1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,850 Commons license. 3 00:00:03,850 --> 00:00:06,060 Your support will help MIT OpenCourseWare 4 00:00:06,060 --> 00:00:10,150 continue to offer high quality educational resources for free. 5 00:00:10,150 --> 00:00:12,690 To make a donation or to view additional materials 6 00:00:12,690 --> 00:00:16,445 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,445 --> 00:00:17,070 at ocw.mit.edu. 8 00:00:20,550 --> 00:00:23,139 CATHERINE DRENNAN: Let's try the countdown again. 9 00:00:23,139 --> 00:00:24,680 You can just give it to them for now. 10 00:00:24,680 --> 00:00:25,820 We'll figure it out later. 11 00:00:43,815 --> 00:00:47,040 I like to ask people to explain, now 12 00:00:47,040 --> 00:00:50,430 that they know what the right answer is, 13 00:00:50,430 --> 00:00:53,219 if someone will explain why that is the right answer. 14 00:00:53,219 --> 00:00:55,260 And I know it's a big class, and people sometimes 15 00:00:55,260 --> 00:00:56,880 get nervous about talking. 16 00:00:56,880 --> 00:00:58,740 So I bribe people. 17 00:00:58,740 --> 00:01:02,630 So today, the person who answers why that is correct 18 00:01:02,630 --> 00:01:07,488 will get an MIT chemistry T-shirt. 19 00:01:07,488 --> 00:01:07,987 OK. 20 00:01:11,070 --> 00:01:13,890 AUDIENCE: All right, let's see. 21 00:01:13,890 --> 00:01:16,590 If you're using 5 moles of N2, you 22 00:01:16,590 --> 00:01:20,450 need 15 moles of hydrogen gas. 23 00:01:20,450 --> 00:01:22,560 Since there's not enough hydrogen gas-- 24 00:01:22,560 --> 00:01:26,160 there's only 10 moles-- that means the hydrogen gas should 25 00:01:26,160 --> 00:01:30,990 be the limiting reactant since you would need roughly 3.33 26 00:01:30,990 --> 00:01:32,619 moles of N2 for it. 27 00:01:32,619 --> 00:01:33,660 CATHERINE DRENNAN: Great. 28 00:01:33,660 --> 00:01:36,932 And here is an MIT chemistry T-shirt. 29 00:01:36,932 --> 00:01:38,580 [APPLAUSE] 30 00:01:42,260 --> 00:01:44,955 CATHERINE DRENNAN: OK, so you'll notice that the prizes are 31 00:01:44,955 --> 00:01:47,330 good in the beginning, get worse throughout the semester, 32 00:01:47,330 --> 00:01:48,580 and get good again at the end. 33 00:01:48,580 --> 00:01:50,950 So keep that in mind. 34 00:01:50,950 --> 00:01:52,780 OK, so let's try to get started. 35 00:01:52,780 --> 00:01:54,530 It's been a little bit of a crazy start. 36 00:01:54,530 --> 00:01:56,363 If people are still having clicker problems, 37 00:01:56,363 --> 00:01:59,660 we have a couple more clicker questions that you can try out. 38 00:01:59,660 --> 00:02:02,930 And we'll get your clickers working by the end of class 39 00:02:02,930 --> 00:02:03,920 today. 40 00:02:03,920 --> 00:02:07,010 So the topics-- today, we're going 41 00:02:07,010 --> 00:02:09,560 to be talking about the discovery of the electron 42 00:02:09,560 --> 00:02:11,420 and of the nucleus. 43 00:02:11,420 --> 00:02:14,420 And I said that there's going to be limited amounts-- 44 00:02:14,420 --> 00:02:17,780 or every time I have a lecture that has some history, 45 00:02:17,780 --> 00:02:20,840 I'm going to counter that with some modern chemistry. 46 00:02:20,840 --> 00:02:22,790 So next week, we're going to have 47 00:02:22,790 --> 00:02:25,870 two examples of modern uses. 48 00:02:25,870 --> 00:02:28,070 But today, we're going to do a little history. 49 00:02:28,070 --> 00:02:31,460 And I like history, especially when 50 00:02:31,460 --> 00:02:32,990 it can lead to a cool demo. 51 00:02:32,990 --> 00:02:36,310 So you might have noticed something demo-like came in 52 00:02:36,310 --> 00:02:37,910 while we were doing the clickers. 53 00:02:37,910 --> 00:02:40,280 So that's always good. 54 00:02:40,280 --> 00:02:42,560 And I also like talking about history 55 00:02:42,560 --> 00:02:46,820 when I feel like it's a great example of a challenge 56 00:02:46,820 --> 00:02:49,370 that chemists face, and really, most scientists 57 00:02:49,370 --> 00:02:52,550 face, that they used to face and still currently face, 58 00:02:52,550 --> 00:02:55,010 which is that chemists study small particles. 59 00:02:55,010 --> 00:02:57,110 They study things that are really tiny. 60 00:02:57,110 --> 00:03:00,690 How do you study something that's really small? 61 00:03:00,690 --> 00:03:02,810 How do you demonstrate that something 62 00:03:02,810 --> 00:03:05,820 that is invisible to the eye actually exists? 63 00:03:05,820 --> 00:03:07,640 So this is a common challenge. 64 00:03:07,640 --> 00:03:09,740 And so today, I'm going to tell you 65 00:03:09,740 --> 00:03:12,230 about how the electron and the nucleus 66 00:03:12,230 --> 00:03:15,830 were discovered at a very low-tech time 67 00:03:15,830 --> 00:03:18,080 in our scientific history, how they 68 00:03:18,080 --> 00:03:19,980 were able to figure this out. 69 00:03:19,980 --> 00:03:25,340 And let me just set the stage of what people were thinking 70 00:03:25,340 --> 00:03:27,860 around this time, and how these discoveries really 71 00:03:27,860 --> 00:03:30,000 changed everything. 72 00:03:30,000 --> 00:03:34,850 So in the late 1890s, chemists were patting each other 73 00:03:34,850 --> 00:03:35,570 on the back. 74 00:03:35,570 --> 00:03:38,840 And physicists too were thinking, boy, we have it 75 00:03:38,840 --> 00:03:40,100 all figured out. 76 00:03:40,100 --> 00:03:44,280 We have a real, complete understanding of our universe. 77 00:03:44,280 --> 00:03:46,460 We have atomic theory of matter. 78 00:03:46,460 --> 00:03:48,960 We have Newtonian mechanics. 79 00:03:48,960 --> 00:03:50,180 This is really great. 80 00:03:50,180 --> 00:03:52,250 And in fact, someone said these words, 81 00:03:52,250 --> 00:03:54,530 which are really dangerous words, 82 00:03:54,530 --> 00:03:56,690 that our future discoveries must be looked 83 00:03:56,690 --> 00:04:00,320 for in the sixth decimal place. 84 00:04:00,320 --> 00:04:03,380 So honestly, when I started studying chemistry, 85 00:04:03,380 --> 00:04:05,420 I thought everything about chemistry 86 00:04:05,420 --> 00:04:06,920 was probably already known. 