 00:18:06,340 Because Rutherford was the brains behind it and Geiger 360 00:18:06,340 --> 00:18:08,060 and Marsden were the guys in the lab. 361 00:18:08,060 --> 00:18:09,390 And so here's the experiment. 362 00:18:09,390 --> 00:18:12,670 So what he's going to do is he's going to put this model 363 00:18:12,670 --> 00:18:15,370 to the test. We're going to see if this model 364 00:18:15,370 --> 00:18:16,690 makes sense or not. 365 00:18:16,690 --> 00:18:19,270 So he's got a gold foil-- now they used different elements, 366 00:18:19,270 --> 00:18:22,430 but ultimately they loved gold because gold, first of all, is 367 00:18:22,430 --> 00:18:23,800 noble and it doesn't oxide. 368 00:18:23,800 --> 00:18:27,830 So it's pure, even in atmospheric oxygen. 369 00:18:27,830 --> 00:18:30,450 And secondly, we've known since antiquity we can 370 00:18:30,450 --> 00:18:33,030 physically deform gold and make it into something 371 00:18:33,030 --> 00:18:34,830 sub-paper thin. 372 00:18:34,830 --> 00:18:35,610 So that's what they did. 373 00:18:35,610 --> 00:18:39,670 They beat this thing down to 600 374 00:18:39,670 --> 00:18:41,990 nanometers thick, 0.6 micron. 375 00:18:41,990 --> 00:18:46,610 And they used alpha particles here. 376 00:18:46,610 --> 00:18:49,840 Radium, polonium, thorium as the source in the lead 377 00:18:49,840 --> 00:18:50,890 container and so on. 378 00:18:50,890 --> 00:18:54,330 And this stream of alpha particles comes zooming out at 379 00:18:54,330 --> 00:18:59,450 energies of 7.68 million electron volts per particle. 380 00:18:59,450 --> 00:19:04,930 So this is like a cannon with a pumpkin in front of it. 381 00:19:04,930 --> 00:19:09,610 And they're going to shoot these at the foil. 382 00:19:09,610 --> 00:19:11,280 So what's the purpose here? 383 00:19:11,280 --> 00:19:12,610 They want to see what's going on. 384 00:19:12,610 --> 00:19:16,230 And if you imagine that we are shooting alpha particles, 385 00:19:16,230 --> 00:19:20,410 which are positive, and I've got a wall here of all of 386 00:19:20,410 --> 00:19:24,250 these nuclei that are essentially positive 387 00:19:24,250 --> 00:19:27,780 chargeness, uniformly distributed with these tiny, 388 00:19:27,780 --> 00:19:30,980 tiny little electrons of almost no mass, you'd expect 389 00:19:30,980 --> 00:19:33,090 that most of these particles are just going to go zooming 390 00:19:33,090 --> 00:19:34,350 on through. 391 00:19:34,350 --> 00:19:37,800 Beyond a certain thickness, I might start seeing some 392 00:19:37,800 --> 00:19:38,650 attenuation. 393 00:19:38,650 --> 00:19:41,010 But if I get the gold film really thin, I should just go 394 00:19:41,010 --> 00:19:42,820 blasting these all through. 395 00:19:42,820 --> 00:19:44,510 Well, what they find is, two things. 396 00:19:44,510 --> 00:19:47,260 First of all, most of the particles do go through. 397 00:19:47,260 --> 00:19:49,450 When they go through, they're deflected a little bit. 398 00:19:49,450 --> 00:19:51,870 They don't just go through, they are deflected. 399 00:19:51,870 --> 00:19:54,220 And most of them are deflected through low angles. 400 00:19:54,220 --> 00:19:58,020 But a small number of them are deflected through high angles. 401 00:19:58,020 --> 00:20:00,190 They almost go straight back at the source. 402 00:20:03,450 --> 00:20:07,790 So if you've got that set of data, that doesn't support 403 00:20:07,790 --> 00:20:09,480 this model. 404 00:20:09,480 --> 00:20:13,950 This model cannot be sustained in the light of those data. 405 00:20:13,950 --> 00:20:15,180 It's a very important experiment. 406 00:20:15,180 --> 00:20:16,560 By the way, how do they count these things? 407 00:20:16,560 --> 00:20:18,420 Well, Geiger is the same guy who give 408 00:20:18,420 --> 00:20:19,620 us the Geiger counter. 409 00:20:19,620 --> 00:20:24,320 Geiger was a technician that worked for Rutherford. 410 00:20:24,320 --> 00:20:26,710 And he developed this screen, they called it a 411 00:20:26,710 --> 00:20:27,650 scintillation screen. 412 00:20:27,650 --> 00:20:30,590 It was coated with zinc sulfide. 413 00:20:30,590 --> 00:20:34,050 And so when alpha particles bounced and they hit the 414 00:20:34,050 --> 00:20:37,560 screen, they would excite electrons in the screen and 415 00:20:37,560 --> 00:20:40,690 then cause a scintilla, a spark. 416 00:20:40,690 --> 00:20:43,230 And then what you do is you just get a graduate student or 417 00:20:43,230 --> 00:20:47,340 some other source of abundant, cheap labor-- and you have a 418 00:20:47,340 --> 00:20:49,340 whole bunch of graduate students sitting here-- and 419 00:20:49,340 --> 00:20:51,700 they count. 420 00:20:51,700 --> 00:20:54,980 That's how it was done in good old days, 1909. 421 00:20:54,980 --> 00:20:59,190 And so they counted what the distribution was. 422 00:20:59,190 --> 00:21:02,206 So that's the experiment. 423 00:21:07,250 --> 00:21:08,500 So this is taken from your book. 424 00:21:08,500 --> 00:21:10,370 So this what you'd expect. 425 00:21:10,370 --> 00:21:11,520 And this is what they saw. 426 00:21:11,520 --> 00:21:13,850 So this is small angles and this is large angles. 427 00:21:13,850 --> 00:21:17,280 Theaters of the angle here. 428 00:21:17,280 --> 00:21:18,530 Now Marsden, who's the third? 429 00:21:18,530 --> 00:21:19,310 There's a third person. 430 00:21:19,310 --> 00:21:19,980 Marsden. 431 00:21:19,980 --> 00:21:22,180 Marsden's not too different from you. 432 00:21:22,180 --> 00:21:24,120 Marsden was about 20 years old at the time. 433 00:21:24,120 --> 00:21:26,565 He dropped out of school and then he came to Rutherford, 434 00:21:26,565 --> 00:21:28,640 and he said, I'm looking for a job. 435 00:21:28,640 --> 00:21:30,590 In those days, you couldn't return to college. 436 00:21:30,590 --> 00:21:32,260 If you dropped out, finished. 437 00:21:32,260 --> 00:21:33,910 You had to stay all the way through. 438 00:21:33,910 --> 00:21:36,380 Once you dropped out, they slam the door behind you. 439 00:21:36,380 --> 00:21:39,620 But Rutherford, he was different. 440 00:21:39,620 --> 00:21:41,090 He looked at people on the basis of 441 00:21:41,090 --> 00:21:42,570 their intrinsic value. 442 00:21:42,570 --> 00:21:44,220 He didn't care about title. 