1 00:00:00,000 --> 00:00:00,042 The following content is provided under a Creative 2 00:00:00,042 --> 00:00:00,063 Commons license. 3 00:00:00,063 --> 00:00:00,148 Your support will help MIT OpenCourseWare continue to 4 00:00:00,148 --> 00:00:00,281 offer high quality educational resources for free. 5 00:00:00,281 --> 00:00:00,452 To make a donation or view additional materials from 6 00:00:00,452 --> 00:00:00,585 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:00,585 --> 00:00:00,620 ocw.mit.edu. 8 00:00:00,620 --> 00:00:23,520 PROFESSOR: So, our first question here is about 9 00:00:23,520 --> 00:00:24,550 limiting reactants. 10 00:00:24,550 --> 00:00:27,620 So, that's something you will encounter in your review 11 00:00:27,620 --> 00:00:30,410 reading for the sections, that kind of review -- what we hope 12 00:00:30,410 --> 00:00:33,220 you have picked up from high school or will pick up quickly 13 00:00:33,220 --> 00:00:34,780 by doing some review. 14 00:00:34,780 --> 00:00:38,140 So, how about we have everyone take ten more seconds on the 15 00:00:38,140 --> 00:00:59,090 clicker question, get your final answer in here. 16 00:00:59,090 --> 00:00:59,460 All right. 17 00:00:59,460 --> 00:01:03,230 So, let's see what we have. 18 00:01:03,230 --> 00:01:05,240 All right, so it looks like we weren't showing the 19 00:01:05,240 --> 00:01:08,700 percentages here, but it looks like hopefully most of you 20 00:01:08,700 --> 00:01:11,990 were able to get the correct answer of H2 being the 21 00:01:11,990 --> 00:01:13,220 limiting reactant. 22 00:01:13,220 --> 00:01:16,060 It looks like we're still figuring out -- this room was 23 00:01:16,060 --> 00:01:18,930 just renovated, we're still working out exactly how the 24 00:01:18,930 --> 00:01:19,870 electronics work. 25 00:01:19,870 --> 00:01:21,910 So, normally we'll see a percentage of how many of you 26 00:01:21,910 --> 00:01:24,600 got it, but I'm going to say it was probably about 95% got 27 00:01:24,600 --> 00:01:25,610 the answer right. 28 00:01:25,610 --> 00:01:27,420 So, good job there. 29 00:01:27,420 --> 00:01:30,590 If you didn't get the answer right -- we'll send these 30 00:01:30,590 --> 00:01:31,860 questions to your TA, so any time you get a clicker 31 00:01:31,860 --> 00:01:34,340 question wrong and you're confused, bring it up in the 32 00:01:34,340 --> 00:01:36,080 next recitation section and you'll be able 33 00:01:36,080 --> 00:01:37,650 to discuss it there. 34 00:01:37,650 --> 00:01:42,480 So, starting in, we can switch over to the to the notes now. 35 00:01:42,480 --> 00:01:46,050 When we left off on Wednesday, what we had really been doing 36 00:01:46,050 --> 00:01:48,480 is trying to give you an overview of all of the 37 00:01:48,480 --> 00:01:49,850 different topics that we're going to be 38 00:01:49,850 --> 00:01:52,200 going over this semester. 39 00:01:52,200 --> 00:01:56,400 And also, to make a couple of those connections between the 40 00:01:56,400 --> 00:01:59,430 principles we're learning, and some of the exciting research 41 00:01:59,430 --> 00:02:02,060 that's going on at MIT in the Chemistry Department, and 42 00:02:02,060 --> 00:02:05,170 also, to give you the idea that we are going to be trying 43 00:02:05,170 --> 00:02:08,040 to make these connections between the chemistry and 44 00:02:08,040 --> 00:02:10,880 things like human health or medicine. 45 00:02:10,880 --> 00:02:15,600 So, now we get to actually take a step back and start at 46 00:02:15,600 --> 00:02:18,560 the beginning, because before we can talk about some of the 47 00:02:18,560 --> 00:02:22,250 more complex issues, which involve interactions between 48 00:02:22,250 --> 00:02:25,590 molecules reacting or even when we're talking about 49 00:02:25,590 --> 00:02:28,490 individual molecules -- the bonds that form between 50 00:02:28,490 --> 00:02:31,670 individual atoms -- before any of that we actually need to 51 00:02:31,670 --> 00:02:35,390 establish a way that we're going to describe and think 52 00:02:35,390 --> 00:02:39,590 about how an individual atom behaves. 53 00:02:39,590 --> 00:02:42,980 And the way that we'll do this is starting with talking about 54 00:02:42,980 --> 00:02:48,070 the discovery of the electron and the nucleus here. 55 00:02:48,070 --> 00:02:52,660 Once we go through that, we will be able to talk about 56 00:02:52,660 --> 00:02:55,880 describing an atom using classical physics. 57 00:02:55,880 --> 00:02:59,560 So, once we have an atom and a nucleus, what we'll try to do 58 00:02:59,560 --> 00:03:03,290 is apply the classical mechanics to 59 00:03:03,290 --> 00:03:05,310 explain how that behaves. 60 00:03:05,310 --> 00:03:09,080 What we'll find is that this fails, and once this fails 61 00:03:09,080 --> 00:03:10,710 we're going to need another option. 62 00:03:10,710 --> 00:03:13,640 Luckily for us, we have quantum mechanics, which we'll 63 00:03:13,640 --> 00:03:16,280 be talking about for the next few lectures, and 64 00:03:16,280 --> 00:03:17,470 we'll dive into that. 65 00:03:17,470 --> 00:03:19,280 We might get a chance to introduce it today, but 66 00:03:19,280 --> 00:03:21,780 certainly in next class we'll be introducing this new kind 67 00:03:21,780 --> 00:03:23,790 of mechanics that's going to allow to describe 68 00:03:23,790 --> 00:03:24,620 the behavior of atoms. 69 00:03:24,620 --> 00:03:28,990 So, I want to point out that it makes a lot of sense for us 70 00:03:28,990 --> 00:03:32,460 to start with the discovery of the electron and the nucleus, 71 00:03:32,460 --> 00:03:35,020 because it really highlights one of the big issues that 72 00:03:35,020 --> 00:03:38,460 comes up in all chemistry research that you do, and that 73 00:03:38,460 --> 00:03:43,190 is how do we actually study, or in this case, how do we 74 00:03:43,190 --> 00:03:47,590 discover atoms or sub-particles that we actually 75 00:03:47,590 --> 00:03:48,820 can't see at all. 76 00:03:48,820 --> 00:03:51,400 And there are lots of solutions that chemists come 77 00:03:51,400 --> 00:03:54,400 up with -- there's always new techniques that allow us to do 78 00:03:54,400 --> 00:03:57,560 this, and these are just some of the first, and we'll go 79 00:03:57,560 --> 00:04:00,680 through them in a little bit of detail here. 80 00:04:00,680 --> 00:04:03,370 So, this all starts, in terms of putting it in its 81 00:04:03,370 --> 00:04:06,190 historical context at the turn of the Century, we said we'd 82 00:04:06,190 --> 00:04:08,410 start right in on the 20th Century of 83 00:04:08,410 --> 00:04:09,620 where chemistry was. 84 00:04:09,620 --> 00:04:12,230 And where we where at the start of the 20th Century in 85 00:04:12,230 --> 00:04:15,450 the late 1890's is that we were at a place where there 86 00:04:15,450 --> 00:04:19,380 was great confidence in our understanding of the universe, 87 00:04:19,380 --> 00:04:21,710 and our understanding of how all matter worked. 88 00:04:21,710 --> 00:04:24,600 So, people in the chemistry community and in the physics 89 00:04:24,600 --> 00:04:27,690 community had this general feeling that the theoretical 90 00:04:27,690 --> 00:04:30,650 structure of the entire universe was pretty well 91 00:04:30,650 --> 00:04:31,620 understood. 92 00:04:31,620 --> 00:04:34,435 And they had this feeling because there had just been 93 00:04:34,435 --> 00:04:38,300 this huge boon of discovery, of scientific advances that 94 00:04:38,300 --> 00:04:42,040 included Newtonian mechanics, it included Dalton's atomic 95 00:04:42,040 --> 00:04:45,080 theory of matter, also thermodynamics and classical 96 00:04:45,080 --> 00:04:46,130 electromagnetism. 97 00:04:46,130 --> 00:04:49,090 So, you can understand they really felt quite confident at 98 00:04:49,090 --> 00:04:52,080 this time that we could explain everything that was 99 00:04:52,080 --> 00:04:55,070 going on, and in fact, a really telling quote from the 100 00:04:55,070 --> 00:04:58,740 time was said by a professor at the University of Chicago, 101 00:04:58,740 --> 00:05:02,760 and what he said is, "Our future discoveries must be 102 00:05:02,760 --> 00:05:06,430 looked for in the sixth decimal place." 103 00:05:06,430 --> 00:05:10,700 So, basically what he's saying here is we pretty much 104 00:05:10,700 --> 00:05:13,870 understand what's going on, there's nothing new to really 105 00:05:13,870 --> 00:05:19,380 discover, all we need to do is measure things more precisely. 106 00:05:19,380 --> 00:05:24,900 So, that's not exactly the case, and we're going to start 107 00:05:24,900 --> 00:05:28,040 in at the point where right around this time of great 108 00:05:28,040 --> 00:05:31,590 confidence of feeling all has been conquered, there are some 109 00:05:31,590 --> 00:05:34,610 observations and discoveries that are made that completely 110 00:05:34,610 --> 00:05:36,170 break down these theories. 