1 00:00:00,000 --> 00:00:00,014 The following content is provided under a Creative 2 00:00:00,014 --> 00:00:00,020 Commons license. 3 00:00:00,020 --> 00:00:00,036 Your support will help MIT OpenCourseWare continue to 4 00:00:00,036 --> 00:00:00,052 offer high quality educational resources for free. 5 00:00:00,052 --> 00:00:00,070 To make a donation or view additional materials from 6 00:00:00,070 --> 00:00:00,086 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:00,086 --> 00:00:00,110 ocw.mit.edu. 8 00:00:00,110 --> 00:00:24,870 PROFESSOR: And this is a question based on where we 9 00:00:24,870 --> 00:00:27,730 left off on Wednesday -- we were talking about Coulomb's 10 00:00:27,730 --> 00:00:31,750 force law to describe the interaction between two 11 00:00:31,750 --> 00:00:35,330 particles, and good job, most of you got this correct. 12 00:00:35,330 --> 00:00:39,910 So, what we're looking at here is the force when we have two 13 00:00:39,910 --> 00:00:42,220 charged particles, one positive, one negative -- 14 00:00:42,220 --> 00:00:46,230 here, the nucleus and an electron. 15 00:00:46,230 --> 00:00:49,810 So, I know this is a simple example and I can see everyone 16 00:00:49,810 --> 00:00:52,210 pretty much got it right, and probably those that didn't 17 00:00:52,210 --> 00:00:55,390 actually made some sort of clicker error is my guess. 18 00:00:55,390 --> 00:00:59,410 But I wanted to use this to point out that in this class 19 00:00:59,410 --> 00:01:03,150 in general, any time you see an equation to explain a 20 00:01:03,150 --> 00:01:06,320 certain phenomenon, such as here looking at force, it's a 21 00:01:06,320 --> 00:01:09,310 good idea to check yourself by first plugging it into the 22 00:01:09,310 --> 00:01:12,220 actual equation, so you can plug in infinity and this 23 00:01:12,220 --> 00:01:15,050 equation here, and what you would see is, of course, the 24 00:01:15,050 --> 00:01:18,460 force, if you just solve the math problem goes to zero. 25 00:01:18,460 --> 00:01:21,240 But you can also look at it qualitatively, so, if you 26 00:01:21,240 --> 00:01:25,060 think about the force between the electron and the proton, 27 00:01:25,060 --> 00:01:27,720 you could just qualitatively think about what's happening. 28 00:01:27,720 --> 00:01:29,940 If they're close together there's a certain force -- 29 00:01:29,940 --> 00:01:32,983 they're attracted because they have opposite charges, but as 30 00:01:32,983 --> 00:01:35,470 that gets further and further away, that force is going to 31 00:01:35,470 --> 00:01:38,695 get smaller and smaller, and eventually the force is going 32 00:01:38,695 --> 00:01:39,860 to approach zero. 33 00:01:39,860 --> 00:01:42,690 So, it's a good kind of mental check as we go through this 34 00:01:42,690 --> 00:01:45,130 course to remember every time there's an equation, usually 35 00:01:45,130 --> 00:01:47,820 there's a very good reason for that equation, and you can go 36 00:01:47,820 --> 00:01:50,600 ahead and just use your qualitative knowledge, you 37 00:01:50,600 --> 00:01:52,870 don't have to just always stick with the math to check 38 00:01:52,870 --> 00:01:54,640 and justify your answers. 39 00:01:54,640 --> 00:01:58,740 So, we can get started with today's lecture notes. 40 00:01:58,740 --> 00:02:02,880 And, as I mentioned, we left off and as we started back 41 00:02:02,880 --> 00:02:06,930 here to describe the atom and how the atom holds together 42 00:02:06,930 --> 00:02:11,010 the nucleus and the electron using classical mechanics. 43 00:02:11,010 --> 00:02:13,820 And today we'll finish that discussion, and, of course, 44 00:02:13,820 --> 00:02:17,830 point out actually the failure of classical mechanics to 45 00:02:17,830 --> 00:02:21,960 appropriately describe what's going on in an atom. 46 00:02:21,960 --> 00:02:24,640 So, then we'll get to turn to a new kind of mechanics or 47 00:02:24,640 --> 00:02:28,310 quantum mechanics, which will in fact be able to describe 48 00:02:28,310 --> 00:02:31,920 what's happening on this very, very small size scale -- so on 49 00:02:31,920 --> 00:02:33,980 the atomic size scale on the order of nanometers or 50 00:02:33,980 --> 00:02:37,060 angstroms, very small particles. 51 00:02:37,060 --> 00:02:39,430 And the reason that quantum mechanics is going to work 52 00:02:39,430 --> 00:02:42,020 where classical mechanics fails is that classical 53 00:02:42,020 --> 00:02:45,980 mechanics did not take into account the fact that matter 54 00:02:45,980 --> 00:02:49,720 has both wave-like and particle-like properties, and 55 00:02:49,720 --> 00:02:52,700 light has both wave-like and particle-like properties. 