443 00:21:44,220 --> 00:21:46,640 And so he said to Marsden, OK, you want to do 444 00:21:46,640 --> 00:21:47,630 something for me? 445 00:21:47,630 --> 00:21:54,240 Here's your question, I like you to imagine an alternative 446 00:21:54,240 --> 00:21:55,880 model of the atom. 447 00:21:55,880 --> 00:21:58,460 And here's the alternative model of the atom. 448 00:21:58,460 --> 00:22:02,380 What Rutherford said was, suppose instead, if this is 449 00:22:02,380 --> 00:22:05,360 the dimension of the atom, instead of having positive 450 00:22:05,360 --> 00:22:09,020 charge uniformly distributed, he said, what if we have 451 00:22:09,020 --> 00:22:13,340 positive charge concentrated at one point and then out here 452 00:22:13,340 --> 00:22:14,730 we have the negative charge? 453 00:22:14,730 --> 00:22:16,230 So here's the positive charge. 454 00:22:18,730 --> 00:22:20,525 And here's a whole bunch of negative charge. 455 00:22:25,300 --> 00:22:27,480 And now here's the next one. 456 00:22:27,480 --> 00:22:29,800 And here's the next one. 457 00:22:29,800 --> 00:22:30,780 And so on. 458 00:22:30,780 --> 00:22:33,820 And now we're going to shoot these helium nuclei. 459 00:22:33,820 --> 00:22:35,130 See what's in between here? 460 00:22:35,130 --> 00:22:38,500 This is a void, taking from Democritus. 461 00:22:38,500 --> 00:22:43,750 And so now if I shoot the positive helium nuclei here, 462 00:22:43,750 --> 00:22:45,910 if they get close to this positive 463 00:22:45,910 --> 00:22:48,090 charge they'll be deflected. 464 00:22:48,090 --> 00:22:51,190 If they don't get close to the positive charge, they just go 465 00:22:51,190 --> 00:22:53,020 right through. 466 00:22:53,020 --> 00:22:56,180 And once in awhile they get almost on axis, in which case 467 00:22:56,180 --> 00:22:57,600 they fling back. 468 00:22:57,600 --> 00:23:00,900 This model would be consistent with the data set I just 469 00:23:00,900 --> 00:23:01,850 showed you. 470 00:23:01,850 --> 00:23:05,290 And then to go further, he says to Marsden, I'm going to 471 00:23:05,290 --> 00:23:09,140 tell you what the distribution of high-angle scattering was, 472 00:23:09,140 --> 00:23:15,320 you tell me what is the ratio between the radius of the 473 00:23:15,320 --> 00:23:19,550 nucleus, where the positive charge is to the-- excuse me, 474 00:23:19,550 --> 00:23:22,520 I'm showing you the diameter, so this is the diameter of the 475 00:23:22,520 --> 00:23:26,570 nucleus versus the diameter of the atom. 476 00:23:26,570 --> 00:23:29,310 What would be the ratio of the two? 477 00:23:29,310 --> 00:23:33,910 I mean, it's gold, so I know I got 79 plus here. 478 00:23:33,910 --> 00:23:35,580 And I've got 2 plus. 479 00:23:35,580 --> 00:23:36,880 And I've got a 79 plus. 480 00:23:36,880 --> 00:23:41,720 What would be the size of the sphere of 79 plus that would 481 00:23:41,720 --> 00:23:45,250 deflect something of 2 plus through this angle? 482 00:23:45,250 --> 00:23:46,160 So that's Marsden. 483 00:23:46,160 --> 00:23:48,210 It's not bad for a kid that's been out of school for a 484 00:23:48,210 --> 00:23:48,820 couple of years. 485 00:23:48,820 --> 00:23:51,090 That's his problem. 486 00:23:51,090 --> 00:23:51,650 So he did. 487 00:23:51,650 --> 00:23:54,580 He did the calculation. 488 00:23:54,580 --> 00:23:58,710 He did the calculation and Marsden figured out that the 489 00:23:58,710 --> 00:24:07,440 radius of the nucleus to the radius of the atom is on the 490 00:24:07,440 --> 00:24:12,840 order of about 1 to 10,000. 491 00:24:12,840 --> 00:24:17,390 That means most of the gold foil is void. 492 00:24:17,390 --> 00:24:20,030 Most of the gold foil is nothing. 493 00:24:20,030 --> 00:24:23,160 And you've got all this mass, highly dense, 494 00:24:23,160 --> 00:24:25,400 concentrated here. 495 00:24:25,400 --> 00:24:29,270 So this is the Rutherford model, which was called the 496 00:24:29,270 --> 00:24:30,520 nuclear model. 497 00:24:34,370 --> 00:24:37,230 This was proposed by Rutherford because it has such 498 00:24:37,230 --> 00:24:38,580 a thing is a nucleus. 499 00:24:38,580 --> 00:24:41,570 He coined the term, nucleus. 500 00:24:41,570 --> 00:24:46,500 So that's a big step forward from this thing here. 501 00:24:46,500 --> 00:24:51,220 So you'd think that the physics 502 00:24:51,220 --> 00:24:52,510 community would be ecstatic. 503 00:24:52,510 --> 00:24:54,570 That now we've got a model that squares with the data. 504 00:24:54,570 --> 00:24:57,810 Well, what do you think the reaction to Rutherford's 505 00:24:57,810 --> 00:24:59,660 announcement was? 506 00:24:59,660 --> 00:25:00,660 Condemnation. 507 00:25:00,660 --> 00:25:02,140 Derision. 508 00:25:02,140 --> 00:25:03,080 People didn't like it. 509 00:25:03,080 --> 00:25:03,840 They laughed at him. 510 00:25:03,840 --> 00:25:06,600 They said, well, this is crazy. 511 00:25:06,600 --> 00:25:08,610 There's a couple of problems with this. 512 00:25:08,610 --> 00:25:20,270 So strong negative reaction to Rutherford's model. 513 00:25:20,270 --> 00:25:24,450 And here the two major objections that people posed. 514 00:25:24,450 --> 00:25:28,600 First of all, they talked about nuclear collapse. 515 00:25:28,600 --> 00:25:35,530 They said if you've got a system of negative particles 516 00:25:35,530 --> 00:25:39,580 revolving around a positive nucleus, electrostatic forces 517 00:25:39,580 --> 00:25:42,800 are going to cause them to be drawn to one another. 518 00:25:42,800 --> 00:25:45,520 What's going to keep the electrons from collapsing into 519 00:25:45,520 --> 00:25:47,060 the nucleus? 520 00:25:47,060 --> 00:25:49,410 That was the first objection. 521 00:25:49,410 --> 00:25:51,800 Coulombic attraction. 522 00:25:51,800 --> 00:25:53,780 Coulombic, electrostatic, same thing. 523 00:25:53,780 --> 00:25:55,710 If you want to use a man's name, Coulombic. 524 00:25:55,710 --> 00:25:58,740 If you don't want to use a man's name, electrostatic. 525 00:25:58,740 --> 00:26:05,930 Coulombic attraction between plus and minus. 526 00:26:05,930 --> 00:26:10,560 And the second one was, OK, suppose for some reason we 527 00:26:10,560 --> 00:26:14,810 don't understand that the electron doesn't collapse, it 528 00:26:14,810 --> 00:26:18,530 stays in orbit, it's still not going to work. 529 00:26:18,530 --> 00:26:20,350 Because you run out of energy. 