111 00:05:36,170 --> 00:05:39,780 For example, in terms of the atomic theory of matter, at 112 00:05:39,780 --> 00:05:42,900 the time at the turn of the Century, the understanding was 113 00:05:42,900 --> 00:05:47,020 that atoms were the most basic constituent of matter, meaning 114 00:05:47,020 --> 00:05:49,790 you couldn't break atoms up into anything smaller -- that 115 00:05:49,790 --> 00:05:51,150 was it, you're done. 116 00:05:51,150 --> 00:05:54,570 And with using Newtonian mechanics, it was assumed 117 00:05:54,570 --> 00:05:58,210 since this type of mechanics worked so well to describe 118 00:05:58,210 --> 00:06:00,355 everything we could see, it could even describe the 119 00:06:00,355 --> 00:06:03,390 universe and planets, that, of course, we could use Newtonian 120 00:06:03,390 --> 00:06:07,310 mechanics to describe how an electron -- actually, we 121 00:06:07,310 --> 00:06:09,400 didn't even know about an electron here, but how atoms 122 00:06:09,400 --> 00:06:14,310 behaved, and it turns out this is not the case, and the first 123 00:06:14,310 --> 00:06:18,030 step in discovering this is not the case, was accomplished 124 00:06:18,030 --> 00:06:21,620 by J.J. Thomson, and J.J. Thomson is credited for 125 00:06:21,620 --> 00:06:24,230 discovering the electron. 126 00:06:24,230 --> 00:06:28,590 He was a physicist in England, and what his laboratory was 127 00:06:28,590 --> 00:06:32,970 studying is something called cathode rays, and cathode rays 128 00:06:32,970 --> 00:06:36,150 are simply rays that are emitted when you have a high 129 00:06:36,150 --> 00:06:39,970 voltage difference between two electrodes. 130 00:06:39,970 --> 00:06:45,000 So, if you look at this set up, what he did when he was 131 00:06:45,000 --> 00:06:48,440 studying these rays is he had an evacuated tube, which is 132 00:06:48,440 --> 00:06:50,904 schematically shown here, where it's evacuated of all 133 00:06:50,904 --> 00:06:55,260 it's air and filled instead just with hydrogen gas, and he 134 00:06:55,260 --> 00:06:57,740 had this high voltage difference between an anode 135 00:06:57,740 --> 00:07:01,200 and a cathode, and he actually put a little hole in the anode 136 00:07:01,200 --> 00:07:04,760 here, so these cathode rays that were produced could shoot 137 00:07:04,760 --> 00:07:08,340 out of the cathode and actually could be detected as 138 00:07:08,340 --> 00:07:11,850 this luminescent spot on a detector screen. 139 00:07:11,850 --> 00:07:14,020 So, lots of people were studying cathode rays at the 140 00:07:14,020 --> 00:07:17,320 time -- one reason is they actually gave off this bright 141 00:07:17,320 --> 00:07:19,580 glow -- if you put them in an evacuated glass tube, you got 142 00:07:19,580 --> 00:07:22,780 these crazy patterns and glowing colors. 143 00:07:22,780 --> 00:07:25,730 So, for that reason it was a very hot 144 00:07:25,730 --> 00:07:27,680 issue in terms of research. 145 00:07:27,680 --> 00:07:30,870 But also, no one really knew what these were and Thomson 146 00:07:30,870 --> 00:07:34,960 was seeking to figure out some more properties of them, and 147 00:07:34,960 --> 00:07:38,150 he had the theory that maybe they were actually charged 148 00:07:38,150 --> 00:07:41,410 particles of some sort, and others had proposed this in 149 00:07:41,410 --> 00:07:43,790 the past, but they didn't really have an experimental 150 00:07:43,790 --> 00:07:44,780 set up to test it. 151 00:07:44,780 --> 00:07:47,370 And that's what Thomson did. 152 00:07:47,370 --> 00:07:50,680 And what we did was he put two detection plates on either 153 00:07:50,680 --> 00:07:55,240 side of these cathode rays, and when he put a voltage 154 00:07:55,240 --> 00:07:57,710 difference between these two plates, he wanted to see if he 155 00:07:57,710 --> 00:08:00,380 could actually bend the rays and test if they're actually 156 00:08:00,380 --> 00:08:01,620 charged or not. 157 00:08:01,620 --> 00:08:04,035 So, when the voltage difference between the plates 158 00:08:04,035 --> 00:08:07,440 is zero, or when we just don't have the plates there at all, 159 00:08:07,440 --> 00:08:10,450 the cathode rays are not bent, they just go right in a 160 00:08:10,450 --> 00:08:15,000 straight line, and they can be detected on this screen. 161 00:08:15,000 --> 00:08:18,260 When he actually cranked up the voltage between these two 162 00:08:18,260 --> 00:08:21,850 plates, what he saw was really amazing to him, which is that 163 00:08:21,850 --> 00:08:24,880 he actually was able to bend these rays -- this had never 164 00:08:24,880 --> 00:08:28,550 been observed before in any capacity, and he was able to 165 00:08:28,550 --> 00:08:31,660 detect on his screen that there was this deflection, and 166 00:08:31,660 --> 00:08:33,730 he could even measure the degree of the 167 00:08:33,730 --> 00:08:35,840 deflection that he had. 168 00:08:35,840 --> 00:08:38,880 So, we know now that we have charged particles. 169 00:08:38,880 --> 00:08:41,620 Are these negatively or positively charged, based on 170 00:08:41,620 --> 00:08:41,800 this evidence? 171 00:08:41,800 --> 00:08:43,580 STUDENT: Negatively. 172 00:08:43,580 --> 00:08:44,400 PROFESSOR: Yeah, that's right. 173 00:08:44,400 --> 00:08:48,300 So, what we have here, cathode rays we now know are 174 00:08:48,300 --> 00:08:51,270 negatively charged particles. 175 00:08:51,270 --> 00:08:56,290 And, in fact, he named these negatively charged particles. 176 00:08:56,290 --> 00:08:59,140 Does anyone know what he named them? 177 00:08:59,140 --> 00:09:01,520 No, not electrons -- very good guess. 178 00:09:01,520 --> 00:09:03,140 He named them corpuscles. 179 00:09:03,140 --> 00:09:05,750 Has anyone heard of corpuscles? 180 00:09:05,750 --> 00:09:07,080 A little bit. 181 00:09:07,080 --> 00:09:10,420 Yeah, so it was later named that these particles were, in 182 00:09:10,420 --> 00:09:13,120 fact, electrons, and that's what they are. 183 00:09:13,120 --> 00:09:15,920 J.J. Thomson continued to call them corpuscles for many, 184 00:09:15,920 --> 00:09:18,040 many, many years after everyone else called them 185 00:09:18,040 --> 00:09:21,010 electrons, but I'm sure no one minded because he did, in 186 00:09:21,010 --> 00:09:22,680 fact, discover them. 187 00:09:22,680 --> 00:09:25,900 And he was actually able to find out more than just that 188 00:09:25,900 --> 00:09:27,670 these were charged. 189 00:09:27,670 --> 00:09:29,940 From classical electromagnetism, he could 190 00:09:29,940 --> 00:09:33,400 actually relate the degree of deflection that he saw to the 191 00:09:33,400 --> 00:09:36,970 charge and the mass of the particles. 192 00:09:36,970 --> 00:09:41,210 So, using that he could say that delta x, and we'll put 193 00:09:41,210 --> 00:09:43,670 sub-negative, because we know now that these are negative 194 00:09:43,670 --> 00:09:53,370 particles, is proportional to the charge on that particle 195 00:09:53,370 --> 00:09:55,230 over m, which is the mass. 196 00:09:55,230 --> 00:09:59,540 So, we have e being equal to the charge of the negative 197 00:09:59,540 --> 00:10:05,100 particles, and m, of course, is equal to the 198 00:10:05,100 --> 00:10:08,990 mass of those particles. 199 00:10:08,990 --> 00:10:13,910 So, Thomson didn't stop here, he actually continued 200 00:10:13,910 --> 00:10:16,150 experimenting with different voltages. 201 00:10:16,150 --> 00:10:21,050 And what he found was if he really, really ramped the 202 00:10:21,050 --> 00:10:25,200 voltage up between those two plates, he could actually 203 00:10:25,200 --> 00:10:26,810 detect something else. 204 00:10:26,810 --> 00:10:30,310 And what he could detect here is that there was this little 205 00:10:30,310 --> 00:10:33,630 spot of luminescence that he could see on the screen that 206 00:10:33,630 --> 00:10:37,520 was barely deflected at all -- certainly in comparison to how 207 00:10:37,520 --> 00:10:39,530 strongly this first particle was deflected. 208 00:10:39,530 --> 00:10:44,220 The second particle was deflected almost not at all. 209 00:10:44,220 --> 00:10:47,150 But what he could tell from the fact that there was a 210 00:10:47,150 --> 00:10:49,550 second particle at all, and the fact that it was in this 211 00:10:49,550 --> 00:10:53,100 direction, is that in addition to his negative particle, he 212 00:10:53,100 --> 00:10:56,390 also, of course, had a positive particle that was 213 00:10:56,390 --> 00:10:58,690 within this stream of rays that were coming out. 214 00:10:58,690 --> 00:11:02,590 So, of course, he can use the same relationship for the 215 00:11:02,590 --> 00:11:08,640 positive particle, so delta x now of the positive is 216 00:11:08,640 --> 00:11:14,960 proportional to the charge on the positive particle all over 217 00:11:14,960 --> 00:11:18,910 the mass of the positive particle. 