87 00:04:06,920 --> 00:04:09,590 And it was just fine tuning things. 88 00:04:09,590 --> 00:04:11,840 I was absolutely wrong at that time. 89 00:04:11,840 --> 00:04:13,670 And this statement was absolutely wrong, 90 00:04:13,670 --> 00:04:16,670 and it really came right before the major discovery 91 00:04:16,670 --> 00:04:19,459 of the electron, where they realized they hadn't really 92 00:04:19,459 --> 00:04:23,330 understood anything about the atomic theory of matter. 93 00:04:23,330 --> 00:04:27,050 So more experiments are always dangerous because they 94 00:04:27,050 --> 00:04:28,610 can change everything. 95 00:04:28,610 --> 00:04:30,830 And that's why I really like science. 96 00:04:30,830 --> 00:04:33,320 All right, so the experiment I'm going to tell you today, 97 00:04:33,320 --> 00:04:36,440 JJ Thompson's discovery of the electron. 98 00:04:36,440 --> 00:04:38,800 Or one of the experiments I'll tell you about today, 99 00:04:38,800 --> 00:04:41,300 and this is really a pretty simple experiment. 100 00:04:41,300 --> 00:04:46,570 So JJ Thompson was interested in this thing called cathode rays. 101 00:04:46,570 --> 00:04:49,810 He had hydrogen gas, and then he took an evacuated glass 102 00:04:49,810 --> 00:04:50,320 cylinder. 103 00:04:50,320 --> 00:04:52,000 And he put hydrogen gas in it. 104 00:04:52,000 --> 00:04:54,280 And then he applied a current to that, 105 00:04:54,280 --> 00:04:56,590 and he could see these rays coming off. 106 00:04:56,590 --> 00:04:58,450 And he thought that was pretty cool. 107 00:04:58,450 --> 00:05:01,000 And so he was wondering about these rays. 108 00:05:01,000 --> 00:05:04,000 Are they made up of negatively charged particles, 109 00:05:04,000 --> 00:05:05,750 possibly charged particles, maybe neutral? 110 00:05:05,750 --> 00:05:07,300 What are these things? 111 00:05:07,300 --> 00:05:09,400 So he decided to do this experiment. 112 00:05:09,400 --> 00:05:12,670 And he wondered whether if he took two plates 113 00:05:12,670 --> 00:05:16,030 and had charges associated with them, whether he 114 00:05:16,030 --> 00:05:18,970 would see the cathode rays deflected or not. 115 00:05:18,970 --> 00:05:21,430 Well, first, he didn't apply any current, 116 00:05:21,430 --> 00:05:25,090 so it was just neutral, just to see if putting these plates in 117 00:05:25,090 --> 00:05:27,790 would affect anything in any way. 118 00:05:27,790 --> 00:05:29,650 And so when he did that, when there 119 00:05:29,650 --> 00:05:34,270 was zero voltage difference between these two plates, 120 00:05:34,270 --> 00:05:38,530 he could see the cathode ray hit this phosphor screen. 121 00:05:38,530 --> 00:05:40,559 And there was no deflection. 122 00:05:40,559 --> 00:05:42,100 All right, then he said, OK, now, I'm 123 00:05:42,100 --> 00:05:46,300 going to charge things up, and see if I can see a deflection. 124 00:05:46,300 --> 00:05:50,110 So he did that, and he saw the following. 125 00:05:50,110 --> 00:05:52,660 There was a deflection. 126 00:05:52,660 --> 00:05:56,710 And so now, the different voltage between the plates 127 00:05:56,710 --> 00:05:58,600 was greater than 0. 128 00:05:58,600 --> 00:06:00,610 And now, he saw the cathode ray was 129 00:06:00,610 --> 00:06:05,470 being deflected a different distance of delta x over here. 130 00:06:05,470 --> 00:06:09,860 And it was being deflected toward the positive plate. 131 00:06:09,860 --> 00:06:13,360 So that said to him that the cathode ray contained 132 00:06:13,360 --> 00:06:16,060 negatively charged particles. 133 00:06:16,060 --> 00:06:19,540 You'll notice that the word "negatively" is the only word 134 00:06:19,540 --> 00:06:21,650 on the screen in blue. 135 00:06:21,650 --> 00:06:24,400 And if you look at your notes, you'll 136 00:06:24,400 --> 00:06:26,650 see that there's a blank spot. 137 00:06:26,650 --> 00:06:29,320 Just pointing out there might be a correlation there. 138 00:06:29,320 --> 00:06:37,120 OK, so he knew some things also from classical work 139 00:06:37,120 --> 00:06:39,520 that was done in the time. 140 00:06:39,520 --> 00:06:44,710 And I didn't reset my boards. 141 00:06:44,710 --> 00:06:48,040 So he knew something about what it meant 142 00:06:48,040 --> 00:06:50,690 if there was just deflection. 143 00:06:50,690 --> 00:06:56,470 So we had our deflection of the negatively charged particles. 144 00:06:56,470 --> 00:06:58,210 And he knew that that was going to be 145 00:06:58,210 --> 00:07:02,200 proportional to the charge of the negatively 146 00:07:02,200 --> 00:07:04,480 charged particle. 147 00:07:04,480 --> 00:07:07,630 And it was going to be directly proportional to that, 148 00:07:07,630 --> 00:07:12,280 and inversely proportional to the mass of the negatively 149 00:07:12,280 --> 00:07:15,190 charged particle. 150 00:07:15,190 --> 00:07:17,830 So it was a pretty big deflection, so he wasn't sure. 151 00:07:17,830 --> 00:07:19,930 Maybe there was a very big charge, 152 00:07:19,930 --> 00:07:23,530 or maybe there was a very small mass, or maybe both. 153 00:07:23,530 --> 00:07:26,560 So then he wanted to see what happened if he really 154 00:07:26,560 --> 00:07:29,020 got things going, and he applied even 155 00:07:29,020 --> 00:07:33,070 more of voltage difference. 156 00:07:33,070 --> 00:07:34,600 So he did that. 157 00:07:34,600 --> 00:07:38,440 And when he did that, he saw this. 158 00:07:38,440 --> 00:07:44,440 He saw another deflection, but this time, it was much smaller. 159 00:07:44,440 --> 00:07:48,910 And it was toward the negatively charged plate. 160 00:07:48,910 --> 00:07:53,320 So he realized that, in addition to the negatively charged 161 00:07:53,320 --> 00:07:58,900 particle, there was also a positively charged particle. 162 00:07:58,900 --> 00:08:05,270 So for that particle, then, the deflection 163 00:08:05,270 --> 00:08:07,850 of the positively charged particle 164 00:08:07,850 --> 00:08:12,320 should also be proportional to the charge on the positively 165 00:08:12,320 --> 00:08:18,500 charged particle, and inversely proportional to the mass 166 00:08:18,500 --> 00:08:21,800 of the positively charged particle. 