530 00:26:20,350 --> 00:26:23,320 If you take a charged particle, a charged particle 531 00:26:23,320 --> 00:26:26,000 that accelerates consumes energy. 532 00:26:26,000 --> 00:26:29,560 Acceleration, as you know, can mean either change in speed or 533 00:26:29,560 --> 00:26:30,910 change in direction. 534 00:26:30,910 --> 00:26:35,660 So if the electron is revolving at a constant speed, 535 00:26:35,660 --> 00:26:37,530 it has to change direction; otherwise, it will 536 00:26:37,530 --> 00:26:39,040 fly out of the room. 537 00:26:39,040 --> 00:26:42,160 So changing direction means acceleration, which means what 538 00:26:42,160 --> 00:26:44,410 keeps the energy in the electron? 539 00:26:44,410 --> 00:26:45,970 Why doesn't the electron just run out of 540 00:26:45,970 --> 00:26:48,080 energy and just stop? 541 00:26:48,080 --> 00:26:50,120 Even if you can prevent it from collapsing, 542 00:26:50,120 --> 00:26:52,000 it will just stop. 543 00:26:52,000 --> 00:26:53,905 So this is the problem of energy deficit. 544 00:26:56,420 --> 00:26:58,760 Energy deficit. 545 00:26:58,760 --> 00:27:00,110 Well, what powers the electron? 546 00:27:03,450 --> 00:27:05,405 What powers the accelerating electron? 547 00:27:14,290 --> 00:27:15,540 So that's a problem. 548 00:27:18,320 --> 00:27:20,960 So now the story continues. 549 00:27:20,960 --> 00:27:23,680 The next chapter is 1912. 550 00:27:23,680 --> 00:27:25,130 Because this is 1911. 551 00:27:25,130 --> 00:27:28,420 In 1912, a young Danish businessman by the name of 552 00:27:28,420 --> 00:27:31,590 Niels Bohr. 553 00:27:31,590 --> 00:27:34,770 Niels Bohr just finished his PhD in Copenhagen and he got a 554 00:27:34,770 --> 00:27:37,700 fellowship from the Carlsburg Brewery Foundation. 555 00:27:37,700 --> 00:27:40,540 Carlsburg Brewery put up money for science. 556 00:27:40,540 --> 00:27:43,310 So he won a Carlsburg fellowship. 557 00:27:43,310 --> 00:27:46,790 And he was a young physicist. And he knew that in the UK 558 00:27:46,790 --> 00:27:49,700 there was a controversy brewing between the model of 559 00:27:49,700 --> 00:27:51,350 Rutherford and the model of J. 560 00:27:51,350 --> 00:27:51,550 J. 561 00:27:51,550 --> 00:27:52,320 Thompson. 562 00:27:52,320 --> 00:27:54,190 So he says, you know what I'm going to do? 563 00:27:54,190 --> 00:27:55,710 I've got a year, I got money. 564 00:27:55,710 --> 00:27:57,250 I'm going to spend six months with J. 565 00:27:57,250 --> 00:27:57,430 J. 566 00:27:57,430 --> 00:27:59,790 Thompson, I'm going to spend six months with Ernest 567 00:27:59,790 --> 00:28:00,580 Rutherford. 568 00:28:00,580 --> 00:28:01,110 And that's what he did. 569 00:28:01,110 --> 00:28:03,910 So he goes and he spends six months at the 570 00:28:03,910 --> 00:28:08,180 Cavendish lab with J. 571 00:28:08,180 --> 00:28:08,890 J. 572 00:28:08,890 --> 00:28:11,660 and then he goes up to Manchester and he spends three 573 00:28:11,660 --> 00:28:16,150 months at Manchester with Rutherford. 574 00:28:16,150 --> 00:28:17,280 Why didn't he spend six months? 575 00:28:17,280 --> 00:28:20,920 Because he got a job offer and he went back to Copenhagen to 576 00:28:20,920 --> 00:28:22,170 start his teaching duties. 577 00:28:25,370 --> 00:28:27,090 And what he did is he developed a 578 00:28:27,090 --> 00:28:29,240 quantitative model for us. 579 00:28:29,240 --> 00:28:32,310 He developed a quantitative model. 580 00:28:32,310 --> 00:28:35,540 And that's all part of what I showed you the other day. 581 00:28:35,540 --> 00:28:37,050 We recognize patterns. 582 00:28:37,050 --> 00:28:39,760 That's what the Rutherford, Geiger, Marsden 583 00:28:39,760 --> 00:28:40,660 experiment gave us. 584 00:28:40,660 --> 00:28:45,320 The pattern of the distribution of alpha particle 585 00:28:45,320 --> 00:28:46,380 deflections. 586 00:28:46,380 --> 00:28:49,380 So now we need to develop a quantitative model that will 587 00:28:49,380 --> 00:28:53,370 explain the observations, and if it's a really good model, 588 00:28:53,370 --> 00:28:56,770 it will make predictions that, again, can be tested by 589 00:28:56,770 --> 00:28:57,360 experiment. 590 00:28:57,360 --> 00:29:01,640 So we ratchet back and forth between experiment, model. 591 00:29:01,640 --> 00:29:04,670 Experiment, model. 592 00:29:04,670 --> 00:29:10,520 So he proposes the model, not with J. 593 00:29:10,520 --> 00:29:11,210 J., because J. 594 00:29:11,210 --> 00:29:13,720 J., I don't know what he did there. 595 00:29:13,720 --> 00:29:16,890 This is where he wants to propose the model. 596 00:29:16,890 --> 00:29:18,140 Quantitative model. 597 00:29:21,880 --> 00:29:25,950 To Rutherford's atom. 598 00:29:30,780 --> 00:29:34,890 Let's take a look at what we've got there. 599 00:29:34,890 --> 00:29:37,830 Now, big lesson here. 600 00:29:37,830 --> 00:29:39,500 How do you announce a model? 601 00:29:39,500 --> 00:29:41,870 You don't put an ad in the newspaper. 602 00:29:41,870 --> 00:29:43,630 This is the scientific literature. 603 00:29:43,630 --> 00:29:44,830 This is not Google. 604 00:29:44,830 --> 00:29:45,980 This is not Wikipedia. 605 00:29:45,980 --> 00:29:47,830 This is a primary source. 606 00:29:47,830 --> 00:29:50,660 This is how science is communicated. 607 00:29:50,660 --> 00:29:52,010 So this is a journal. 608 00:29:52,010 --> 00:29:54,180 It's called Philosophical Magazine 609 00:29:54,180 --> 00:29:55,760 and Journal of Science. 610 00:29:55,760 --> 00:29:57,790 It goes all the way back to the 1600s. 611 00:29:57,790 --> 00:30:00,860 In fact, when I was a freshman at the University of Toronto 612 00:30:00,860 --> 00:30:04,360 we had copies of Phil Mag going back all 613 00:30:04,360 --> 00:30:05,980 the way to the 1600s. 614 00:30:05,980 --> 00:30:08,810 And these were not facsimiles, these were real copies. 615 00:30:08,810 --> 00:30:11,920 And I was in the stacks and I was reading something by-- 616 00:30:11,920 --> 00:30:12,280 I don't know-- 617 00:30:12,280 --> 00:30:15,310 Lord Kelvin, you know late 1800s, and I said gee, well, 618 00:30:15,310 --> 00:30:17,470 if I've got Lord Kelvin, then maybe I can go over here to 619 00:30:17,470 --> 00:30:21,580 the early 1800s and read Humphry Davy and, gee, if can 620 00:30:21,580 --> 00:30:25,260 keep going, and going and I pull out a leather-bound 621 00:30:25,260 --> 00:30:30,320 edition of Phil Mag from the 1660s, and I open the book and 622 00:30:30,320 --> 00:30:34,530 there's a paper about gravity by Isaac Newton. 