218 00:11:18,910 --> 00:11:21,880 So, this is interesting for several reasons. 219 00:11:21,880 --> 00:11:26,680 What did he manage to pull out information-wise from using 220 00:11:26,680 --> 00:11:28,020 these two relationships? 221 00:11:28,020 --> 00:11:31,290 And actually to do this, he made a few more observations. 222 00:11:31,290 --> 00:11:33,950 The first, which I just stated, is that the deflection 223 00:11:33,950 --> 00:11:37,620 of that negative particle was just far and away more 224 00:11:37,620 --> 00:11:39,950 extreme, much, much larger than that of 225 00:11:39,950 --> 00:11:42,360 the positive particle. 226 00:11:42,360 --> 00:11:45,770 The other assumption that he made here is that the charge 227 00:11:45,770 --> 00:11:47,870 on the two particles was equal. 228 00:11:47,870 --> 00:11:49,700 So, how could he know that the charge on the two 229 00:11:49,700 --> 00:11:51,020 particles was equal? 230 00:11:51,020 --> 00:11:53,120 And actually he couldn't exactly know it -- it was a 231 00:11:53,120 --> 00:11:56,920 very good assumption that he made, and he could make the 232 00:11:56,920 --> 00:12:00,110 assumption because he, in fact, did know that what he 233 00:12:00,110 --> 00:12:02,890 started with was this hydrogen gas. 234 00:12:02,890 --> 00:12:04,900 So, he was starting with hydrogen. 235 00:12:04,900 --> 00:12:08,900 If some negative particle was popping out from the hydrogen, 236 00:12:08,900 --> 00:12:13,020 then what he must be left with is h-plus, and since hydrogen 237 00:12:13,020 --> 00:12:17,040 itself is neutral, the h-plus and the electron had to add up 238 00:12:17,040 --> 00:12:18,220 to be a neutral charge. 239 00:12:18,220 --> 00:12:21,020 So, that means the charges of the two pieces, the positive 240 00:12:21,020 --> 00:12:23,760 and negative particle, must be equal in 241 00:12:23,760 --> 00:12:27,250 terms of absolute charge. 242 00:12:27,250 --> 00:12:30,820 So, using this relationship, he could then actually figure 243 00:12:30,820 --> 00:12:35,130 out by knowing, which he knows how much each of them were 244 00:12:35,130 --> 00:12:40,820 deflected, he could now try to think about whether or not he 245 00:12:40,820 --> 00:12:44,300 could make some relationship between the masses -- between 246 00:12:44,300 --> 00:12:48,510 the mass of the positive and the negative particle. 247 00:12:48,510 --> 00:12:53,150 So, this relationship he was looking at was starting with 248 00:12:53,150 --> 00:12:58,720 the deflection, and the absolute distance that the 249 00:12:58,720 --> 00:12:59,830 particles were deflected. 250 00:12:59,830 --> 00:13:03,660 So, what he could set that equal to is he knows what x is 251 00:13:03,660 --> 00:13:07,090 proportional to in terms of the negative particle, so 252 00:13:07,090 --> 00:13:12,360 that's just the absolute value of the charge over the mass of 253 00:13:12,360 --> 00:13:13,510 the negative particle. 254 00:13:13,510 --> 00:13:20,340 He could divide all of that by the absolute value of the 255 00:13:20,340 --> 00:13:24,450 charge of the positive particle, all over the mass of 256 00:13:24,450 --> 00:13:26,780 the positive particle. 257 00:13:26,780 --> 00:13:29,640 And as we said, he made the assumption that those two 258 00:13:29,640 --> 00:13:32,350 charges were equal, so we can go ahead and 259 00:13:32,350 --> 00:13:34,190 cross those right out. 260 00:13:34,190 --> 00:13:37,130 So, what that told him was if he knew the relationship 261 00:13:37,130 --> 00:13:40,400 between how far they were each displaced, he could also know 262 00:13:40,400 --> 00:13:41,150 something about the 263 00:13:41,150 --> 00:13:44,180 relationship of the two masses. 264 00:13:44,180 --> 00:13:48,130 So essentially, there was an inversely proportional 265 00:13:48,130 --> 00:13:51,960 relationship between how far the particles were displaced, 266 00:13:51,960 --> 00:13:56,450 and what the mass of the two particles turned out to be. 267 00:13:56,450 --> 00:14:00,290 So, because he, of course, observed that the negative 268 00:14:00,290 --> 00:14:02,990 particle travelled -- it was deflected much, much further 269 00:14:02,990 --> 00:14:06,710 by those plates, what he could also assume and make the 270 00:14:06,710 --> 00:14:11,490 conclusion of is that the mass of that negative particle is 271 00:14:11,490 --> 00:14:13,450 actually larger or smaller? 272 00:14:13,450 --> 00:14:15,100 STUDENT: Smaller. 273 00:14:15,100 --> 00:14:19,210 PROFESSOR: Much, much smaller, exactly, then the mass of the 274 00:14:19,210 --> 00:14:20,440 positive particle. 275 00:14:20,440 --> 00:14:23,620 So essentially, what he found here is the relationship 276 00:14:23,620 --> 00:14:28,080 between the mass of an electron and the mass of the 277 00:14:28,080 --> 00:14:31,090 rest of the atom, the rest of the hydrogen atom there, which 278 00:14:31,090 --> 00:14:32,740 is an ion in this case. 279 00:14:32,740 --> 00:14:36,940 And, in fact, it's so much smaller, it's close to 2,000 280 00:14:36,940 --> 00:14:41,480 times smaller, that we can make the assumption that 281 00:14:41,480 --> 00:14:44,480 essentially the electrons take up no mass. 282 00:14:44,480 --> 00:14:47,140 I mean they take up a teeny bit, but essentially, when 283 00:14:47,140 --> 00:14:50,390 we're thinking about the set up of the atom, we don't have 284 00:14:50,390 --> 00:14:53,070 to account for them as using up a lot of the mass we're 285 00:14:53,070 --> 00:14:55,610 discussing. 286 00:14:55,610 --> 00:15:00,360 So, Thomson came up with a model for the atom due to 287 00:15:00,360 --> 00:15:03,370 this, and this is called the Plum Pudding model of the 288 00:15:03,370 --> 00:15:08,600 atom, and he was, as we said, English, so plum pudding is 289 00:15:08,600 --> 00:15:10,100 kind of a British food. 290 00:15:10,100 --> 00:15:13,360 Has anyone here ever had plum pudding? 291 00:15:13,360 --> 00:15:14,240 A couple of people. 292 00:15:14,240 --> 00:15:14,860 Okay. 293 00:15:14,860 --> 00:15:17,880 I've never even seen it, so that's good -- you must be 294 00:15:17,880 --> 00:15:19,660 better travelled than I. 295 00:15:19,660 --> 00:15:23,170 So, the idea that he had here was he treated the whole of 296 00:15:23,170 --> 00:15:34,480 the atom as sort of this positive pudding, so the 297 00:15:34,480 --> 00:15:37,480 majority of the atom was just kind of this goopy, positive 298 00:15:37,480 --> 00:15:40,340 stuff that you could think about, and within the pudding, 299 00:15:40,340 --> 00:15:44,280 he had all these negative charges, which were the 300 00:15:44,280 --> 00:15:48,910 electrons, and they were the raisins or the plums that were 301 00:15:48,910 --> 00:15:50,230 in the pudding. 302 00:15:50,230 --> 00:15:54,500 So this was a revolutionary model of an atom when we 303 00:15:54,500 --> 00:15:57,070 thought of the fact that before this experiment, the 304 00:15:57,070 --> 00:15:59,600 understanding was an atom could not be divisible into 305 00:15:59,600 --> 00:16:03,040 smaller parts, and now here we are with subatomic particles 306 00:16:03,040 --> 00:16:08,500 with electrons, and this wonderful Plum Pudding model. 307 00:16:08,500 --> 00:16:10,880 So, for those of you that haven't actually had plum 308 00:16:10,880 --> 00:16:13,080 pudding, which myself is included, I threw 309 00:16:13,080 --> 00:16:15,050 a picture up here. 310 00:16:15,050 --> 00:16:18,020 This was my first glance at plum pudding, and I guess you 311 00:16:18,020 --> 00:16:22,280 can see that this must be that positive part -- most of the 312 00:16:22,280 --> 00:16:25,660 plums are within that, and you can see all these little 313 00:16:25,660 --> 00:16:29,750 raisins or plums in here, that would be that negative charge. 314 00:16:29,750 --> 00:16:32,850 So, that already was a big advancement from where the 315 00:16:32,850 --> 00:16:34,370 understanding was at the time. 316 00:16:34,370 --> 00:16:37,990 We already moved way forward and completely revolutionizing 317 00:16:37,990 --> 00:16:40,550 the understanding of an atom in that there's something in 318 00:16:40,550 --> 00:16:44,380 an atom -- it's not the smallest thing there is. 319 00:16:44,380 --> 00:16:47,950 However, as you know, we didn't stop at the plum 320 00:16:47,950 --> 00:16:50,460 pudding model, which is good, because it's a little goofy, 321 00:16:50,460 --> 00:16:53,870 so it's nice to move on from that and move on we did. 322 00:16:53,870 --> 00:16:58,180 About 10 to 15 years later, another physicist, Ernest 323 00:16:58,180 --> 00:17:02,820 Rutherford, actually put this plum pudding model to test, 324 00:17:02,820 --> 00:17:06,170 and he did it through studies that he'd been doing on 325 00:17:06,170 --> 00:17:08,670 radiation that was emitting something 326 00:17:08,670 --> 00:17:11,460 called alpha particles. 