167 00:08:21,800 --> 00:08:24,980 But there was a big difference in this deflection. 168 00:08:24,980 --> 00:08:27,830 Toward the positive plate, there was a big deflection. 169 00:08:27,830 --> 00:08:31,580 And toward the negative plate, it was pretty small. 170 00:08:31,580 --> 00:08:38,030 So he knew that this deflection was much bigger than that one. 171 00:08:38,030 --> 00:08:39,890 And then he thought about-- is that going 172 00:08:39,890 --> 00:08:41,990 to be due to charge or mass? 173 00:08:41,990 --> 00:08:47,980 But he said, the charges should be the same 174 00:08:47,980 --> 00:08:51,530 because it's neutral normally. 175 00:08:51,530 --> 00:08:54,920 So those charges must equal each other, the absolute values 176 00:08:54,920 --> 00:08:57,270 at least, must equal each other. 177 00:08:57,270 --> 00:09:00,440 So then we can think about the comparison 178 00:09:00,440 --> 00:09:01,462 of these deflections. 179 00:09:07,770 --> 00:09:12,440 So if we can take the absolute value of the deflection 180 00:09:12,440 --> 00:09:15,050 of the negatively charged particle 181 00:09:15,050 --> 00:09:19,430 over the absolute value of the deflection of the positively 182 00:09:19,430 --> 00:09:22,430 charged particle, on the top here, 183 00:09:22,430 --> 00:09:26,390 we're going to have the charge of the negatively 184 00:09:26,390 --> 00:09:29,030 charged particle over the mass of the negatively 185 00:09:29,030 --> 00:09:30,020 charged particle. 186 00:09:30,020 --> 00:09:32,960 And the absolute value of that term 187 00:09:32,960 --> 00:09:37,150 over the charge of the positively 188 00:09:37,150 --> 00:09:40,690 charged particle, over the mass of the positively charged 189 00:09:40,690 --> 00:09:42,220 particle. 190 00:09:42,220 --> 00:09:46,240 But now, if you say that the charges are 191 00:09:46,240 --> 00:09:51,120 equal to each other, at least the absolute values of them, 192 00:09:51,120 --> 00:09:53,760 we can get rid of that term. 193 00:09:53,760 --> 00:09:57,550 And just see that the mass then, of the positively charged 194 00:09:57,550 --> 00:10:02,440 particle over the negatively charged particle, remains. 195 00:10:02,440 --> 00:10:05,980 So if this is going to be big, and we know it is, 196 00:10:05,980 --> 00:10:07,530 it's a big difference. 197 00:10:07,530 --> 00:10:09,460 The negatively charged particle deflected 198 00:10:09,460 --> 00:10:12,970 a lot more than the positively charged particle. 199 00:10:12,970 --> 00:10:17,760 That means that the difference in masses also has to be big, 200 00:10:17,760 --> 00:10:21,970 and that that negatively charged particle must be a lot smaller 201 00:10:21,970 --> 00:10:25,500 in mass than the positively charged particle. 202 00:10:25,500 --> 00:10:30,197 So if we go up a little bit here-- oops. 203 00:10:33,220 --> 00:10:38,050 So the mass of the negatively charged particle 204 00:10:38,050 --> 00:10:43,960 must be a lot smaller than the mass of the positively charged 205 00:10:43,960 --> 00:10:44,860 particle. 206 00:10:44,860 --> 00:10:49,020 And actually, it's about 2,000 times smaller. 207 00:10:49,020 --> 00:10:51,480 So he was able to figure all this out 208 00:10:51,480 --> 00:10:54,430 by just doing this pretty simple experiment. 209 00:10:54,430 --> 00:10:59,860 So he had now a small, negatively charged particle, 210 00:10:59,860 --> 00:11:02,680 and also a positively charged particle. 211 00:11:02,680 --> 00:11:06,390 And later, the negatively charged particle got a name. 212 00:11:06,390 --> 00:11:09,820 The negatively charged particle got the name of the electron. 213 00:11:09,820 --> 00:11:12,310 And its mass was determined in an another interesting 214 00:11:12,310 --> 00:11:14,210 experiment I won't tell you about. 215 00:11:14,210 --> 00:11:17,980 And it was determined to be really small, about 9 times 10 216 00:11:17,980 --> 00:11:21,360 to the minus 31 kilograms. 217 00:11:21,360 --> 00:11:23,410 So through this experiment, he was 218 00:11:23,410 --> 00:11:26,010 able to figure out, that in these cathode rays, 219 00:11:26,010 --> 00:11:29,520 you had something that was tiny, this electron. 220 00:11:29,520 --> 00:11:33,780 And that means this idea that atoms were the smallest thing 221 00:11:33,780 --> 00:11:34,995 out there was incorrect. 222 00:11:34,995 --> 00:11:36,340 That's what everyone believed. 223 00:11:36,340 --> 00:11:37,810 They were patting themselves on the back. 224 00:11:37,810 --> 00:11:39,080 They had figured it all out. 225 00:11:39,080 --> 00:11:40,996 But there was something smaller than the atom. 226 00:11:40,996 --> 00:11:43,210 There was this electron, this negatively 227 00:11:43,210 --> 00:11:47,196 charged particle that was really tiny. 228 00:11:47,196 --> 00:11:48,070 So it is pretty cool. 229 00:11:48,070 --> 00:11:49,444 It's a pretty low-tech experiment 230 00:11:49,444 --> 00:11:52,270 that figured out something that really changed the way that we 231 00:11:52,270 --> 00:11:55,210 thought about science. 232 00:11:55,210 --> 00:11:56,410 So what about the nucleus? 233 00:11:56,410 --> 00:11:58,360 So we had the electron, and we also 234 00:11:58,360 --> 00:12:00,310 had this idea there was something positively 235 00:12:00,310 --> 00:12:01,690 charged going on there. 236 00:12:01,690 --> 00:12:04,720 And of course, in that experiment, that was H plus. 237 00:12:04,720 --> 00:12:07,810 But what about the nucleus? 238 00:12:07,810 --> 00:12:11,230 So Rutherford is credited with the discovery of the nucleus. 239 00:12:11,230 --> 00:12:12,800 So this was a little later. 240 00:12:12,800 --> 00:12:15,990 And he had been studying radioactive material. 241 00:12:15,990 --> 00:12:19,360 And his good friend, Marie Curie, from France 242 00:12:19,360 --> 00:12:23,130 would often send him interesting samples for him to study. 243 00:12:23,130 --> 00:12:26,570 I'm not sure quite how they got from France to England. 244 00:12:26,570 --> 00:12:29,340 Some of these were really cancer causing things. 