623 00:30:34,530 --> 00:30:37,510 And that's how science is communicated. 624 00:30:37,510 --> 00:30:39,490 So I urge you to go to the library and 625 00:30:39,490 --> 00:30:40,610 read primary sources. 626 00:30:40,610 --> 00:30:42,280 Most of this stuff is available online. 627 00:30:42,280 --> 00:30:44,100 You can just sit at your desk and you 628 00:30:44,100 --> 00:30:46,520 can zoom in to history. 629 00:30:46,520 --> 00:30:49,860 So this is Phil Mag and this is London, 630 00:30:49,860 --> 00:30:52,630 Edinburgh and dublin. 631 00:30:52,630 --> 00:30:56,490 See this is 1913, so Ireland was not a free state yet. 632 00:30:56,490 --> 00:31:01,680 So Dublin was a British city. 633 00:31:01,680 --> 00:31:04,420 London, Edinburgh, Dublin. 634 00:31:04,420 --> 00:31:05,920 There's a close-up of it. 635 00:31:05,920 --> 00:31:09,990 July 1913, On the Constitution of Atoms and Molecules by 636 00:31:09,990 --> 00:31:13,430 Niels Bohr, Doctor of Philosophy, Copenhagen. 637 00:31:13,430 --> 00:31:16,030 And it was communicated by Professor Ernest Rutherford, 638 00:31:16,030 --> 00:31:20,910 FRS, Fellow of the Royal Society. 639 00:31:20,910 --> 00:31:23,260 So, let's read. 640 00:31:23,260 --> 00:31:24,960 It's in English. 641 00:31:24,960 --> 00:31:28,080 In order to explain results of experiments on scattering of 642 00:31:28,080 --> 00:31:31,160 alpha rays by matter, Professor Rutherford has given 643 00:31:31,160 --> 00:31:33,790 a theory of the structure of atoms. You 644 00:31:33,790 --> 00:31:34,930 see the dagger here? 645 00:31:34,930 --> 00:31:37,790 Down here, Ernest Rutherford, Phil Mag, duh-duh-duh-duh. 646 00:31:37,790 --> 00:31:38,810 There's a citation. 647 00:31:38,810 --> 00:31:40,900 See, attribution. 648 00:31:40,900 --> 00:31:44,330 According to this theory, the atoms consist of a positively 649 00:31:44,330 --> 00:31:47,660 charged nucleus surrounded by a system of electrons kept 650 00:31:47,660 --> 00:31:51,270 together by attractive forces from the nucleus. 651 00:31:51,270 --> 00:31:53,440 That's what keeps them from just fleeing anywhere, and 652 00:31:53,440 --> 00:31:55,720 they don't go in, but they vwomp. 653 00:31:55,720 --> 00:31:58,060 The total negative charge of the electrons is equal to the 654 00:31:58,060 --> 00:31:59,450 positive charge of the nucleus. 655 00:31:59,450 --> 00:32:04,140 Further, the nucleus is assumed to be the seat of the 656 00:32:04,140 --> 00:32:06,810 essential part of the mass of the atom and have linear 657 00:32:06,810 --> 00:32:09,600 dimensions exceedingly small compared with the linear 658 00:32:09,600 --> 00:32:12,330 dimensions of the whole atom. 659 00:32:12,330 --> 00:32:14,700 This is beautifully written. 660 00:32:14,700 --> 00:32:16,216 Clear. 661 00:32:16,216 --> 00:32:19,320 It's textbook quality and it's written by a man whose native 662 00:32:19,320 --> 00:32:21,980 language isn't even English. 663 00:32:21,980 --> 00:32:24,050 Read the literature. 664 00:32:24,050 --> 00:32:26,530 The number of electrons in an atom is deduced to be 665 00:32:26,530 --> 00:32:29,380 approximately equal to half the atomic weight. 666 00:32:29,380 --> 00:32:32,470 Great interest is to be attributed to this atom model. 667 00:32:32,470 --> 00:32:34,240 You have to know a little bit about Bohr. 668 00:32:34,240 --> 00:32:36,530 Bohr used this phrase, great interest. That was his way of 669 00:32:36,530 --> 00:32:39,720 saying, embroiled in controversy. 670 00:32:39,720 --> 00:32:43,240 If someone said something that he didn't agree with, instead 671 00:32:43,240 --> 00:32:46,400 of saying, I think that's nonsense, he say, very 672 00:32:46,400 --> 00:32:47,290 interesting. 673 00:32:47,290 --> 00:32:48,140 Very interesting. 674 00:32:48,140 --> 00:32:51,120 So great interest is to be attributed to this atom model. 675 00:32:51,120 --> 00:32:55,650 That means people are in pitched battle on both sides. 676 00:32:55,650 --> 00:32:57,810 For as Rutherford has shown, the assumption of the 677 00:32:57,810 --> 00:33:01,030 existence of nuclei as those in question seems to be 678 00:33:01,030 --> 00:33:03,510 necessary in order to account for the results of experiments 679 00:33:03,510 --> 00:33:06,720 on large-angle scattering of the alpha rays. 680 00:33:06,720 --> 00:33:08,970 Another footnote: Geiger and Marsden. 681 00:33:08,970 --> 00:33:13,110 Geiger and Marsden published their results in this journal. 682 00:33:13,110 --> 00:33:15,480 In an attempt to explain some of the properties of matter on 683 00:33:15,480 --> 00:33:17,800 the basis of this atom model, we meet, however, with 684 00:33:17,800 --> 00:33:21,590 difficulties of a serious nature arising from the 685 00:33:21,590 --> 00:33:24,870 apparent instability of the system of electrons. 686 00:33:24,870 --> 00:33:28,950 Difficulties purposely avoided in atom models previously 687 00:33:28,950 --> 00:33:29,540 considered. 688 00:33:29,540 --> 00:33:32,240 For instance, in the one proposed by Sir J. 689 00:33:32,240 --> 00:33:32,510 J. 690 00:33:32,510 --> 00:33:37,240 Thompson, which is to say, mmm, you know, it's curious. 691 00:33:37,240 --> 00:33:43,040 You condemn the Rutherford model because he's got 692 00:33:43,040 --> 00:33:45,930 electrons in motion, which means they're accelerating in 693 00:33:45,930 --> 00:33:47,100 energy deficit. 694 00:33:47,100 --> 00:33:50,100 But in the Plum Pudding Model, the electrons are 695 00:33:50,100 --> 00:33:51,090 in motion, and J. 696 00:33:51,090 --> 00:33:51,310 J. 697 00:33:51,310 --> 00:33:53,140 Thompson is silent about it. 698 00:33:53,140 --> 00:33:56,770 So this is a very aimed barb right at J. 699 00:33:56,770 --> 00:33:56,990 J. 700 00:33:56,990 --> 00:33:58,500 Thompson done elegantly. 701 00:33:58,500 --> 00:34:01,490 With this elegant slap in the face. 702 00:34:01,490 --> 00:34:03,950 You know this is how scientists do it. 703 00:34:03,950 --> 00:34:06,140 They don't go, oh you're ugly , and your 704 00:34:06,140 --> 00:34:07,390 mother dresses you funny. 