327 00:17:11,460 --> 00:17:14,940 So, Rutherford, some of you may recognize that name, is a 328 00:17:14,940 --> 00:17:18,820 very famous physicist who made a lot of contributions in 329 00:17:18,820 --> 00:17:20,610 terms of radioactivity. 330 00:17:20,610 --> 00:17:23,080 When he was studying these alpha particles, he was 331 00:17:23,080 --> 00:17:25,290 actually the first person to identify the difference 332 00:17:25,290 --> 00:17:28,530 between different types of particles that radioactive 333 00:17:28,530 --> 00:17:30,400 materials emit. 334 00:17:30,400 --> 00:17:34,030 And he got this particular material that he was studying, 335 00:17:34,030 --> 00:17:37,150 radium bromide from his good friend, Marie Curie, who, 336 00:17:37,150 --> 00:17:42,650 obviously, also was a leader, really the leader in figuring 337 00:17:42,650 --> 00:17:45,350 out much of how radioactive materials work. 338 00:17:45,350 --> 00:17:47,850 She has two Nobel Prizes for her work 339 00:17:47,850 --> 00:17:50,360 in radioactive materials. 340 00:17:50,360 --> 00:17:53,540 And something that maybe many of you think, which I know I 341 00:17:53,540 --> 00:17:57,120 always think when I hear about radioactivity studies in the 342 00:17:57,120 --> 00:18:01,195 early 1900's, is oh, my gosh, this sounds really dangerous, 343 00:18:01,195 --> 00:18:04,470 right, they're using radium bromide, and this is pretty 344 00:18:04,470 --> 00:18:06,720 dangerous radioactive material. 345 00:18:06,720 --> 00:18:10,300 So, for those of you that don't know radium is extremely 346 00:18:10,300 --> 00:18:14,640 radioactive, even in the range of radioactivity, and one of 347 00:18:14,640 --> 00:18:17,250 the major problems with it is that if it does get in your 348 00:18:17,250 --> 00:18:21,020 body, the radium is treated as calcium in your body. 349 00:18:21,020 --> 00:18:23,910 So, you can imagine what happens as it gets deposited 350 00:18:23,910 --> 00:18:28,330 into your bones, which is not the ideal situation after a 351 00:18:28,330 --> 00:18:30,390 long day in the lab. 352 00:18:30,390 --> 00:18:33,650 So, this is really a pretty dangerous situation that's 353 00:18:33,650 --> 00:18:35,080 always interesting to point out. 354 00:18:35,080 --> 00:18:37,410 He got this from Marie Curie -- you can imagine they used 355 00:18:37,410 --> 00:18:39,410 the postal service, I'm not sure how else they would have 356 00:18:39,410 --> 00:18:41,380 transferred it to each other. 357 00:18:41,380 --> 00:18:44,320 So, it really brings up some issues. 358 00:18:44,320 --> 00:18:48,540 The first thing I did when I heard that is actually look up 359 00:18:48,540 --> 00:18:53,080 to see how, in fact, Ernest Rutherford did die in 1937, 360 00:18:53,080 --> 00:18:54,430 and you'll be happy to know, it actually wasn't from 361 00:18:54,430 --> 00:18:57,610 radiation poisoning or from bone cancer, so that's really 362 00:18:57,610 --> 00:19:03,880 good that that worked out okay for him, and that he did get 363 00:19:03,880 --> 00:19:07,010 to, sort of safely, at least end his life before the 364 00:19:07,010 --> 00:19:08,190 radiation ended it. 365 00:19:08,190 --> 00:19:10,960 But it's really interesting the studies that he did do 366 00:19:10,960 --> 00:19:13,430 with radium bromide, and he was 367 00:19:13,430 --> 00:19:15,340 studying the alpha particles. 368 00:19:15,340 --> 00:19:18,280 And what was known about alpha particles at the time is that 369 00:19:18,280 --> 00:19:20,230 they were these charged particles and that they were 370 00:19:20,230 --> 00:19:21,460 very heavy. 371 00:19:21,460 --> 00:19:23,950 Does anyone know more than what Rutherford knew at the 372 00:19:23,950 --> 00:19:27,590 time, what alpha particles actually are? 373 00:19:27,590 --> 00:19:28,380 Yeah, good. 374 00:19:28,380 --> 00:19:30,940 So, they're actually helium atoms, helium ions. 375 00:19:30,940 --> 00:19:35,060 And this wasn't really important for the studies, it 376 00:19:35,060 --> 00:19:37,720 didn't matter that didn't know what they are, but it's nice 377 00:19:37,720 --> 00:19:41,390 to kind of know now -- that we do know what they were using. 378 00:19:41,390 --> 00:19:44,820 And he was doing quite a few studies with them. 379 00:19:44,820 --> 00:19:48,840 One experiment that he was doing is detecting the number 380 00:19:48,840 --> 00:19:52,160 of particles that were being emitted by this radium bromide 381 00:19:52,160 --> 00:19:54,920 as a rate, so he would measure the number of particles per 382 00:19:54,920 --> 00:19:58,580 minute that the radium bromide was emitting. 383 00:19:58,580 --> 00:20:02,570 And what he used was a detector here, so he here 384 00:20:02,570 --> 00:20:04,760 could detect how many particles were 385 00:20:04,760 --> 00:20:06,250 hitting this detector. 386 00:20:06,250 --> 00:20:10,340 He had actually developed this detector with a postdoc by the 387 00:20:10,340 --> 00:20:11,170 name of Hans Geiger. 388 00:20:11,170 --> 00:20:14,430 Does that name ring a bell? 389 00:20:14,430 --> 00:20:15,020 STUDENT: Geiger counter. 390 00:20:15,020 --> 00:20:15,410 PROFESSOR: Um-hmm, a Geiger counter. 391 00:20:15,410 --> 00:20:20,750 So, this, in fact, is my very schematic representation of a 392 00:20:20,750 --> 00:20:21,730 Geiger counter. 393 00:20:21,730 --> 00:20:24,320 For those of you don't know what that is, it's simply an 394 00:20:24,320 --> 00:20:29,430 instrument that counts radioactive particles in the 395 00:20:29,430 --> 00:20:33,110 air, and now that you're at MIT, you'll all have a chance 396 00:20:33,110 --> 00:20:35,250 to see one first hand, if you're ever in any of the 397 00:20:35,250 --> 00:20:38,370 labs, especially in the chemistry or bio labs. 398 00:20:38,370 --> 00:20:42,160 As carefully as people work with radioactivity here, and 399 00:20:42,160 --> 00:20:45,000 using often much, much safer radioactive materials than 400 00:20:45,000 --> 00:20:47,860 radium bromide, and using them, and special hoods, and 401 00:20:47,860 --> 00:20:50,100 having special procedures, they still do a lot of 402 00:20:50,100 --> 00:20:52,040 checking with these Geiger counters to make sure 403 00:20:52,040 --> 00:20:53,340 everything's safe. 404 00:20:53,340 --> 00:20:55,870 You'll actually see a man walking around with one, 405 00:20:55,870 --> 00:20:58,450 sometimes in the halls, just kind of like this -- you hear 406 00:20:58,450 --> 00:21:01,650 that click, click, click. 407 00:21:01,650 --> 00:21:05,160 That's a good sound, it means low levels of radiation. 408 00:21:05,160 --> 00:21:08,770 He'll walk by your hood, so click by your hood -- 409 00:21:08,770 --> 00:21:11,060 I always get a little nervous when he walked by my hood, I 410 00:21:11,060 --> 00:21:14,250 don't know why, I never worked with radioactive material. 411 00:21:14,250 --> 00:21:16,500 But I was convinced I'd hear the 412 00:21:16,500 --> 00:21:18,320 click-click-click-click-click, which is what tells you you're 413 00:21:18,320 --> 00:21:20,240 in trouble. 414 00:21:20,240 --> 00:21:22,780 So, I've never heard the click-click-click-click-click, 415 00:21:22,780 --> 00:21:25,400 and we might bring a Geiger counter in here some time 416 00:21:25,400 --> 00:21:28,440 later in the semester so we can check all of you out, and 417 00:21:28,440 --> 00:21:31,730 hopefully we won't hear any when we do that either. 418 00:21:31,730 --> 00:21:33,990 So, one thing that he discovered with this detector 419 00:21:33,990 --> 00:21:37,090 initially, and he was the first to discover this, is 420 00:21:37,090 --> 00:21:40,700 that radioactive material, including radium bromide, have 421 00:21:40,700 --> 00:21:45,350 a characteristic rate that they emit, radioactive decay. 422 00:21:45,350 --> 00:21:48,250 So basically they're decaying at a constant rate, which 423 00:21:48,250 --> 00:21:53,820 means, of course, that you can figure out how old things are 424 00:21:53,820 --> 00:21:56,050 by seeing how much they've decayed. 425 00:21:56,050 --> 00:21:58,480 So, he was really the first person to discover you could 426 00:21:58,480 --> 00:22:02,690 do this, which was used to make the first somewhat close 427 00:22:02,690 --> 00:22:04,490 approximation of the age of the earth. 