245 00:12:29,340 --> 00:12:31,810 I don't know how many people touched them without safety 246 00:12:31,810 --> 00:12:33,740 precautions on the way. 247 00:12:33,740 --> 00:12:37,870 But anyway, it's interesting to note that Rutherford actually 248 00:12:37,870 --> 00:12:41,250 did not die of cancer, despite this research. 249 00:12:41,250 --> 00:12:45,830 He was literally the victim of his own success. 250 00:12:45,830 --> 00:12:49,480 So after his great discovery of the nucleus, 251 00:12:49,480 --> 00:12:55,570 which I'll tell you about, he was made into a knight. 252 00:12:55,570 --> 00:12:58,530 And at one point, he became sick. 253 00:12:58,530 --> 00:12:59,880 And he needed a doctor. 254 00:12:59,880 --> 00:13:01,720 Well, if you're a knight in England, 255 00:13:01,720 --> 00:13:03,910 you can't just have any old doctor treat you. 256 00:13:03,910 --> 00:13:06,580 You need to have a doctor that is also a knight. 257 00:13:06,580 --> 00:13:09,580 And so while he was waiting for a doctor 258 00:13:09,580 --> 00:13:13,420 of the appropriate ranking to come and treat him, he died. 259 00:13:13,420 --> 00:13:17,770 So he literally died of his own success. 260 00:13:17,770 --> 00:13:20,410 He was a victim of his own success. 261 00:13:20,410 --> 00:13:24,220 But it wasn't just his success as I'll tell you about. 262 00:13:24,220 --> 00:13:24,977 He had some help. 263 00:13:24,977 --> 00:13:26,560 He had a really good graduate student, 264 00:13:26,560 --> 00:13:29,370 a really good undergraduate student helping him out. 265 00:13:29,370 --> 00:13:32,040 So he was studying these alpha particles 266 00:13:32,040 --> 00:13:35,250 that were being emitted from this radioactive material. 267 00:13:35,250 --> 00:13:38,280 And we know now that this is Helium plus 2 ions. 268 00:13:38,280 --> 00:13:39,820 But that was not known at the time. 269 00:13:39,820 --> 00:13:42,100 They just knew something was coming out 270 00:13:42,100 --> 00:13:45,370 of this radioactive material, and they 271 00:13:45,370 --> 00:13:48,490 wanted to find out what it was, and characterize 272 00:13:48,490 --> 00:13:50,040 the properties of this. 273 00:13:50,040 --> 00:13:52,980 So he had a post-doc named Hans Geiger. 274 00:13:52,980 --> 00:13:56,140 And this is the Geiger of the Geiger counter. 275 00:13:56,140 --> 00:13:59,860 And he also had an undergraduate student, E. Marsden. 276 00:13:59,860 --> 00:14:02,230 And so together, they did the following experiment. 277 00:14:02,230 --> 00:14:06,970 And I wasn't obviously there, but I'm imagining that by "they 278 00:14:06,970 --> 00:14:08,530 did the following experiment," it 279 00:14:08,530 --> 00:14:10,860 meant the undergraduate and the graduate student, 280 00:14:10,860 --> 00:14:13,500 or maybe even just the undergraduate. 281 00:14:13,500 --> 00:14:16,770 OK, so here is the experiment. 282 00:14:16,770 --> 00:14:19,050 They had the radioactive material. 283 00:14:19,050 --> 00:14:21,240 Alpha particles were coming off, and they 284 00:14:21,240 --> 00:14:25,270 had built a detector that would count how many alpha particles 285 00:14:25,270 --> 00:14:26,860 were coming off. 286 00:14:26,860 --> 00:14:30,840 And so they did the experiment, and they counted. 287 00:14:30,840 --> 00:14:33,060 And they found there were a lot of particles, 288 00:14:33,060 --> 00:14:37,950 132,000 alpha particles per minute, in fact. 289 00:14:37,950 --> 00:14:40,230 So then they said, OK, let's see what 290 00:14:40,230 --> 00:14:44,520 happens if we put a piece of foil 291 00:14:44,520 --> 00:14:47,340 in the path of the alpha particles. 292 00:14:47,340 --> 00:14:51,720 And we're going to have really, really thin gold foil. 293 00:14:51,720 --> 00:14:53,670 So this is like smaller than a human hair. 294 00:14:53,670 --> 00:14:56,610 This is really, really thin foil. 295 00:14:56,610 --> 00:14:59,130 And they shot alpha particles at it. 296 00:14:59,130 --> 00:15:01,260 And they counted. 297 00:15:01,260 --> 00:15:04,350 And they got approximately-- I don't 298 00:15:04,350 --> 00:15:08,460 know how many significant figures-- but 132,000 alpha 299 00:15:08,460 --> 00:15:09,780 particles. 300 00:15:09,780 --> 00:15:15,780 Seemed to be, in terms of the significant figures, the same. 301 00:15:15,780 --> 00:15:17,990 So it was just going through. 302 00:15:17,990 --> 00:15:19,560 These alpha particles were just going 303 00:15:19,560 --> 00:15:22,170 through this thin, gold foil. 304 00:15:22,170 --> 00:15:26,220 So they had this vision then of the gold atoms 305 00:15:26,220 --> 00:15:31,140 being all empty space, and the alpha particles were just 306 00:15:31,140 --> 00:15:33,910 going through, no problem. 307 00:15:33,910 --> 00:15:38,100 But then they did one more experiment. 308 00:15:38,100 --> 00:15:40,530 And by then, I think this was the undergraduate. 309 00:15:40,530 --> 00:15:43,080 So they built this detector. 310 00:15:43,080 --> 00:15:47,670 And they had built the detector so it could move. 311 00:15:47,670 --> 00:15:50,640 So sometimes when you design something to do something, 312 00:15:50,640 --> 00:15:52,840 you actually want to use it for that. 313 00:15:52,840 --> 00:15:55,680 So if we have the alpha particles coming this way 314 00:15:55,680 --> 00:15:57,600 and on the detector over here. 315 00:15:57,600 --> 00:15:59,850 And it had been sitting, and I've been collecting it. 316 00:15:59,850 --> 00:16:01,380 The undergraduate was told, well, 317 00:16:01,380 --> 00:16:04,210 put the detector over there, and see what happens. 318 00:16:04,210 --> 00:16:09,130 So the undergraduate moved the detector over here. 319 00:16:09,130 --> 00:16:13,320 And he said, you're going to see if the alpha particles hit 320 00:16:13,320 --> 00:16:15,600 the gold foil and backscatter. 321 00:16:15,600 --> 00:16:18,210 So we'll have the detector over here. 322 00:16:18,210 --> 00:16:19,460 So the undergraduate did this. 323 00:16:19,460 --> 00:16:21,376 They didn't think it was going to do anything. 324 00:16:21,376 --> 00:16:23,970 They needed something for the undergraduate to do. 325 00:16:23,970 --> 00:16:26,160 So they had him do that. 326 00:16:26,160 --> 00:16:29,070 And then they counted. 