705 00:34:07,390 --> 00:34:11,860 Instead they write things like this, difficulties purposely 706 00:34:11,860 --> 00:34:13,660 avoided in atom models previously 707 00:34:13,660 --> 00:34:15,440 considered for instance. 708 00:34:15,440 --> 00:34:19,360 So this is sort of yeah, how about you, huh? 709 00:34:19,360 --> 00:34:20,680 But anyway, we can go on and on. 710 00:34:20,680 --> 00:34:23,150 But down here, the result of the discussion of these 711 00:34:23,150 --> 00:34:25,990 questions seems to be a general acknowledgment of the 712 00:34:25,990 --> 00:34:30,090 inadequacy of classical electrodynamics in describing 713 00:34:30,090 --> 00:34:33,560 the behavior of systems of atomic size. 714 00:34:33,560 --> 00:34:38,310 So he's saying that you can't use classical electrodynamics 715 00:34:38,310 --> 00:34:40,256 down to subatomic dimensions. 716 00:34:42,760 --> 00:34:45,340 He's saying that those models, any more than you can use 717 00:34:45,340 --> 00:34:50,240 planetary models down to human dimensions, this, in many 718 00:34:50,240 --> 00:34:54,300 respects, is foretelling nanotechnology. 719 00:34:54,300 --> 00:34:58,890 He's saying the properties we know, of how things behave in 720 00:34:58,890 --> 00:35:04,930 the Newtonian world are not necessarily valid at atomic 721 00:35:04,930 --> 00:35:06,376 dimensions. 722 00:35:06,376 --> 00:35:08,320 This is very important stuff. 723 00:35:11,460 --> 00:35:14,780 Anyway, so what I did is I went through the paper and 724 00:35:14,780 --> 00:35:17,140 I've reduced the content of the paper to these things 725 00:35:17,140 --> 00:35:19,210 called postulates. 726 00:35:19,210 --> 00:35:21,380 So Rutherford's atom is correct. 727 00:35:21,380 --> 00:35:22,940 That's the first thing. 728 00:35:22,940 --> 00:35:25,660 Classical electromagnetic theory not applicable to the 729 00:35:25,660 --> 00:35:27,340 orbiting electron. 730 00:35:27,340 --> 00:35:29,080 And you're going to get-- the PDF and all this is going to 731 00:35:29,080 --> 00:35:33,170 be posted, so don't feel like you have to be a super 732 00:35:33,170 --> 00:35:34,260 stenographer here. 733 00:35:34,260 --> 00:35:36,310 Newtonian mechanics is applicable to 734 00:35:36,310 --> 00:35:37,350 the orbiting electron. 735 00:35:37,350 --> 00:35:39,370 So you can see, wait a minute it's sort of like cafeteria 736 00:35:39,370 --> 00:35:40,360 physics here. 737 00:35:40,360 --> 00:35:42,640 Electrodynamics doesn't apply, Newtonian 738 00:35:42,640 --> 00:35:43,930 mechanics does apply. 739 00:35:43,930 --> 00:35:45,670 And the answer is, yeah. 740 00:35:45,670 --> 00:35:46,770 That's what we're going to do here. 741 00:35:46,770 --> 00:35:49,410 We'll build a model and we're going to try these ideas out. 742 00:35:49,410 --> 00:35:51,140 And if they're crazy, how are we going to 743 00:35:51,140 --> 00:35:52,160 know they're crazy? 744 00:35:52,160 --> 00:35:54,330 Because there's going to be data that refute. 745 00:35:54,330 --> 00:35:56,360 But if we get data that supports all this, then 746 00:35:56,360 --> 00:35:57,650 there's only one conclusion. 747 00:35:57,650 --> 00:36:02,460 This thing makes sense up to a point. 748 00:36:02,460 --> 00:36:04,860 The energy of the electron is conserved in the system. 749 00:36:04,860 --> 00:36:07,610 It's bond is kinetic plus potential. 750 00:36:07,610 --> 00:36:09,970 The quantization through angular momentum. 751 00:36:09,970 --> 00:36:12,630 And lastly, the Planck-Einstein relation 752 00:36:12,630 --> 00:36:14,220 applying to electron transition. 753 00:36:14,220 --> 00:36:16,570 So now I'm going to take all this and I'm going to write 754 00:36:16,570 --> 00:36:17,820 out the model for you. 755 00:36:17,820 --> 00:36:19,540 Now, I don't want you to say, oh, he's 756 00:36:19,540 --> 00:36:20,460 going to derive something. 757 00:36:20,460 --> 00:36:21,870 Do we have to know derivations? 758 00:36:21,870 --> 00:36:23,090 This is the only time I'm going to derive 759 00:36:23,090 --> 00:36:24,080 something for you. 760 00:36:24,080 --> 00:36:26,610 The reason is, it teaches the model. 761 00:36:26,610 --> 00:36:28,640 It teaches how the model is based on 762 00:36:28,640 --> 00:36:29,890 assumptions and so on. 763 00:36:29,890 --> 00:36:32,880 But I don't expect you to memorize things because that's 764 00:36:32,880 --> 00:36:34,190 not the way things work. 765 00:36:34,190 --> 00:36:39,280 So let's go starting with this point here. 766 00:36:39,280 --> 00:36:48,790 This point here is Bohr model atom. 767 00:36:48,790 --> 00:36:51,430 So it's Bohr's representation of the Rutherford model. 768 00:36:51,430 --> 00:36:54,500 We can call it a nuclear model or a planetary model. 769 00:36:57,590 --> 00:37:01,580 Because you've got orbiting electrons. 770 00:37:01,580 --> 00:37:03,890 Now, first important point. 771 00:37:03,890 --> 00:37:05,810 The Bohr model is the simplest model. 772 00:37:05,810 --> 00:37:07,900 It works for a one electron system. 773 00:37:07,900 --> 00:37:09,870 So he has a single electron. 774 00:37:09,870 --> 00:37:12,420 Planetary model, single electron. 775 00:37:15,640 --> 00:37:21,105 And this orbits the positive nucleus. 776 00:37:23,630 --> 00:37:24,655 So you might say, one electron, 777 00:37:24,655 --> 00:37:25,420 well, what's that mean? 778 00:37:25,420 --> 00:37:27,710 Well, obviously it means atomic hydrogen. 779 00:37:27,710 --> 00:37:31,250 But it could mean helium plus. 780 00:37:31,250 --> 00:37:33,260 That's a one electron system. 781 00:37:33,260 --> 00:37:36,040 It could mean lithium 2 plus. 782 00:37:36,040 --> 00:37:40,270 It could mean roentgenium 110 plus. 783 00:37:40,270 --> 00:37:41,710 That's a one electron system. 784 00:37:41,710 --> 00:37:43,630 And this is all gas. 785 00:37:43,630 --> 00:37:44,650 Gas phase. 786 00:37:44,650 --> 00:37:45,420 No solids here. 787 00:37:45,420 --> 00:37:46,740 Gas phase. 788 00:37:46,740 --> 00:37:51,330 So it's an isolated nucleus with one electron around it. 789 00:37:51,330 --> 00:37:53,770 That's how we're going to begin. 