428 00:22:04,490 --> 00:22:07,860 So that's a pretty exciting set of experiments he did. 429 00:22:07,860 --> 00:22:10,215 But one thing that he wanted to do specific to 430 00:22:10,215 --> 00:22:13,580 understanding the atom, and using these alpha particles, 431 00:22:13,580 --> 00:22:16,800 these heavy-charged particles, was to test if this Plum 432 00:22:16,800 --> 00:22:21,370 Pudding model actually fit what he could observe. 433 00:22:21,370 --> 00:22:24,710 So, what he did was he first recorded the count rate of 434 00:22:24,710 --> 00:22:28,440 radium bromide before it's going through any kind of a 435 00:22:28,440 --> 00:22:31,250 plum pudding atom, and he found that it had a count rate 436 00:22:31,250 --> 00:22:36,190 of 132,000 alpha particles per minute were being detected by 437 00:22:36,190 --> 00:22:39,480 this Geiger counter. 438 00:22:39,480 --> 00:22:43,310 He then set up a situation where he put a very, very thin 439 00:22:43,310 --> 00:22:47,620 piece of gold foil right in what would be in the stream of 440 00:22:47,620 --> 00:22:49,120 the alpha particles. 441 00:22:49,120 --> 00:22:53,010 So, it was only 10 to the negative, 9 meters thick, so 442 00:22:53,010 --> 00:22:56,320 about one nanometer, so that's really thin, it's thinner than 443 00:22:56,320 --> 00:22:57,500 a strand of hair. 444 00:22:57,500 --> 00:23:00,410 So you can imagine, we actually don't need to think 445 00:23:00,410 --> 00:23:03,060 of it as a piece of gold foil, it might be easier to think of 446 00:23:03,060 --> 00:23:05,680 it as a couple of layers of atoms. 447 00:23:05,680 --> 00:23:09,960 So basically he's trying to put some atoms in the way of 448 00:23:09,960 --> 00:23:12,000 the alpha particle. 449 00:23:12,000 --> 00:23:17,340 And what he would expect is if this Plum Pudding model is 450 00:23:17,340 --> 00:23:20,450 true, nothing's really going to happen to the particles, 451 00:23:20,450 --> 00:23:22,470 right, they should go straight through, because if they hit 452 00:23:22,470 --> 00:23:24,140 an electron, those are so small. 453 00:23:24,140 --> 00:23:27,510 We figured out the mass is so tiny that it shouldn't really 454 00:23:27,510 --> 00:23:29,310 deflect them very much. 455 00:23:29,310 --> 00:23:33,240 And, of course, all that's left is this positive pudding. 456 00:23:33,240 --> 00:23:35,560 So that's not going to do anything either. 457 00:23:35,560 --> 00:23:38,855 And what he found when he did this experiment, was that the 458 00:23:38,855 --> 00:23:45,950 count rate with still 132,000 counts per minute. 459 00:23:45,950 --> 00:23:49,570 So, what he could conclude thus far was that this was 460 00:23:49,570 --> 00:23:52,360 really consistent with the Plum Pudding model. 461 00:23:52,360 --> 00:23:56,300 All of his heavily-charged alpha particles were going 462 00:23:56,300 --> 00:24:00,340 right through this thin layer of gold atoms. 463 00:24:00,340 --> 00:24:02,710 So, you might think that he would stop his experiments 464 00:24:02,710 --> 00:24:05,660 here, and maybe he would have, but as I mentioned, he did 465 00:24:05,660 --> 00:24:08,410 have a postdoc working with him by the name of Geiger. 466 00:24:08,410 --> 00:24:13,380 He also had an undergraduate, we could say maybe even a UROP 467 00:24:13,380 --> 00:24:18,420 working with him, and this was by the name of Marsden was the 468 00:24:18,420 --> 00:24:19,250 name of this UROP. 469 00:24:19,250 --> 00:24:23,740 And Rutherford realized, you know I have these two people 470 00:24:23,740 --> 00:24:26,750 that are very excited to work on this project, I don't need 471 00:24:26,750 --> 00:24:27,810 to spend time doing it. 472 00:24:27,810 --> 00:24:30,440 Maybe it's not the best way for me to spend time looking 473 00:24:30,440 --> 00:24:33,760 to see if I can find any bounced-back particles since 474 00:24:33,760 --> 00:24:35,770 all the particles are accounted for. 475 00:24:35,770 --> 00:24:38,600 But, you know, this undergraduate's very eager to 476 00:24:38,600 --> 00:24:41,710 do it, let's let him have a try. 477 00:24:41,710 --> 00:24:45,060 And something you might find in your UROP experience is you 478 00:24:45,060 --> 00:24:47,820 have a unique advantage as an undergraduate, which is that 479 00:24:47,820 --> 00:24:50,880 there's not a lot of pressure to actually make a huge 480 00:24:50,880 --> 00:24:53,770 discovery or necessarily accomplish a great amount. 481 00:24:53,770 --> 00:24:56,330 You have a little more pressure in grad school, but 482 00:24:56,330 --> 00:24:58,610 sometimes that means when you're an undergrad your 483 00:24:58,610 --> 00:25:01,790 advisor will decide to put you on projects that maybe when 484 00:25:01,790 --> 00:25:03,990 you look at them seem a little bit silly. 485 00:25:03,990 --> 00:25:08,130 So this project was, let's see if we can detect any alpha 486 00:25:08,130 --> 00:25:11,770 particles by making a detector that swings around. 487 00:25:11,770 --> 00:25:14,150 So, some people might say, why are we doing this? 488 00:25:14,150 --> 00:25:17,660 We know we started with a 132,000 alpha particles. 489 00:25:17,660 --> 00:25:21,330 We detected a 132,000 alpha particles. 490 00:25:21,330 --> 00:25:23,010 What are we even looking for? 491 00:25:23,010 --> 00:25:25,280 We have to build this whole new detector, is this really 492 00:25:25,280 --> 00:25:26,790 the best use of my time? 493 00:25:26,790 --> 00:25:29,050 As an undergrad, you don't have to worry about it, you're 494 00:25:29,050 --> 00:25:30,420 just worried about learning. 495 00:25:30,420 --> 00:25:33,370 You can take these big risks of time, and if at the end of 496 00:25:33,370 --> 00:25:35,960 the day there's nothing to detect, you still know how to 497 00:25:35,960 --> 00:25:37,050 build a detector. 498 00:25:37,050 --> 00:25:39,820 So, keep that in mind if you're not over-the-top 499 00:25:39,820 --> 00:25:42,260 excited about the prospects of some of your research. 500 00:25:42,260 --> 00:25:43,900 You might be surprised at what you find out. 501 00:25:43,900 --> 00:25:47,340 And this is exactly what happened with Marsden who 502 00:25:47,340 --> 00:25:50,170 discovered that when he shot the alpha particles at the 503 00:25:50,170 --> 00:25:54,600 gold foil, he detected something on his detector that 504 00:25:54,600 --> 00:25:59,000 click, click, click went a little bit faster. 505 00:25:59,000 --> 00:26:02,460 So, what he detected was that there were 20 alpha particles 506 00:26:02,460 --> 00:26:03,910 per minute. 507 00:26:03,910 --> 00:26:05,360 Does that sound significant? 508 00:26:05,360 --> 00:26:08,490 It depends, right? 509 00:26:08,490 --> 00:26:11,140 So hopefully, the first experiment he did, which I 510 00:26:11,140 --> 00:26:13,980 know that they certainly did do was maybe it's just 511 00:26:13,980 --> 00:26:15,080 background noise, right? 512 00:26:15,080 --> 00:26:18,510 So, they took away that gold foil and said is just the 513 00:26:18,510 --> 00:26:20,710 alpha particles hitting it some other way? 514 00:26:20,710 --> 00:26:21,710 And no, it wasn't. 515 00:26:21,710 --> 00:26:24,500 When he took away the gold foil, the count rate 516 00:26:24,500 --> 00:26:26,990 went down to zero. 517 00:26:26,990 --> 00:26:31,280 If he switched from gold to let's say iron, he also tried 518 00:26:31,280 --> 00:26:33,830 platinum, a number of different foils, he found that 519 00:26:33,830 --> 00:26:38,780 they count rate, it still was 20 alpha particles per minute. 520 00:26:38,780 --> 00:26:41,970 So, this is an absolutely outstanding discovery, even 521 00:26:41,970 --> 00:26:44,920 though, if we think about it, what is the probability that 522 00:26:44,920 --> 00:26:46,720 this happened, how often did this happen? 523 00:26:46,720 --> 00:26:48,420 It actually almost happened not at all. 524 00:26:48,420 --> 00:26:51,230 We can figure out exactly what the probability of this 525 00:26:51,230 --> 00:26:54,890 backscattering was just by dividing the count rate of the 526 00:26:54,890 --> 00:26:57,950 number particle that were backscattered divided by the 527 00:26:57,950 --> 00:27:00,170 count rate of the incident particles. 528 00:27:00,170 --> 00:27:03,730 So essentially, we just have 20, and our 20 529 00:27:03,730 --> 00:27:06,440 is divided by 132,000. 530 00:27:06,440 --> 00:27:10,266 So, we end up with a not so large probability of 2 times 531 00:27:10,266 --> 00:27:14,250 10 to the negative 4. 532 00:27:14,250 --> 00:27:17,910 But still, we can't even overstate how exciting this 533 00:27:17,910 --> 00:27:19,080 discovery was. 534 00:27:19,080 --> 00:27:22,440 Rutherford, the advisor here, he had a lot of good things 535 00:27:22,440 --> 00:27:25,150 happen in his life, as I mentioned. 