327 00:16:29,070 --> 00:16:33,970 And sure enough, click, click. 328 00:16:33,970 --> 00:16:36,720 It wasn't a lot, but there seemed 329 00:16:36,720 --> 00:16:40,440 to be some backscatter, about 20 counts, 330 00:16:40,440 --> 00:16:43,740 20 alpha particles per minute. 331 00:16:43,740 --> 00:16:45,540 That was not expected. 332 00:16:45,540 --> 00:16:49,140 They were expecting 0. 333 00:16:49,140 --> 00:16:53,680 So they were detecting backscattering. 334 00:16:53,680 --> 00:16:56,490 The alpha particles were bouncing off 335 00:16:56,490 --> 00:17:02,070 that thin, gold foil, and coming back at the moved detector. 336 00:17:02,070 --> 00:17:07,170 So they could calculate this probability of backscattering, 337 00:17:07,170 --> 00:17:09,210 the account rate of the backscattering 338 00:17:09,210 --> 00:17:13,560 over the normal count of the particles. 339 00:17:13,560 --> 00:17:17,700 And so they had 20 backscattering events, 340 00:17:17,700 --> 00:17:25,359 or 20 counts over the 132,000, 2 times 10 to the minus 4, 341 00:17:25,359 --> 00:17:28,349 or 0.02%. 342 00:17:28,349 --> 00:17:30,290 This is small, very small. 343 00:17:30,290 --> 00:17:32,190 But it was not 0. 344 00:17:32,190 --> 00:17:34,830 And I don't know how many times they did this experiment, 345 00:17:34,830 --> 00:17:36,626 but I can imagine there were lots 346 00:17:36,626 --> 00:17:39,000 of times they did the experiment that no one would really 347 00:17:39,000 --> 00:17:40,470 believe this result. 348 00:17:40,470 --> 00:17:44,240 And Rutherford himself said, "it was about as credible 349 00:17:44,240 --> 00:17:46,560 as if you had fired a 15-inch shell 350 00:17:46,560 --> 00:17:50,060 at a piece of tissue paper, and it came back and hit you." 351 00:17:50,060 --> 00:17:51,450 So that's how he felt about it. 352 00:17:51,450 --> 00:17:54,240 He was like, I don't understand how this is working. 353 00:17:54,240 --> 00:17:55,590 This is so thin. 354 00:17:55,590 --> 00:17:58,920 It's like tissue paper, but yet these alpha particles 355 00:17:58,920 --> 00:18:02,640 are bouncing off something. 356 00:18:02,640 --> 00:18:04,980 So what did this all mean, once they had repeated 357 00:18:04,980 --> 00:18:07,080 the experiment many times? 358 00:18:07,080 --> 00:18:11,130 So their interpretation, then, was that these gold atoms 359 00:18:11,130 --> 00:18:14,100 were, in fact, mostly empty. 360 00:18:14,100 --> 00:18:16,860 It seemed like all the alpha particles were just 361 00:18:16,860 --> 00:18:18,020 going through. 362 00:18:18,020 --> 00:18:19,950 Most of them were just passing through and not 363 00:18:19,950 --> 00:18:21,090 hitting anything. 364 00:18:21,090 --> 00:18:25,350 But there was something in there that could be hit. 365 00:18:25,350 --> 00:18:30,240 There was some concentrated mass in this volume 366 00:18:30,240 --> 00:18:34,240 that, when the alpha particle hit that directly, it 367 00:18:34,240 --> 00:18:35,310 backscattered. 368 00:18:35,310 --> 00:18:39,290 And they later called this the nucleus. 369 00:18:39,290 --> 00:18:43,040 So they came up then with this new model, the Rutherford 370 00:18:43,040 --> 00:18:46,140 model, where you had mostly empty space. 371 00:18:46,140 --> 00:18:50,060 But you had concentrated mass inside 372 00:18:50,060 --> 00:18:55,790 that an alpha particle might hit and then backscatter. 373 00:18:55,790 --> 00:18:59,190 And Rutherford assumed that the electrons would 374 00:18:59,190 --> 00:19:03,360 be in that empty space, and that this positive mass was 375 00:19:03,360 --> 00:19:05,070 going to be positively charged. 376 00:19:05,070 --> 00:19:08,880 Because he knew the overall atom was going to be neutral. 377 00:19:08,880 --> 00:19:11,060 So just a little nomenclature. 378 00:19:11,060 --> 00:19:15,770 We can think about the charge of the electrons in the atom 379 00:19:15,770 --> 00:19:19,910 as being equal to minus Z to the e, where 380 00:19:19,910 --> 00:19:23,220 Z is our atomic number, and e is the absolute value 381 00:19:23,220 --> 00:19:25,110 of the electron's charge. 382 00:19:25,110 --> 00:19:30,810 And if this term is negative, then the charge on the nucleus 383 00:19:30,810 --> 00:19:32,080 is going to be positive. 384 00:19:32,080 --> 00:19:35,610 So we have positive Z to the e, because overall, the atom 385 00:19:35,610 --> 00:19:38,880 is going to be neutral. 386 00:19:38,880 --> 00:19:42,480 Then Rutherford went on to actually use 387 00:19:42,480 --> 00:19:48,510 this backscattering to measure the diameter of this positively 388 00:19:48,510 --> 00:19:53,880 charged, dense part of the atom, of the nucleus. 389 00:19:53,880 --> 00:19:57,390 And he was able to measure that diameter 390 00:19:57,390 --> 00:20:02,520 as a very small number, 10 to the minus 14th meters. 391 00:20:02,520 --> 00:20:05,970 So he did this with this back scattering experiment. 392 00:20:05,970 --> 00:20:08,970 So you might say, how can you get a diameter 393 00:20:08,970 --> 00:20:11,380 from this backscattering? 394 00:20:11,380 --> 00:20:14,340 And so that's what we're going to try right now ourselves. 395 00:20:14,340 --> 00:20:17,460 We're going to do an experiment, and Professor Sylvia Ceyer 396 00:20:17,460 --> 00:20:20,590 originally came up with the experiment to do in class. 397 00:20:20,590 --> 00:20:27,560 And so she built the first version of this gold foil 398 00:20:27,560 --> 00:20:29,430 right here. 399 00:20:29,430 --> 00:20:32,430 And originally, she took something apart 400 00:20:32,430 --> 00:20:33,930 from her own research program. 401 00:20:33,930 --> 00:20:37,110 Since then, it's been replicated so that she doesn't 402 00:20:37,110 --> 00:20:40,170 have to shut down her research lab every year when 403 00:20:40,170 --> 00:20:42,720 we do this experiment in class. 404 00:20:42,720 --> 00:20:46,680 So here, imagine this as a piece of gold foil. 405 00:20:46,680 --> 00:20:51,180 And it's mostly empty space, but there 406 00:20:51,180 --> 00:20:57,780 are some small, concentrated nuclei, gold nuclei, 407 00:20:57,780 --> 00:20:59,790 these Styrofoam balls. 