790 00:37:53,770 --> 00:37:55,430 And here's what it looks like. 791 00:37:55,430 --> 00:37:59,140 I'm going to put the nucleus, first of all not to scale, 792 00:37:59,140 --> 00:38:04,020 because we're not going to draw 10,000 to 1. 793 00:38:04,020 --> 00:38:12,750 Over here is the nucleus with z positive charge. 794 00:38:12,750 --> 00:38:17,020 And then out here is the electron in orbit. 795 00:38:17,020 --> 00:38:21,160 This is the lone electron in orbit. 796 00:38:21,160 --> 00:38:25,390 And this distance is r. 797 00:38:25,390 --> 00:38:27,760 The distance from the nucleus. 798 00:38:27,760 --> 00:38:28,680 You're going to say, well, is that from the 799 00:38:28,680 --> 00:38:29,570 outside or the inside? 800 00:38:29,570 --> 00:38:32,630 It's 10,000 to 1; it doesn't matter. 801 00:38:32,630 --> 00:38:33,880 Forget about it. 802 00:38:36,600 --> 00:38:38,960 So now let's use this concept. 803 00:38:38,960 --> 00:38:41,360 We're going to say it's a conservative system and so the 804 00:38:41,360 --> 00:38:43,920 energy of the system is simply going to be the 805 00:38:43,920 --> 00:38:45,770 energy of the electron. 806 00:38:48,820 --> 00:38:50,270 You might say, well, why don't you consider the 807 00:38:50,270 --> 00:38:50,770 energy of the nucleus? 808 00:38:50,770 --> 00:38:52,530 Because the nucleus is, relatively speaking, 809 00:38:52,530 --> 00:38:54,020 stationary. 810 00:38:54,020 --> 00:38:56,710 To use Rutherford's colorful language, he says when an 811 00:38:56,710 --> 00:39:00,190 elephant has fleas, it's the fleas that do the jumping. 812 00:39:00,190 --> 00:39:03,710 So you don't care about that energy of the 813 00:39:03,710 --> 00:39:04,830 nucleus in this case. 814 00:39:04,830 --> 00:39:07,120 So the energy of the electron is the 815 00:39:07,120 --> 00:39:09,020 kinetic plus the potential. 816 00:39:09,020 --> 00:39:12,950 So the kinetic energy, we're saying it's 1/2 mv squared 817 00:39:12,950 --> 00:39:16,580 because it's Newtonian mechanics apply. 818 00:39:16,580 --> 00:39:19,480 See number 3. 819 00:39:19,480 --> 00:39:24,090 So that's 1/2 mv squared, where v is the velocity. 820 00:39:24,090 --> 00:39:25,500 So that's the kinetic, and then what's 821 00:39:25,500 --> 00:39:26,430 the potential energy? 822 00:39:26,430 --> 00:39:28,830 The potential energy here is electrostatic. 823 00:39:28,830 --> 00:39:31,270 Because that's the energy that's stored here is due to 824 00:39:31,270 --> 00:39:33,200 the Coulombic forces between them. 825 00:39:33,200 --> 00:39:38,520 So that's going to be q1, q2 over 4 pi epsilon 826 00:39:38,520 --> 00:39:40,610 0 divided by r. 827 00:39:45,880 --> 00:39:48,830 So what I'm going to do here, we have to just for convention 828 00:39:48,830 --> 00:39:53,090 I'm going to always choose that q1 in my derivation, q1 829 00:39:53,090 --> 00:39:56,700 will be the charge on the nucleus. so q1 will equal z, 830 00:39:56,700 --> 00:39:59,200 which is the proton number here, times 831 00:39:59,200 --> 00:40:00,260 the elementary charge. 832 00:40:00,260 --> 00:40:02,270 Remember e is the elementary charge. 833 00:40:02,270 --> 00:40:03,690 It's not the charge on the electron. 834 00:40:03,690 --> 00:40:07,060 So sometimes I use the word e with a minus 835 00:40:07,060 --> 00:40:08,680 sign, meaning the electron. 836 00:40:08,680 --> 00:40:12,170 But this is e meaning the elementary charge. 837 00:40:12,170 --> 00:40:16,000 z times e and then q2, which is the charge on the electron, 838 00:40:16,000 --> 00:40:18,800 is minus the elementary charge e. 839 00:40:18,800 --> 00:40:21,020 So we're always going to have minus e out here. 840 00:40:21,020 --> 00:40:22,270 What varies is z. 841 00:40:25,390 --> 00:40:27,600 And so we're going to make some substitutions. 842 00:40:27,600 --> 00:40:29,250 So this is going to be what? 843 00:40:29,250 --> 00:40:34,850 It's going to be 1/2 mass of the electron times velocity of 844 00:40:34,850 --> 00:40:36,070 the electron squared. 845 00:40:36,070 --> 00:40:40,030 And now q1 is ze and q2 is minus z, so 846 00:40:40,030 --> 00:40:42,880 that's minus ze squared. 847 00:40:42,880 --> 00:40:49,350 And then that'll be over 4 pi epsilon 0 r. 848 00:40:49,350 --> 00:40:53,990 And I'm going to call this thing equation 1. 849 00:40:53,990 --> 00:41:00,620 And by the way you can find all of this information by 850 00:41:00,620 --> 00:41:03,100 looking at your table of constants. 851 00:41:03,100 --> 00:41:05,210 So see, epsilon 0 sitting here. 852 00:41:05,210 --> 00:41:06,840 Permittivity of vacuum. 853 00:41:06,840 --> 00:41:10,730 There it is, 8.85 times 10 to the minus 12 farads per meter. 854 00:41:10,730 --> 00:41:13,930 Elementary charge 1.6 times 10 to the minus 19 Coulombs. 855 00:41:13,930 --> 00:41:19,770 Electron mass, 9.1 times 10 to the minus 31 kilograms. And 856 00:41:19,770 --> 00:41:22,070 what's this 4 pi epsilon 0 doing here? 857 00:41:22,070 --> 00:41:24,320 Well we know this is going to give us joules. 858 00:41:24,320 --> 00:41:26,540 And this is going to give us joules. 859 00:41:26,540 --> 00:41:30,240 And the epsilon 0 is the factor that renders 860 00:41:30,240 --> 00:41:33,730 electrostatic units on to the same plane 861 00:41:33,730 --> 00:41:36,850 as mechanical units. 862 00:41:36,850 --> 00:41:39,150 If I plug in-- this is going to be Coulombs, it's Coulombs 863 00:41:39,150 --> 00:41:42,330 squared, and this is going to be meters, and now this things 864 00:41:42,330 --> 00:41:44,050 is farads per meter. 865 00:41:44,050 --> 00:41:46,350 And I got farads per meter times meters divided by 866 00:41:46,350 --> 00:41:47,120 Coulombs squared. 867 00:41:47,120 --> 00:41:48,660 I don't care. 868 00:41:48,660 --> 00:41:51,340 This, with impunity is joules. 869 00:41:51,340 --> 00:41:52,510 Because this is an energy unit. 870 00:41:52,510 --> 00:41:56,170 And this is Systeme Internationale. 871 00:41:56,170 --> 00:42:00,950 And this is kilograms times meters per second, meters per 872 00:42:00,950 --> 00:42:06,040 second and how many apples in a bushel and-- 873 00:42:06,040 --> 00:42:07,020 forget it! 874 00:42:07,020 --> 00:42:09,630 Put this in kilograms. Put this in in meters per second. 875 00:42:09,630 --> 00:42:12,990 With impunity, it's in joules. 876 00:42:12,990 --> 00:42:14,710 So that's what that thing does there. 