536 00:27:25,150 --> 00:27:28,370 He was the person responsible for being able to first date 537 00:27:28,370 --> 00:27:29,600 the age of our earth. 538 00:27:29,600 --> 00:27:31,150 That's a pretty nice thing. 539 00:27:31,150 --> 00:27:34,270 He was also married, he had a child, which I hear is very 540 00:27:34,270 --> 00:27:36,930 nice, very exciting, also. 541 00:27:36,930 --> 00:27:41,680 But yet, when he saw this one single experiment from this 542 00:27:41,680 --> 00:27:46,480 undergraduate, he described this as the most incredible 543 00:27:46,480 --> 00:27:50,460 event that had ever happened to him in his life. 544 00:27:50,460 --> 00:27:54,150 So, this was a pretty big deal. 545 00:27:54,150 --> 00:27:57,490 We won't tell his daughter. 546 00:27:57,490 --> 00:28:00,530 And he gave a very good analogy in saying, "It was 547 00:28:00,530 --> 00:28:04,810 almost as incredible as if you'd fired a 15 inch shell at 548 00:28:04,810 --> 00:28:09,440 a piece of tissue paper, and it came back and hit you." 549 00:28:09,440 --> 00:28:11,680 And that really illustrates what's happening here, because 550 00:28:11,680 --> 00:28:17,880 if we think of the Plum Pudding model, it's 551 00:28:17,880 --> 00:28:21,100 essentially this very thin film, right, there's nothing 552 00:28:21,100 --> 00:28:24,270 that should hit if we send alpha particles through it. 553 00:28:24,270 --> 00:28:25,990 But what we actually have is that 554 00:28:25,990 --> 00:28:27,880 something's bouncing back. 555 00:28:27,880 --> 00:28:29,910 So, what happened is Rutherford needed to come up 556 00:28:29,910 --> 00:28:34,620 with a new model for the atom with several interpretations 557 00:28:34,620 --> 00:28:37,870 that came out of these experiments, and some of these 558 00:28:37,870 --> 00:28:41,880 interpretations were that, of course, we now know that these 559 00:28:41,880 --> 00:28:44,580 gold atoms, they must be mostly empty, and the reason 560 00:28:44,580 --> 00:28:47,340 that we know that they must be mostly empty is because all 561 00:28:47,340 --> 00:28:51,710 but 20 of these 132,000 particles 562 00:28:51,710 --> 00:28:53,430 went all the way through. 563 00:28:53,430 --> 00:28:55,270 So they weren't hitting anything, we're dealing with 564 00:28:55,270 --> 00:28:57,990 mostly empty space. 565 00:28:57,990 --> 00:29:02,390 But he also realized that when they did hit something, what 566 00:29:02,390 --> 00:29:07,110 they hit what unbelievably massive, but also that that 567 00:29:07,110 --> 00:29:11,160 mass was concentrated into this very, very small space. 568 00:29:11,160 --> 00:29:14,460 So eventually, this is what we have come to call the nucleus 569 00:29:14,460 --> 00:29:15,970 of an atom. 570 00:29:15,970 --> 00:29:18,770 And the nucleus name was used as an analogy to the nucleus 571 00:29:18,770 --> 00:29:22,220 of a cell, so in some ways that makes it easier to see 572 00:29:22,220 --> 00:29:24,190 the connection, but I think it can also be a little bit 573 00:29:24,190 --> 00:29:27,360 confusing for maybe 7th graders that are learning both 574 00:29:27,360 --> 00:29:30,270 at the same time, that this nucleus acts very different 575 00:29:30,270 --> 00:29:33,270 from a nucleus in a cell, although, of course, there 576 00:29:33,270 --> 00:29:36,930 many of them in the nucleus of a cell. 577 00:29:36,930 --> 00:29:39,510 There are some other things that Rutherford was able to 578 00:29:39,510 --> 00:29:40,030 figure out. 579 00:29:40,030 --> 00:29:43,670 One is the diameter of the nucleus, and that turns out to 580 00:29:43,670 --> 00:29:47,210 be 10 to the negative 14 meters. 581 00:29:47,210 --> 00:29:50,820 If we think about the size of a typical cell -- excuse me, 582 00:29:50,820 --> 00:29:52,380 now I'm getting confused about nuclei. 583 00:29:52,380 --> 00:29:55,970 If we think of the size of a typical atom, we would say 584 00:29:55,970 --> 00:29:58,170 that would be about 10 to the negative 10 meters. 585 00:29:58,170 --> 00:30:02,480 So, we can see the diameter of a nucleus is absolutely 586 00:30:02,480 --> 00:30:05,110 smaller, really concentrating that mass into 587 00:30:05,110 --> 00:30:06,490 a very small space. 588 00:30:06,490 --> 00:30:08,080 So, you might be asking how did he 589 00:30:08,080 --> 00:30:09,420 actually figure that out? 590 00:30:09,420 --> 00:30:11,150 We'll do the calculation ourselves. 591 00:30:11,150 --> 00:30:14,300 In fact, we'll do the whole experiment ourselves, minus 592 00:30:14,300 --> 00:30:17,290 the radioactivity in just a minute, so we'll be able to 593 00:30:17,290 --> 00:30:19,120 answer that question for you. 594 00:30:19,120 --> 00:30:21,410 He also figured out that the charge of the 595 00:30:21,410 --> 00:30:24,350 nucleus was a plus ze. 596 00:30:24,350 --> 00:30:28,100 This makes sense intuitively as well, because z is just the 597 00:30:28,100 --> 00:30:29,240 atomic number. 598 00:30:29,240 --> 00:30:32,210 So, let's say we have an atomic number of 3, that means 599 00:30:32,210 --> 00:30:35,670 we have 3 electrons, so we better hope to get our neutral 600 00:30:35,670 --> 00:30:40,220 atom that we have a charge of plus 3 in the nucleus. 601 00:30:40,220 --> 00:30:42,240 So, I mentioned at the beginning, while he was 602 00:30:42,240 --> 00:30:45,920 working with this radium bromide, that I was very 603 00:30:45,920 --> 00:30:49,740 relieved to see that it did not kill him to do these 604 00:30:49,740 --> 00:30:50,270 experiments. 605 00:30:50,270 --> 00:30:53,110 However, I think I will share with you that the cause of his 606 00:30:53,110 --> 00:30:57,370 death was, in fact, related to his research here, even though 607 00:30:57,370 --> 00:30:58,900 it was a little more tangled up. 608 00:30:58,900 --> 00:31:01,630 So, what happened, of course, after he discovered the 609 00:31:01,630 --> 00:31:04,670 nucleus, not surprising, he won a Nobel Prize for this -- 610 00:31:04,670 --> 00:31:06,300 I would hope that he would. 611 00:31:06,300 --> 00:31:09,510 And in addition to winning a Nobel Prize, he was also 612 00:31:09,510 --> 00:31:12,200 knighted, which was a nice bonus for someone born in 613 00:31:12,200 --> 00:31:14,660 England, that's a great thing to happen to them. 614 00:31:14,660 --> 00:31:17,590 The problem that he ran into is at some point a little bit 615 00:31:17,590 --> 00:31:20,920 later in his life, he had a hernia which was a pretty 616 00:31:20,920 --> 00:31:23,620 standard case, but what he was going to need was an 617 00:31:23,620 --> 00:31:24,980 operation on it. 618 00:31:24,980 --> 00:31:28,880 And the glitch came that at least at the time, if you were 619 00:31:28,880 --> 00:31:34,320 a knight, you could only be operated on by a doctor that 620 00:31:34,320 --> 00:31:36,300 was also titled. 621 00:31:36,300 --> 00:31:39,870 So, Rutherford had a little bit of waiting to do for that 622 00:31:39,870 --> 00:31:42,940 doctor to show up, and it turns out the wait was too 623 00:31:42,940 --> 00:31:45,830 long, and he actually passed away because he discovered the 624 00:31:45,830 --> 00:31:48,030 nucleus and got a Noble Prize and became knighted. 625 00:31:48,030 --> 00:31:51,630 So, it's still dangerous. 626 00:31:51,630 --> 00:31:54,560 If that opportunity comes up for you, maybe you want to 627 00:31:54,560 --> 00:31:57,150 check into the policies of how that works with the doctor 628 00:31:57,150 --> 00:31:58,070 situation now. 629 00:31:58,070 --> 00:32:01,380 Hopefully they've cleared it up a little bit. 630 00:32:01,380 --> 00:32:04,820 So, what we want to do now is see if we can understand how 631 00:32:04,820 --> 00:32:06,930 this backscattering experiment worked. 632 00:32:06,930 --> 00:32:10,510 So, we will do our own backscattering experiment. 633 00:32:10,510 --> 00:32:12,970 And we'll ask you to imagine a few things. 634 00:32:12,970 --> 00:32:18,170 First is that we have this mono layer of gold particles. 635 00:32:18,170 --> 00:32:23,300 So let's see if Professor Drennan is able 636 00:32:23,300 --> 00:32:24,160 to help us out here. 637 00:32:24,160 --> 00:32:32,340 Oh, great. 638 00:32:32,340 --> 00:32:35,820 So, that is her daughter, Sam that you see strapped to the 639 00:32:35,820 --> 00:32:45,440 chest, and Dr. Patti Christie helping us out here. 640 00:32:45,440 --> 00:32:45,890 All right. 641 00:32:45,890 --> 00:32:48,400 So, we'll move this up to the front in just a minute, but 642 00:32:48,400 --> 00:32:50,920 I'm going to explain how this experiment works, and we'll do 643 00:32:50,920 --> 00:32:54,360 the calculation first before the excitement breaks out. 644 00:32:54,360 --> 00:32:57,480 But I'm sure you can easily see how these styrofoam balls 645 00:32:57,480 --> 00:33:01,250 could, in fact, be a mono layer of gold nuclei. 