408 00:20:59,790 --> 00:21:05,820 And if we have, over here, some alpha 409 00:21:05,820 --> 00:21:11,130 particles, which we happen to have 502 alpha particles. 410 00:21:15,210 --> 00:21:19,740 If the alpha particle hits the concentrated part, 411 00:21:19,740 --> 00:21:21,150 it should back scatter. 412 00:21:21,150 --> 00:21:23,100 Otherwise, it should go through. 413 00:21:23,100 --> 00:21:27,299 So you are now going to be radioactive material. 414 00:21:27,299 --> 00:21:27,840 I don't know. 415 00:21:27,840 --> 00:21:29,160 Is that the first time you've been called 416 00:21:29,160 --> 00:21:30,340 radioactive material? 417 00:21:30,340 --> 00:21:30,986 I'm not sure. 418 00:21:34,124 --> 00:21:35,415 But we're going to come around. 419 00:21:43,200 --> 00:21:47,880 Everyone can have one or two of these. 420 00:21:47,880 --> 00:21:49,635 So let me just tell you. 421 00:21:49,635 --> 00:21:53,040 You need to watch your ping pong ball. 422 00:21:53,040 --> 00:21:56,130 Once you get it, you can move to the center. 423 00:21:56,130 --> 00:21:58,020 Watch your ping pong ball. 424 00:21:58,020 --> 00:22:02,250 If it hits the edge of this, it's not a backscatter. 425 00:22:02,250 --> 00:22:05,370 Watch if it goes through or if it backscatters. 426 00:22:05,370 --> 00:22:09,180 And you will click in whether you had a backscatter event 427 00:22:09,180 --> 00:22:10,140 or not. 428 00:22:10,140 --> 00:22:13,740 And from that information, we will calculate 429 00:22:13,740 --> 00:22:15,645 the diameter of the nucleus. 430 00:22:19,284 --> 00:22:20,700 Do you want to put up the clicker? 431 00:22:34,760 --> 00:22:35,770 I think everyone's good. 432 00:22:43,354 --> 00:22:44,340 Do we have any more? 433 00:23:00,640 --> 00:23:05,820 OK, everyone, if you want to get up and get a better vantage 434 00:23:05,820 --> 00:23:07,260 point, do so. 435 00:23:07,260 --> 00:23:10,210 And let the experiment begin. 436 00:23:10,210 --> 00:23:11,670 I'm moving out of the way. 437 00:24:05,940 --> 00:24:20,930 OK, so go ahead, and say whether you had 1, 2, or 0 backscatter 438 00:24:20,930 --> 00:24:21,430 events. 439 00:24:21,430 --> 00:24:22,980 And if your clicker isn't working, 440 00:24:22,980 --> 00:24:24,900 we'll ask you to raise your hand and tell us, 441 00:24:24,900 --> 00:24:26,895 especially if it was a backscatter event. 442 00:24:54,010 --> 00:24:56,520 Has everyone had a chance to click in? 443 00:25:02,330 --> 00:25:03,990 Has everyone clicked in? 444 00:25:03,990 --> 00:25:05,230 You can't tell. 445 00:25:05,230 --> 00:25:08,040 All right, we're going to countdown. 446 00:25:08,040 --> 00:25:09,709 Go ahead and click in, and then we're 447 00:25:09,709 --> 00:25:10,875 going to do the calculation. 448 00:25:34,000 --> 00:25:38,550 OK, actually, we need to calculate the actual number 449 00:25:38,550 --> 00:25:40,394 of them, not the percent. 450 00:25:45,140 --> 00:25:50,800 All right, so we had some backscatter events. 451 00:25:50,800 --> 00:25:53,040 So let's see if we can use this information 452 00:25:53,040 --> 00:25:59,760 to actually calculate the diameter of the gold nuclei. 453 00:25:59,760 --> 00:26:03,180 All right, so we are going to talk about the probability 454 00:26:03,180 --> 00:26:05,130 of backscattering. 455 00:26:05,130 --> 00:26:11,820 So we have a probability is equal to the number of ping 456 00:26:11,820 --> 00:26:25,630 pong balls backscattered, backscattered 457 00:26:25,630 --> 00:26:30,210 over the total number. 458 00:26:33,310 --> 00:26:38,620 And this will be related to the radius of those gold nuclei 459 00:26:38,620 --> 00:26:40,310 by the following. 460 00:26:40,310 --> 00:26:41,950 So we have the probability is going 461 00:26:41,950 --> 00:26:49,600 to be equal to the area of the nuclei, the total area 462 00:26:49,600 --> 00:26:54,620 over the area of the whole atom. 463 00:26:54,620 --> 00:26:58,720 So basically, the piece of foil-- and then that's 464 00:26:58,720 --> 00:27:06,580 going to be further equal to the number of nuclei times 465 00:27:06,580 --> 00:27:22,150 the area per nucleus, again, over the area of all the atoms, 466 00:27:22,150 --> 00:27:25,060 or the piece of foil. 467 00:27:25,060 --> 00:27:27,980 OK, so we know some of this information. 468 00:27:27,980 --> 00:27:31,540 So I'm going to move this up. 469 00:27:31,540 --> 00:27:34,070 You have an actual number. 470 00:27:34,070 --> 00:27:35,022 36 total? 471 00:27:35,022 --> 00:27:35,980 Oh, that's interesting. 472 00:27:35,980 --> 00:27:38,230 OK, that's a lot of backscattering. 473 00:27:38,230 --> 00:27:41,740 OK, so we can plug in some of these numbers now. 474 00:27:41,740 --> 00:27:44,650 So we have the probability is going to be equal. 475 00:27:44,650 --> 00:27:45,850 Someone counted. 476 00:27:45,850 --> 00:27:48,210 I didn't count, but someone counted 477 00:27:48,210 --> 00:27:50,155 that there were 120 nuclei. 478 00:27:53,170 --> 00:27:58,990 And the area is going to be pi r squared. 479 00:27:58,990 --> 00:28:01,480 And someone measured the entire frame, 480 00:28:01,480 --> 00:28:10,780 or the size of the piece of film, as a 139,000 centimeters 481 00:28:10,780 --> 00:28:12,040 squared. 482 00:28:12,040 --> 00:28:19,280 Or it was 1.39 meters squared. 483 00:28:19,280 --> 00:28:21,910 OK, so we'll assume that they counted the nuclei 484 00:28:21,910 --> 00:28:23,420 to three significant figures. 485 00:28:23,420 --> 00:28:25,780 So it's exactly 120. 486 00:28:25,780 --> 00:28:29,980 And we'll assume that they measured the box with three 487 00:28:29,980 --> 00:28:32,830 significant figures as well. 488 00:28:32,830 --> 00:28:37,090 So now we can solve this for r, the radius, 489 00:28:37,090 --> 00:28:39,040 or for the diameter. 490 00:28:39,040 --> 00:28:42,590 So if we now solve for the radius, 491 00:28:42,590 --> 00:28:44,420 we'll bring the radius over. 492 00:28:44,420 --> 00:28:47,870 And we'll have the square root of the probability. 493 00:28:47,870 --> 00:28:52,349 And if we take these numbers, and I did the math. 494 00:28:52,349 --> 00:28:53,890 I have a calculator, if someone wants 495 00:28:53,890 --> 00:29:02,600 to check-- 6.072 centimeters. 