877 00:42:14,710 --> 00:42:15,030 Alright. 878 00:42:15,030 --> 00:42:15,650 Good. 879 00:42:15,650 --> 00:42:18,720 So let's keep going. 880 00:42:18,720 --> 00:42:19,620 Postulate 3. 881 00:42:19,620 --> 00:42:22,600 Newtonian mechanics applies to orbiting electrons. 882 00:42:22,600 --> 00:42:25,680 So orbiting electron, it's in a stationary orbit. 883 00:42:25,680 --> 00:42:28,440 So that's the thing. 884 00:42:28,440 --> 00:42:37,130 So postulate 3 implies that the sum of the forces acting 885 00:42:37,130 --> 00:42:39,360 on the electron must be 0. 886 00:42:39,360 --> 00:42:42,330 This is a force balance, right? 887 00:42:42,330 --> 00:42:44,650 If the forces are out of balance, the electrons are 888 00:42:44,650 --> 00:42:47,320 either going to move closer to the nucleus or move farther 889 00:42:47,320 --> 00:42:48,700 from the nucleus. 890 00:42:48,700 --> 00:42:51,010 So that's equal to, again-- 891 00:42:51,010 --> 00:42:57,470 it's a sum of a dynamic force and a Coulombic force, or 892 00:42:57,470 --> 00:42:58,950 electrostatic. 893 00:42:58,950 --> 00:43:01,990 Here I just noticed a nice parity here. 894 00:43:01,990 --> 00:43:05,230 So these are technical terms, but we can give them human 895 00:43:05,230 --> 00:43:08,920 terms. So the dynamic force, there's a Newtonian force, 896 00:43:08,920 --> 00:43:12,160 this is a Newtonian force and this is a Coulombic force, 897 00:43:12,160 --> 00:43:15,290 after the two people that are associated with the ideas. 898 00:43:15,290 --> 00:43:19,760 Charges interaction are Coulombic, 899 00:43:19,760 --> 00:43:20,750 blah, blah, blah, blah. 900 00:43:20,750 --> 00:43:24,080 So now lets substitute in. 901 00:43:24,080 --> 00:43:27,700 So we know that if you've got something orbiting, something 902 00:43:27,700 --> 00:43:30,730 tethered, then the dynamic force on that, that pulls the 903 00:43:30,730 --> 00:43:36,080 object away on a tether is mv squared over r. 904 00:43:36,080 --> 00:43:45,660 And the electrostatic is q1 q2 over 4 pi epsilon 0 r squared. 905 00:43:45,660 --> 00:43:47,920 Force goes as 1 over r squared. 906 00:43:47,920 --> 00:43:49,620 Energy goes as 1 over r. 907 00:43:49,620 --> 00:43:50,620 How do you know? 908 00:43:50,620 --> 00:43:54,590 Well, one way to think about it is, you know energy is the 909 00:43:54,590 --> 00:43:57,210 result of a force moving through a distance. 910 00:43:57,210 --> 00:43:59,680 You say, I'm working really hard, and I say I don't see 911 00:43:59,680 --> 00:44:02,300 any force moving through a distance. 912 00:44:02,300 --> 00:44:03,270 That's a joke. 913 00:44:03,270 --> 00:44:04,840 So here's energy. 914 00:44:04,840 --> 00:44:05,370 So force. 915 00:44:05,370 --> 00:44:08,760 So if this is 1 over r squared, the integral of 1 916 00:44:08,760 --> 00:44:10,700 over r squared is minus 1 over r. 917 00:44:10,700 --> 00:44:13,080 If you get these backwards, you integrate 1 over r, you're 918 00:44:13,080 --> 00:44:15,660 going to get natural log of r, which makes no sense. 919 00:44:15,660 --> 00:44:16,190 That's one way. 920 00:44:16,190 --> 00:44:19,650 Or the other way is, you can just remember. 921 00:44:19,650 --> 00:44:22,420 So anyways we're going to plug into those values. 922 00:44:22,420 --> 00:44:24,340 And what do we get? 923 00:44:24,340 --> 00:44:26,160 What we get there is this. 924 00:44:26,160 --> 00:44:30,780 We get mv squared over r. 925 00:44:30,780 --> 00:44:34,190 q1 is z times e. q2 is minus z. 926 00:44:34,190 --> 00:44:40,506 So it's minus ze squared over 4 pi epsilon 0 r squared. 927 00:44:40,506 --> 00:44:42,626 And I'm going to call this equation 2. 928 00:44:48,400 --> 00:44:49,950 So now we keep going. 929 00:44:49,950 --> 00:44:55,160 Next one, energy quantized through its angular momentum. 930 00:44:55,160 --> 00:44:56,190 This is really critical. 931 00:44:56,190 --> 00:44:59,330 This is the major breakthrough by Bohr. 932 00:44:59,330 --> 00:45:01,210 Now what do we mean by quantization? 933 00:45:01,210 --> 00:45:05,640 I told you that in 1909, Millikan had figured out that 934 00:45:05,640 --> 00:45:07,960 electrical charge is quantized. 935 00:45:07,960 --> 00:45:10,910 Now quantization had already been annunciated by 936 00:45:10,910 --> 00:45:12,880 Max Planck in 1909. 937 00:45:12,880 --> 00:45:17,090 You see, the classical theory of radiation gave this 938 00:45:17,090 --> 00:45:20,110 prediction for intensity as a function of wavelength. 939 00:45:20,110 --> 00:45:23,400 They called this the explosion, the 940 00:45:23,400 --> 00:45:24,490 collapse of the theory. 941 00:45:24,490 --> 00:45:27,020 As you go to low wavelength, the intensity 942 00:45:27,020 --> 00:45:28,420 goes without abatement. 943 00:45:28,420 --> 00:45:31,100 But these are the spectra that were measured. 944 00:45:31,100 --> 00:45:34,590 Depending on the temperature of the gas, you get this 945 00:45:34,590 --> 00:45:35,360 distribution. 946 00:45:35,360 --> 00:45:39,150 So how to get the distribution to turn around at lower values 947 00:45:39,150 --> 00:45:40,040 of wavelength? 948 00:45:40,040 --> 00:45:43,070 And in order to do that, Planck suggested that light is 949 00:45:43,070 --> 00:45:46,370 composed of energy packets, or quanta. 950 00:45:46,370 --> 00:45:52,590 That light is a stream of individual energy bits. 951 00:45:52,590 --> 00:45:55,460 And the elementary unit of electromagnetic radiation is 952 00:45:55,460 --> 00:45:57,490 the photon. 953 00:45:57,490 --> 00:45:58,780 And you can say, well I don't understand, where 954 00:45:58,780 --> 00:46:00,000 goes he get that from? 955 00:46:00,000 --> 00:46:01,270 That's not the way to think about it. 956 00:46:01,270 --> 00:46:03,340 Say, if you make this assumption 957 00:46:03,340 --> 00:46:05,900 you get these curves. 958 00:46:05,900 --> 00:46:07,180 And then figure out what it means. 959 00:46:07,180 --> 00:46:10,535 You can't make everything anthropomorphic. 