646 00:33:01,250 --> 00:33:07,570 We have 266, as some of you might know who saw me counting 647 00:33:07,570 --> 00:33:09,700 ping-pong balls the other day in office hours. 648 00:33:09,700 --> 00:33:13,680 We have 266 ping-pong balls, and we need someone, hopefully 649 00:33:13,680 --> 00:33:16,160 you, to be some radioactive material that are going to be 650 00:33:16,160 --> 00:33:19,110 emitting these ping-pong balls. 651 00:33:19,110 --> 00:33:21,460 And when the time comes, in just a minute, I'll ask the 652 00:33:21,460 --> 00:33:26,240 TAs to come down and hand these out very quickly to you, 653 00:33:26,240 --> 00:33:27,800 so we can do this experiment. 654 00:33:27,800 --> 00:33:31,040 But first, let's go through how we're going to determine 655 00:33:31,040 --> 00:33:34,210 what Rutherford determined, which was he was interested in 656 00:33:34,210 --> 00:33:36,320 knowing, which we said what the diameter 657 00:33:36,320 --> 00:33:38,320 of the nuclei were. 658 00:33:38,320 --> 00:33:40,150 So, we're going to do the same thing and figure out the 659 00:33:40,150 --> 00:33:51,710 diameter of these styrofoam balls here, and we can do it 660 00:33:51,710 --> 00:33:57,300 by using the relationship of how many backscatter. 661 00:33:57,300 --> 00:34:00,600 So, if we think about the probability of backscattering, 662 00:34:00,600 --> 00:34:04,440 which is the exact same thing that we saw Rutherford 663 00:34:04,440 --> 00:34:08,670 calculate, using the 20 divided by 132,000. 664 00:34:08,670 --> 00:34:11,790 But in our case, the probability of backscattering 665 00:34:11,790 --> 00:34:20,400 is going to be the number of balls that backscatter, and 666 00:34:20,400 --> 00:34:25,740 that's going to be divided by the total number 667 00:34:25,740 --> 00:34:26,990 of ping-pong balls. 668 00:34:26,990 --> 00:34:28,600 So, do you remember what that was? 669 00:34:28,600 --> 00:34:30,180 STUDENT: 266. 670 00:34:30,180 --> 00:34:31,030 PROFESSOR: 266. 671 00:34:31,030 --> 00:34:32,510 Good information retention. 672 00:34:32,510 --> 00:34:33,570 All right. 673 00:34:33,570 --> 00:34:36,580 So, we have the probability here. 674 00:34:36,580 --> 00:34:40,970 So, in terms of the number of balls scattered over the 675 00:34:40,970 --> 00:34:47,770 total, we can also relate the probability to the area of all 676 00:34:47,770 --> 00:34:56,440 of those nuclei divided by the total area that 677 00:34:56,440 --> 00:34:59,760 the atoms take up. 678 00:34:59,760 --> 00:35:02,710 Right, this makes a lot of sense, because if the entire 679 00:35:02,710 --> 00:35:05,930 atom was made up of nuclei, then we would have 100% 680 00:35:05,930 --> 00:35:09,340 probability of hitting one of these nuclei and having things 681 00:35:09,340 --> 00:35:10,490 bounce back. 682 00:35:10,490 --> 00:35:14,020 So, here we have the area of the nuclei we'll figure out 683 00:35:14,020 --> 00:35:17,260 adding those all together versus the space of all of the 684 00:35:17,260 --> 00:35:18,710 atoms put together. 685 00:35:18,710 --> 00:35:22,600 So, not only did Professor Sayer, who's in the Chemistry 686 00:35:22,600 --> 00:35:25,690 Department who put together this contraption for all of 687 00:35:25,690 --> 00:35:31,220 you, not only did she magnify the size of these gold nuclei, 688 00:35:31,220 --> 00:35:34,160 but she actually had to smoosh all of these atoms closer 689 00:35:34,160 --> 00:35:35,740 together then they normally would be. 690 00:35:35,740 --> 00:35:39,530 If, in fact, a gold nucleus was this size here, we would 691 00:35:39,530 --> 00:35:42,540 need to use another lecture hall in order to find a place 692 00:35:42,540 --> 00:35:45,110 to put this nucleus right here. 693 00:35:45,110 --> 00:35:47,180 This is a little bit of a tricky experiment, so we 694 00:35:47,180 --> 00:35:49,340 decided we'll just smoosh it all in, and we'll actually be 695 00:35:49,340 --> 00:35:51,620 able to account for it, because we'll take into 696 00:35:51,620 --> 00:35:56,000 account the area of all of those atoms. 697 00:35:56,000 --> 00:35:58,750 I think this board does not like to go by itself. 698 00:35:58,750 --> 00:35:59,780 All right. 699 00:35:59,780 --> 00:36:04,670 So we can figure out what that is, the area of all of the 700 00:36:04,670 --> 00:36:11,550 nuclei is going to be the number of nuclei times the 701 00:36:11,550 --> 00:36:16,170 area per nucleus, and we're going to talk about the 702 00:36:16,170 --> 00:36:20,780 cross-section here to keep it simple. 703 00:36:20,780 --> 00:36:25,110 And all of that is divided by the area of the 704 00:36:25,110 --> 00:36:26,680 atoms, which is 1 . 705 00:36:26,680 --> 00:36:33,770 39 meters squared, measuring that space there. 706 00:36:33,770 --> 00:36:37,190 So, the number of nuclei, if we were to sit and count these 707 00:36:37,190 --> 00:36:41,390 as well, is 119. 708 00:36:41,390 --> 00:36:47,350 So, we'll multiply that by just pi, r squared, to get 709 00:36:47,350 --> 00:36:50,962 that cross-section, and divide all of that by 1 . 710 00:36:50,962 --> 00:36:54,310 39 meters squared. 711 00:36:54,310 --> 00:36:58,450 So, what we have here is a relationship that can tell us 712 00:36:58,450 --> 00:37:01,520 what the probability of backscattering is, but what we 713 00:37:01,520 --> 00:37:05,470 want to pull out, since we can experimentally measure what 714 00:37:05,470 --> 00:37:08,250 the probability is, what we need to pull out is the radius 715 00:37:08,250 --> 00:37:14,190 or the diameter of these nuclei, so we can just, 716 00:37:14,190 --> 00:37:17,690 instead of solving for p, we can switch it around and solve 717 00:37:17,690 --> 00:37:19,020 for the radius. 718 00:37:19,020 --> 00:37:21,640 So, that's going to be equal to the probability raised to 719 00:37:21,640 --> 00:37:21,995 the 1/2 times 6 . 720 00:37:21,995 --> 00:37:28,790 098 times 10 to the negative 2 meters. 721 00:37:28,790 --> 00:37:35,380 So, actually, just for discussion sake, it makes a 722 00:37:35,380 --> 00:37:39,070 little more sense for us to talk about the diameter, so 723 00:37:39,070 --> 00:37:41,040 that's just twice the radius. 724 00:37:41,040 --> 00:37:43,780 So, once we figure out what our probability of 725 00:37:43,780 --> 00:37:48,010 backscattering is, we'll just raise that to the 1/2, and 726 00:37:48,010 --> 00:37:50,720 we'll multiply that by 12 . 727 00:37:50,720 --> 00:37:54,080 20 centimeters. 728 00:37:54,080 --> 00:37:54,350 All right. 729 00:37:54,350 --> 00:37:57,580 So now all we have to do is figure out this probability of 730 00:37:57,580 --> 00:37:58,760 backscattering. 731 00:37:58,760 --> 00:38:02,870 We know we need to divide by 266, but what we need you to 732 00:38:02,870 --> 00:38:06,160 help us with is to figure out this top number here and see 733 00:38:06,160 --> 00:38:08,600 how many particles are going to backscatter. 734 00:38:08,600 --> 00:38:13,650 So, if the TAs can come up and quickly hand out 735 00:38:13,650 --> 00:38:21,520 1 particle to everyone. 736 00:38:21,520 --> 00:38:25,385 And a few people will need to throw 2, if you feel like you 737 00:38:25,385 --> 00:38:31,360 have particularly good aim. 738 00:38:31,360 --> 00:38:43,390 PROFESSOR: So, as you're getting your ping-pong balls 739 00:38:43,390 --> 00:38:46,960 -- do not throw them yet. 740 00:38:46,960 --> 00:38:48,960 Let me explain to you what constitutes 741 00:38:48,960 --> 00:38:49,830 a backscatter event. 742 00:38:49,830 --> 00:38:54,570 So, it'll be considered a backscatter event if your 743 00:38:54,570 --> 00:38:58,090 ping-pong ball hits one of the nuclei. 744 00:38:58,090 --> 00:39:00,410 It's not going to be a backscatter event if your 745 00:39:00,410 --> 00:39:03,800 ping-pong ball hits the frame or these 746 00:39:03,800 --> 00:39:05,990 strings, or the top part. 747 00:39:05,990 --> 00:39:09,360 So, in a few minutes, not now, we're going to ask you to 748 00:39:09,360 --> 00:39:11,960 stand up, and you can kind of come over more toward the 749 00:39:11,960 --> 00:39:15,280 center of the room if you want, and aim your ping-pong 750 00:39:15,280 --> 00:39:19,110 ball at the lattice here, follow the ping-pong ball with 751 00:39:19,110 --> 00:39:24,220 your eye, and discover, watching it, whether it's a 752 00:39:24,220 --> 00:39:27,040 backscatter -- it hits one of the nuclei and bounces back 753 00:39:27,040 --> 00:39:30,570 towards you, or if it goes through, and also if your 754 00:39:30,570 --> 00:39:33,920 ping-pong ball doesn't land anywhere in the vicinity of 755 00:39:33,920 --> 00:39:37,190 this at all, then keep that in mind. 756 00:39:37,190 --> 00:39:40,440 And then at the end of the experiment we'll ask you what 757 00:39:40,440 --> 00:39:42,940 happened to your ping-pong ball, and you'll let us know, 758 00:39:42,940 --> 00:39:46,520 and we can calculate the number of backscatter events. 