496 00:29:02,600 --> 00:29:07,230 And then the diameter is going to just be equal to twice that. 497 00:29:07,230 --> 00:29:09,500 So we have the square root of the probability 498 00:29:09,500 --> 00:29:16,330 times 12.14 centimeters. 499 00:29:16,330 --> 00:29:20,890 And now, we need to calculate the probability. 500 00:29:20,890 --> 00:29:25,810 So the probability is going to be the number of backscatter, 501 00:29:25,810 --> 00:29:28,520 which was 36. 502 00:29:28,520 --> 00:29:36,340 36 over 502, someone have a calculator? 503 00:29:36,340 --> 00:29:37,660 Someone check my math. 504 00:29:37,660 --> 00:29:39,280 Check math for me. 505 00:29:39,280 --> 00:29:40,815 Check math, anybody. 506 00:29:40,815 --> 00:29:41,940 I don't have another prize. 507 00:29:41,940 --> 00:29:44,480 Thank you. 508 00:29:44,480 --> 00:29:48,940 Was it 26 or 36? 509 00:29:48,940 --> 00:29:50,104 I can't read up there. 510 00:29:50,104 --> 00:29:52,097 AUDIENCE: You said it's 12 single or double? 511 00:29:52,097 --> 00:29:53,180 CATHERINE DRENNAN: Double. 512 00:29:53,180 --> 00:29:57,670 AUDIENCE: [CHATTER] 513 00:29:57,670 --> 00:30:00,172 CATHERINE DRENNAN: Excellent, checking math for me, here. 514 00:30:00,172 --> 00:30:01,857 AUDIENCE: I can't do math in my head. 515 00:30:04,719 --> 00:30:07,330 AUDIENCE: Yeah, it's roughly 500 [INAUDIBLE]. 516 00:30:07,330 --> 00:30:09,570 CATHERINE DRENNAN: OK, 26, and so 517 00:30:09,570 --> 00:30:11,650 what does this come out to be? 518 00:30:11,650 --> 00:30:14,150 {} 519 00:30:14,150 --> 00:30:17,470 AUDIENCE: 0.050. 520 00:30:17,470 --> 00:30:22,420 CATHERINE DRENNAN: 0.050, And now we need to plug that in. 521 00:30:22,420 --> 00:30:37,560 So we have d equals the square root of 0.050 times 12.14. 522 00:30:37,560 --> 00:30:39,246 And what does that come out to be? 523 00:30:45,910 --> 00:31:00,240 2.71-- and the actual was 2.5. 524 00:31:00,240 --> 00:31:00,740 Not bad. 525 00:31:05,070 --> 00:31:08,700 So using methods very similar to this, 526 00:31:08,700 --> 00:31:10,830 Rutherford was able to figure out 527 00:31:10,830 --> 00:31:14,130 what the diameter of the nucleus was. 528 00:31:14,130 --> 00:31:20,280 And this was a really important achievement of the time. 529 00:31:20,280 --> 00:31:29,790 OK, so in the last few minutes, maybe I'll move this down. 530 00:31:29,790 --> 00:31:31,750 In the last few minutes, I want to talk 531 00:31:31,750 --> 00:31:35,620 about the fall out of all of these great experiments 532 00:31:35,620 --> 00:31:37,730 and all of these great results. 533 00:31:37,730 --> 00:31:42,590 So we now know there is an electron and a nucleus. 534 00:31:42,590 --> 00:31:44,920 So there are subatomic particles. 535 00:31:44,920 --> 00:31:47,530 What does that mean in terms of what people thought they 536 00:31:47,530 --> 00:31:50,325 understood about atomic theory? 537 00:31:53,850 --> 00:31:56,660 So we had this question then. 538 00:31:56,660 --> 00:32:00,940 OK, so we have a nucleus, positively charged, 539 00:32:00,940 --> 00:32:02,540 and electron, negatively charged. 540 00:32:02,540 --> 00:32:05,010 And there's a distance between them. 541 00:32:05,010 --> 00:32:11,550 And wanted to know, why do they stay apart? 542 00:32:11,550 --> 00:32:16,000 Why does the electron not crash into the nucleus? 543 00:32:16,000 --> 00:32:19,210 So from classical description, we 544 00:32:19,210 --> 00:32:22,990 have Coulomb's Force Law, which tells us 545 00:32:22,990 --> 00:32:26,950 about the force when you have two 546 00:32:26,950 --> 00:32:33,280 charged particles, Q1 and Q2, so the charge on the particles. 547 00:32:33,280 --> 00:32:38,230 And you have over 4 times pi times 548 00:32:38,230 --> 00:32:43,900 this permittivity constant times the distance, r, squared. 549 00:32:43,900 --> 00:32:49,990 So if you apply a force then, and you have charged particles, 550 00:32:49,990 --> 00:32:53,180 if those particles have the same sign, 551 00:32:53,180 --> 00:32:56,200 then acceleration should push them apart. 552 00:32:56,200 --> 00:32:59,170 The force should be positive and repulsive. 553 00:32:59,170 --> 00:33:02,020 So two things with the same charge 554 00:33:02,020 --> 00:33:03,730 don't want to be near each other. 555 00:33:03,730 --> 00:33:06,190 It's going to be repulsive. 556 00:33:06,190 --> 00:33:09,190 If, like in this case, you have two things 557 00:33:09,190 --> 00:33:12,520 that have opposite signs, acceleration 558 00:33:12,520 --> 00:33:15,520 should pull them together. 559 00:33:15,520 --> 00:33:20,110 And here the force should be negative and attractive. 560 00:33:20,110 --> 00:33:22,240 So that's the situation we're in here, 561 00:33:22,240 --> 00:33:28,000 positively charged nucleus, negatively charged electron. 562 00:33:28,000 --> 00:33:32,866 So let's consider then a hydrogen atom. 563 00:33:32,866 --> 00:33:38,290 It equals one electron, one proton. 564 00:33:38,290 --> 00:33:41,620 Let's think about what happens when 565 00:33:41,620 --> 00:33:46,220 you have an infinite distance between them. 566 00:33:46,220 --> 00:33:48,860 So if they're infinitely far apart, 567 00:33:48,860 --> 00:33:50,110 what is going to be the force? 568 00:33:50,110 --> 00:33:51,370 You can just yell out the answer. 569 00:33:51,370 --> 00:33:51,910 AUDIENCE: 0. 570 00:33:51,910 --> 00:33:53,306 CATHERINE DRENNAN: 0, right. 571 00:33:53,306 --> 00:33:54,430 They don't feel each other. 572 00:33:54,430 --> 00:33:56,380 They don't know anything about each other. 573 00:33:56,380 --> 00:33:58,260 They're infinitely far apart. 574 00:33:58,260 --> 00:34:00,430 There's no force. 575 00:34:00,430 --> 00:34:02,780 But that's not going to be the situation in the atom. 576 00:34:02,780 --> 00:34:04,750 Atoms are small. 577 00:34:04,750 --> 00:34:07,601 So they're going to be somewhat near each other. 578 00:34:07,601 --> 00:34:09,100 Now, we can think about what happens 579 00:34:09,100 --> 00:34:12,064 if they're right on top of each other and are a 0. 