960 00:46:10,535 --> 00:46:14,630 If this were the case, and furthermore if the energy of 961 00:46:14,630 --> 00:46:18,700 one of these quanta was related to its frequency-- 962 00:46:18,700 --> 00:46:21,790 and wavelength and frequency are inversely related-- 963 00:46:21,790 --> 00:46:25,020 then the proportionality constant is h, which we now 964 00:46:25,020 --> 00:46:28,170 have designated the Planck constant in honor of Planck, 965 00:46:28,170 --> 00:46:30,200 then you get this. 966 00:46:30,200 --> 00:46:32,270 People grew to accept it. 967 00:46:32,270 --> 00:46:34,430 1900, he gets a Nobel Prize for it. 968 00:46:34,430 --> 00:46:35,040 La de da! 969 00:46:35,040 --> 00:46:36,710 But who knows what light is anyways. 970 00:46:36,710 --> 00:46:39,220 It has no mass, it's kind of mysterious. 971 00:46:39,220 --> 00:46:43,040 1900, the whole concept of action at a distance was 972 00:46:43,040 --> 00:46:44,470 strange to people. 973 00:46:44,470 --> 00:46:49,330 The notion that something could affect you, from me, 974 00:46:49,330 --> 00:46:52,490 without physical contact, this was a new idea. 975 00:46:52,490 --> 00:46:55,970 We take it for granted, but this was very new. 976 00:46:55,970 --> 00:46:58,190 So it's kind of mysterious, they said, OK, he's a 977 00:46:58,190 --> 00:46:59,330 physicist, who knows? 978 00:46:59,330 --> 00:47:01,780 And it worked! 979 00:47:01,780 --> 00:47:03,350 But it's light. 980 00:47:03,350 --> 00:47:08,920 Now what Bohr is going to say is the electron moving in 981 00:47:08,920 --> 00:47:12,180 orbit, he says, I'm going to apply the same concept of 982 00:47:12,180 --> 00:47:15,130 quantization to the electron moving in orbit. 983 00:47:18,770 --> 00:47:21,120 Well, that's different. 984 00:47:21,120 --> 00:47:30,750 And using this value he gives us mvr, which is the angular 985 00:47:30,750 --> 00:47:36,900 momentum is quantized n h over 2 pi. 986 00:47:36,900 --> 00:47:39,890 h is the Planck Constant and n is an integer. 987 00:47:39,890 --> 00:47:43,330 1, 2 3 4, et cetera. 988 00:47:43,330 --> 00:47:45,450 So this is the quantum condition and this will be 989 00:47:45,450 --> 00:47:46,690 equation 3. 990 00:47:46,690 --> 00:47:49,510 And I have three equations and three unknowns, and what I'm 991 00:47:49,510 --> 00:47:52,430 going to do next day is come back and show you the solution 992 00:47:52,430 --> 00:47:58,260 of the equations and how they give us a set of equations 993 00:47:58,260 --> 00:48:00,850 that allow us to compare with data. 994 00:48:00,850 --> 00:48:04,490 So let's jump to the thing. 995 00:48:04,490 --> 00:48:07,010 And by the way the Planck constant is there. 996 00:48:07,010 --> 00:48:09,110 Now Niels Bohr eventually won the Nobel Prize. 997 00:48:09,110 --> 00:48:10,490 He was widely revered. 998 00:48:10,490 --> 00:48:13,470 He achieved the stature on a par with Einstein. 999 00:48:13,470 --> 00:48:16,340 If you go to Denmark, it's still not part of the European 1000 00:48:16,340 --> 00:48:19,050 Union, you can still get the 500 Kroner note if you change 1001 00:48:19,050 --> 00:48:19,960 a 100-dollar bill there. 1002 00:48:19,960 --> 00:48:22,550 And there's Niels Bohr with this pipe. 1003 00:48:22,550 --> 00:48:26,700 And you can see the concept of things rotating 1004 00:48:26,700 --> 00:48:28,400 around it an so on. 1005 00:48:28,400 --> 00:48:31,040 There's a young Niels Bohr. 1006 00:48:31,040 --> 00:48:32,900 This is Bohr with Werner Heisenberg. 1007 00:48:32,900 --> 00:48:37,630 Heisenberg was a post-doc who worked with Bohr in 1925 and 1008 00:48:37,630 --> 00:48:40,650 annunciated the Uncertainty Principle, which we will study 1009 00:48:40,650 --> 00:48:42,450 a few lectures from now. 1010 00:48:42,450 --> 00:48:45,900 This is a chemical conference sponsored by 1011 00:48:45,900 --> 00:48:48,420 chemical company Solvay. 1012 00:48:48,420 --> 00:48:51,140 Brussels 1930, there's Bohr and Einstein. 1013 00:48:51,140 --> 00:48:52,330 They loved hats. 1014 00:48:52,330 --> 00:48:55,450 This is the Hamburg, this is Borsalino. 1015 00:48:55,450 --> 00:48:57,160 Here's Bohr mixing it up with royalty. 1016 00:48:57,160 --> 00:48:58,835 This is a young Queen Elizabeth of England. 1017 00:48:58,835 --> 00:49:00,190 There's Prince Phillip. 1018 00:49:00,190 --> 00:49:03,720 This is the royalty Danish family. 1019 00:49:03,720 --> 00:49:06,500 Bohr loved music and here is with Louis Armstrong 1020 00:49:06,500 --> 00:49:10,960 undoubtedly talking about the resonant structures within the 1021 00:49:10,960 --> 00:49:13,330 tube here and how to get the various 1022 00:49:13,330 --> 00:49:14,580 harmonics and overtones. 1023 00:49:16,940 --> 00:49:18,580 Now last thing, a little bit about hydrogen. 1024 00:49:18,580 --> 00:49:20,860 We've been studying hydrogen here, the one electron atom. 1025 00:49:20,860 --> 00:49:25,120 But there are isotopes of hydrogen. 1026 00:49:25,120 --> 00:49:27,480 The original was discovered by Henry Cavendish. 1027 00:49:30,180 --> 00:49:35,350 There is one form of hydrogen that has a neutron in addition 1028 00:49:35,350 --> 00:49:36,050 to the proton. 1029 00:49:36,050 --> 00:49:38,880 That's the deuterium, from which we can get 1030 00:49:38,880 --> 00:49:40,170 heavy water, D2O. 1031 00:49:40,170 --> 00:49:42,800 This was discovered here in New York at Columbia 1032 00:49:42,800 --> 00:49:45,010 University by Harold Urey. 1033 00:49:45,010 --> 00:49:49,220 And then lastly, there's a second isotope of hydrogen 1034 00:49:49,220 --> 00:49:51,430 that consists of two neutrons and a proton. 1035 00:49:51,430 --> 00:49:53,930 That's tritium and it was discovered at the Cavendish 1036 00:49:53,930 --> 00:49:55,280 lab by Ernest Rutherford. 1037 00:49:55,280 --> 00:49:58,030 He was active right up to his death. 1038 00:49:58,030 --> 00:50:01,380 In fact, it is argued that Rutherford did his best work 1039 00:50:01,380 --> 00:50:04,330 after he got the Nobel Prize. 1040 00:50:04,330 --> 00:50:05,550 Your book is showing this. 1041 00:50:05,550 --> 00:50:07,360 It's nice to follow. 1042 00:50:07,360 --> 00:50:10,630 We started with Dalton and now we're here and then later, in 1043 00:50:10,630 --> 00:50:12,430 another week or so, we'll be down here. 1044 00:50:12,430 --> 00:50:16,230 And here's the sort of the intellectual road map that 1045 00:50:16,230 --> 00:50:19,060 takes you to modern atomic theory. 1046 00:50:19,060 --> 00:50:22,950 So with that I'll dismiss the class and 1047 00:50:22,950 --> 00:50:24,910 we'll see you on Wednesday.