759 00:39:46,520 --> 00:39:50,880 Are there any questions before we get started? 760 00:39:50,880 --> 00:39:53,030 Raise your hand if you don't if you don't have a 761 00:39:53,030 --> 00:40:12,000 ping-pong ball yet. 762 00:40:12,000 --> 00:40:20,480 Any questions before we get started? 763 00:40:20,480 --> 00:40:21,150 All right. 764 00:40:21,150 --> 00:40:23,020 So, we'll come around and get ping-pong balls 765 00:40:23,020 --> 00:40:24,130 to the rest of you. 766 00:40:24,130 --> 00:40:27,360 Those of you who have your ping-pong balls can now begin 767 00:40:27,360 --> 00:41:25,070 the experiment. 768 00:41:25,070 --> 00:41:25,350 [EXPERIMENTING] 769 00:41:25,350 --> 00:41:25,590 PROFESSOR: All right. 770 00:41:25,590 --> 00:41:26,850 Any last shots? 771 00:41:26,850 --> 00:41:36,800 There we go. 772 00:41:36,800 --> 00:41:37,270 All right. 773 00:41:37,270 --> 00:41:40,060 So, it looks like we were a little bit successful, I saw 774 00:41:40,060 --> 00:41:42,730 some backbouncing. 775 00:41:42,730 --> 00:41:46,040 We were going to have a clicker slide on how many 776 00:41:46,040 --> 00:41:48,030 bounced back, but it looks like we're having a little 777 00:41:48,030 --> 00:41:49,350 technical difficulty with that. 778 00:41:49,350 --> 00:41:51,750 So, what I'll ask is can you stand up if you had your 779 00:41:51,750 --> 00:41:58,390 particle bounce back? 780 00:41:58,390 --> 00:42:01,420 All right, so let's count how many we have here. 781 00:42:01,420 --> 00:42:04,860 So, 13 backscattered. 782 00:42:04,860 --> 00:42:24,190 TAs, if you can maybe pick up these ping-pong balls for me. 783 00:42:24,190 --> 00:42:26,270 I'm sure it would be very amusing if I fell, but I'd 784 00:42:26,270 --> 00:42:27,700 rather not. 785 00:42:27,700 --> 00:42:32,620 All right, so, we have 13 divided by 266. 786 00:42:32,620 --> 00:42:40,320 All right, MIT students, who has a calculator on them? 787 00:42:40,320 --> 00:42:42,370 Actually, I should probably do it as well, so I know I'm 788 00:42:42,370 --> 00:42:49,280 hearing correctly. 789 00:42:49,280 --> 00:42:51,690 So, are you getting 0 . 790 00:42:51,690 --> 00:42:56,710 0489 or so? 791 00:42:56,710 --> 00:42:57,770 All right. 792 00:42:57,770 --> 00:42:59,460 So, we've got our probability. 793 00:42:59,460 --> 00:43:02,900 We can go ahead and plug that in, take the square root of 794 00:43:02,900 --> 00:43:06,840 it, multiply it by 12 . 795 00:43:06,840 --> 00:43:08,450 2. 796 00:43:08,450 --> 00:43:15,090 What are you getting for your diameters? 797 00:43:15,090 --> 00:43:16,410 Yup, that's what I got, too. 798 00:43:16,410 --> 00:43:16,900 All right. 799 00:43:16,900 --> 00:43:20,670 So, we have 2 . 800 00:43:20,670 --> 00:43:26,140 70 for our diameter, and that's in centimeters. 801 00:43:26,140 --> 00:43:28,310 So, we actually did a pretty good job here. 802 00:43:28,310 --> 00:43:31,880 It turns out that the diameter is actually 2 . 803 00:43:31,880 --> 00:43:33,550 5 centimeters. 804 00:43:33,550 --> 00:43:37,470 So, good job, experiment well done, plus we were not exposed 805 00:43:37,470 --> 00:43:41,350 to radioactivity, which is a bonus. 806 00:43:41,350 --> 00:43:45,460 So, this is exactly how Rutherford did discover that 807 00:43:45,460 --> 00:43:52,740 these particles were present and made this new model for 808 00:43:52,740 --> 00:43:56,080 the atom that we now know has both a nucleus, and we know 809 00:43:56,080 --> 00:43:58,840 the size, and also has electrons. 810 00:43:58,840 --> 00:44:01,910 So, to finish up today, we won't get through all of it. 811 00:44:01,910 --> 00:44:04,830 But the next thing we can actually talk about is now 812 00:44:04,830 --> 00:44:09,130 that we know we have an atom that has a nucleus, let's say 813 00:44:09,130 --> 00:44:12,480 somewhere in the center, and it has electrons around it, 814 00:44:12,480 --> 00:44:16,090 thinking on our most simple example, which is hydrogen, we 815 00:44:16,090 --> 00:44:20,580 have a nucleus and an electron that have to hang together in 816 00:44:20,580 --> 00:44:23,470 the atom in some way, and we need to think about well how 817 00:44:23,470 --> 00:44:25,950 can we describe how atoms behave, and specifically, how 818 00:44:25,950 --> 00:44:32,230 do we describe how any single atom stays together where the 819 00:44:32,230 --> 00:44:34,690 two are associated, but at the same time they don't 820 00:44:34,690 --> 00:44:37,070 immediately collapse into themselves. 821 00:44:37,070 --> 00:44:40,930 So, what we can do is try using the classical 822 00:44:40,930 --> 00:44:44,820 description of the atom and see where this takes us. 823 00:44:44,820 --> 00:44:48,240 So, if we think about the force that occurs between a 824 00:44:48,240 --> 00:44:52,840 positively and a negatively charged particle, what we have 825 00:44:52,840 --> 00:44:56,680 is essentially a Coulomb force, so we can describe this 826 00:44:56,680 --> 00:44:59,310 as a force of attraction. 827 00:44:59,310 --> 00:45:03,660 We can use the Coulomb force law to explain this where we 828 00:45:03,660 --> 00:45:06,050 can describe the force as a function of r. 829 00:45:06,050 --> 00:45:08,670 So, let's think about what we're saying here. 830 00:45:08,670 --> 00:45:11,610 We're describing the force that's holding these two 831 00:45:11,610 --> 00:45:16,260 particles together, and it's related to the charge of each 832 00:45:16,260 --> 00:45:20,380 of the particles, where e is the absolute value of an 833 00:45:20,380 --> 00:45:22,050 electron's charge. 834 00:45:22,050 --> 00:45:25,080 So, an electron has a charge of negative e, we've written 835 00:45:25,080 --> 00:45:28,950 here, and the nucleus has a charge of positive e. 836 00:45:28,950 --> 00:45:32,460 And then we have r, which is simply the distance between 837 00:45:32,460 --> 00:45:33,830 the two charges. 838 00:45:33,830 --> 00:45:38,020 And what we see is that the force is inversely related to 839 00:45:38,020 --> 00:45:41,200 the distance between the two charges. 840 00:45:41,200 --> 00:45:43,910 And we can simplify this expression as saying negative 841 00:45:43,910 --> 00:45:47,700 e squared over 4 pi, epsilon nought r squared. 842 00:45:47,700 --> 00:45:51,580 Epsilon nought is a constant, it's something you might see 843 00:45:51,580 --> 00:45:52,890 in physics as well. 844 00:45:52,890 --> 00:45:55,450 Essentially for our purposes here, you can just think of it 845 00:45:55,450 --> 00:45:57,260 as a conversion factor. 846 00:45:57,260 --> 00:46:00,390 What we need to do is get rid of the Coulomb tag that we 847 00:46:00,390 --> 00:46:03,470 have -- that's how we measure our electron charges -- 848 00:46:03,470 --> 00:46:08,780 charge, and so we use this epsilon nought quite often, 849 00:46:08,780 --> 00:46:11,950 this permativity constant of a vacuum to make that 850 00:46:11,950 --> 00:46:12,380 conversion. 851 00:46:12,380 --> 00:46:18,450 And I'll just point out here also, this is a conversion 852 00:46:18,450 --> 00:46:21,120 factor you'll use quite frequently -- many of you, 853 00:46:21,120 --> 00:46:24,060 quite on accident, will memorize it as you use it over 854 00:46:24,060 --> 00:46:25,000 and over again. 855 00:46:25,000 --> 00:46:27,080 But I do want to point out that you don't have to 856 00:46:27,080 --> 00:46:29,690 memorize it for any exams in this class, we will give you a 857 00:46:29,690 --> 00:46:32,920 sheet that has all the needed constants that you're going to 858 00:46:32,920 --> 00:46:35,990 use on there, so save up that brain space for other 859 00:46:35,990 --> 00:46:38,280 information. ah 860 00:46:38,280 --> 00:46:42,540 So, we can use Coulomb's force law, and we can think about 861 00:46:42,540 --> 00:46:43,530 these different scenarios. 862 00:46:43,530 --> 00:46:46,140 So, when you come in on Monday, we're going to start 863 00:46:46,140 --> 00:46:48,120 off, you can think for the weekend -- you probably only 864 00:46:48,120 --> 00:46:50,610 need to think for a second about what happens when r goes 865 00:46:50,610 --> 00:46:54,590 to infinity, but that's where we'll start on Monday. 866 00:46:54,590 --> 00:46:58,080 And let me just suggest to all of you also, that you get 867 00:46:58,080 --> 00:46:59,970 those problem sets started this weekend. 868 00:46:59,970 --> 00:47:03,570 You should absolutely finish, at least through part a this 869 00:47:03,570 --> 00:47:06,220 weekend, and save part b for next week. 870 00:47:06,220 --> 00:47:08,860 So, have a great weekend.