580 00:34:12,064 --> 00:34:14,230 And here, we can try out the clickers one more time. 581 00:34:27,030 --> 00:34:28,889 OK, so we'll do 10 seconds. 582 00:34:28,889 --> 00:34:30,041 Oh, the colors changed. 583 00:34:42,449 --> 00:34:46,889 So most people had it's infinitely attractive. 584 00:34:46,889 --> 00:34:53,969 So infinitely attractive, like most chemists, except Avogadro. 585 00:34:53,969 --> 00:34:55,469 He's very strange looking. 586 00:34:55,469 --> 00:35:00,370 OK, so if these things are going to be close to each other, 587 00:35:00,370 --> 00:35:02,190 then they should be attracted to each other 588 00:35:02,190 --> 00:35:04,710 and collapse into each other. 589 00:35:04,710 --> 00:35:07,860 So why then are the electron and the nucleus 590 00:35:07,860 --> 00:35:09,570 that are infinitely attracted to each 591 00:35:09,570 --> 00:35:11,736 other-- why do they stay apart? 592 00:35:14,670 --> 00:35:19,730 So Coulomb's Law is not helping us understand this. 593 00:35:19,730 --> 00:35:22,730 But it's really just talking about the force with respect 594 00:35:22,730 --> 00:35:24,210 to a distance. 595 00:35:24,210 --> 00:35:27,230 It's not telling us anything about what happens 596 00:35:27,230 --> 00:35:29,520 when r changes with time. 597 00:35:29,520 --> 00:35:32,820 So we'll find in chemistry sometimes that things 598 00:35:32,820 --> 00:35:35,550 are spontaneous in one direction, 599 00:35:35,550 --> 00:35:37,190 but they're also very slow. 600 00:35:37,190 --> 00:35:39,360 So you don't have that the thing doesn't happen, 601 00:35:39,360 --> 00:35:41,730 it's just kinetically very slow. 602 00:35:41,730 --> 00:35:43,310 So let's consider time now. 603 00:35:43,310 --> 00:35:45,300 Maybe that will help us understand 604 00:35:45,300 --> 00:35:46,880 why this is not working. 605 00:35:46,880 --> 00:35:50,020 It doesn't, but let's look at that. 606 00:35:50,020 --> 00:35:51,270 So what do we know about time? 607 00:35:51,270 --> 00:35:54,480 What do we know about acceleration and force in time? 608 00:35:54,480 --> 00:35:58,020 We need a classical equation of motion 609 00:35:58,020 --> 00:36:01,830 that can explain how the electron and the nucleus 610 00:36:01,830 --> 00:36:03,510 could move under force. 611 00:36:03,510 --> 00:36:05,400 So we have our good friend. 612 00:36:05,400 --> 00:36:07,590 We have Newton's Second Law. 613 00:36:07,590 --> 00:36:12,210 We have f equals Ma, force equals mass times acceleration. 614 00:36:12,210 --> 00:36:14,360 So let's think about what this tells us 615 00:36:14,360 --> 00:36:18,230 about the electron and the nucleus. 616 00:36:18,230 --> 00:36:23,250 So we can express force as a function of velocity. 617 00:36:23,250 --> 00:36:28,940 We can also do that in terms of distance. 618 00:36:28,940 --> 00:36:31,750 So now, let's think about what's happening. 619 00:36:31,750 --> 00:36:32,820 We know the force. 620 00:36:32,820 --> 00:36:35,970 We can calculate the force from the Coulomb's Force 621 00:36:35,970 --> 00:36:41,420 Law, the force between the nucleus and the electron. 622 00:36:41,420 --> 00:36:44,400 And then we can think about two different distances, 623 00:36:44,400 --> 00:36:48,360 and with that force, how fast the particles should 624 00:36:48,360 --> 00:36:50,520 move toward each other. 625 00:36:50,520 --> 00:36:54,810 So for the initial distance, we can put take 0.5 angstroms, 626 00:36:54,810 --> 00:36:57,380 or 0.5 times 10 to the 10th meters, 627 00:36:57,380 --> 00:37:00,090 so that's about the radius of a hydrogen atom. 628 00:37:00,090 --> 00:37:03,000 So we take that distance. 629 00:37:03,000 --> 00:37:06,360 And then we want to think about how fast that would then 630 00:37:06,360 --> 00:37:10,110 go to 0. 631 00:37:10,110 --> 00:37:15,510 And it's fast, approximately 10 to the 10th seconds. 632 00:37:15,510 --> 00:37:19,190 Or the electron should plummet into the nucleus 633 00:37:19,190 --> 00:37:20,946 in about 0.1 nanoseconds. 634 00:37:24,280 --> 00:37:26,426 It doesn't do that though. 635 00:37:26,426 --> 00:37:29,000 So we have these beautiful classical laws. 636 00:37:29,000 --> 00:37:31,360 I'm a big fan of f equals Ma. 637 00:37:31,360 --> 00:37:33,210 I like all these things. 638 00:37:33,210 --> 00:37:36,450 But it's not working to describe what's happening here. 639 00:37:36,450 --> 00:37:39,050 So we discovered the electron, discovered the nucleus, 640 00:37:39,050 --> 00:37:40,410 but now we have a new problem. 641 00:37:40,410 --> 00:37:43,550 We don't understand why the electron isn't 642 00:37:43,550 --> 00:37:45,920 plummeting into the nucleus. 643 00:37:45,920 --> 00:37:49,160 So what's the problem here? 644 00:37:49,160 --> 00:37:56,530 So is the problem Coulomb's Force or Newton's Second Law? 645 00:37:56,530 --> 00:38:00,280 And it turns out, as most of you are probably aware, 646 00:38:00,280 --> 00:38:04,100 it's that classical mechanics doesn't work when you consider 647 00:38:04,100 --> 00:38:06,320 things on this size scale. 648 00:38:06,320 --> 00:38:11,750 So we need a new way to describe what's going on here. 649 00:38:11,750 --> 00:38:14,550 Classical mechanics isn't working. 650 00:38:14,550 --> 00:38:17,990 And so we need quantum mechanics. 651 00:38:17,990 --> 00:38:21,860 And so that is allowing us to understand the behavior 652 00:38:21,860 --> 00:38:23,530 that we're actually observing. 653 00:38:23,530 --> 00:38:25,460 We're not observing this plummeting, 654 00:38:25,460 --> 00:38:27,650 so there must be a better way to do this. 655 00:38:27,650 --> 00:38:30,380 And when you're on this really small scale, 656 00:38:30,380 --> 00:38:33,110 you need a different way to describe the behavior. 657 00:38:33,110 --> 00:38:35,570 And so next week, we're going to be moving in, and thinking 658 00:38:35,570 --> 00:38:37,980 about quantum mechanics. 659 00:38:37,980 --> 00:38:41,270 And if anyone's still having clicker questions 660 00:38:41,270 --> 00:38:45,950 or needs a clicker, we'll be down here to help you out. 661 00:38:45,950 --> 00:38:50,140 And otherwise, I will see you on Monday.