56 00:02:52,700 --> 00:02:55,280 So, we'll take a little bit of a step back after we introduce 57 00:02:55,280 --> 00:02:58,880 quantum mechanics, and talk about light as a wave, and the 58 00:02:58,880 --> 00:03:02,880 characteristic of waves, and then light as a particle. 59 00:03:02,880 --> 00:03:08,070 And one example of this is in the photoelectric effect. 60 00:03:08,070 --> 00:03:12,000 So, we just talked about the force law to describe the 61 00:03:12,000 --> 00:03:15,090 interaction between a proton and an electron. 62 00:03:15,090 --> 00:03:18,150 You told me that when the distance went to infinity, the 63 00:03:18,150 --> 00:03:19,610 force went to zero. 64 00:03:19,610 --> 00:03:23,300 What happens instead when the distance goes to zero? 65 00:03:23,300 --> 00:03:26,810 What happens to the force? 66 00:03:26,810 --> 00:03:27,080 Yeah. 67 00:03:27,080 --> 00:03:30,010 So, the force actually goes to infinity, and specifically it 68 00:03:30,010 --> 00:03:31,910 goes to negative infinity. 69 00:03:31,910 --> 00:03:34,290 Infinity is the force when we're thinking about it and 70 00:03:34,290 --> 00:03:37,270 our brains, negative infinity is when we actually plug it 71 00:03:37,270 --> 00:03:39,870 into the equation here, and the reason is the convention 72 00:03:39,870 --> 00:03:42,280 that the negative sign is just telling us the direction that 73 00:03:42,280 --> 00:03:46,000 the force is coming together instead of pushing apart. 74 00:03:46,000 --> 00:03:49,100 So, we can use Coulomb's force law to think about the force 75 00:03:49,100 --> 00:03:52,130 between these two particles -- and it does that, it tells us 76 00:03:52,130 --> 00:03:54,720 the force is a function of that distance. 77 00:03:54,720 --> 00:03:57,380 But what it does not tell us, which if we're trying to 78 00:03:57,380 --> 00:04:02,460 describe an atom we really want to know, is what happens 79 00:04:02,460 --> 00:04:04,750 to the distance as time passes? 80 00:04:04,750 --> 00:04:07,570 So, r is a function of time. 81 00:04:07,570 --> 00:04:10,770 But luckily for us, there's a classical equation of motion 82 00:04:10,770 --> 00:04:14,190 that will, in fact, describe how the electron and nucleus 83 00:04:14,190 --> 00:04:17,350 change position or change their radius as 84 00:04:17,350 --> 00:04:19,280 a function of time. 85 00:04:19,280 --> 00:04:22,390 So, that's -- does anyone know which classical law of motion 86 00:04:22,390 --> 00:04:25,370 that would be? 87 00:04:25,370 --> 00:04:28,680 Yup, so it's going to be Newton's second law, force 88 00:04:28,680 --> 00:04:31,070 equals mass times acceleration -- those of you that are quick 89 00:04:31,070 --> 00:04:35,130 page-turners, have a little one-up on answering that. 90 00:04:35,130 --> 00:04:39,070 And that tells us force as a function of acceleration, we 91 00:04:39,070 --> 00:04:42,070 want to know it though as a function of radius, so we can 92 00:04:42,070 --> 00:04:45,520 just take the first derivative and get ourselves to velocity. 93 00:04:45,520 --> 00:04:49,570 So, force is equal to mass times dv /dt. 94 00:04:49,570 --> 00:04:52,120 But, of course, we want to go all the way to distance, so we 95 00:04:52,120 --> 00:04:55,130 take the second derivative and we have this equation for 96 00:04:55,130 --> 00:04:56,670 force here. 97 00:04:56,670 --> 00:04:59,640 And what we can do in order to bring the two equations 98 00:04:59,640 --> 00:05:04,940 together, is to plug in the Coulomb force law right here. 99 00:05:04,940 --> 00:05:08,170 So, now we have our Coulomb force law all plugged in here, 100 00:05:08,170 --> 00:05:10,930 and we have this differential equation that we could solve, 101 00:05:10,930 --> 00:05:14,020 if we wanted to figure out what the force was at 102 00:05:14,020 --> 00:05:17,470 different times t, or at different positions of r. 103 00:05:17,470 --> 00:05:19,810 So, all you will have the opportunity to solve 104 00:05:19,810 --> 00:05:21,920 differential equations in your math courses here. 105 00:05:21,920 --> 00:05:24,310 We won't do it in this chemistry course. 106 00:05:24,310 --> 00:05:26,260 In later chemistry courses, you'll also get to solve 107 00:05:26,260 --> 00:05:27,800 differential equations. 108 00:05:27,800 --> 00:05:30,730 But instead in this chemistry course, I will just tell you 109 00:05:30,730 --> 00:05:33,030 the solutions to differential equations. 110 00:05:33,030 --> 00:05:36,260 And what we can do is we can start with some initial value 111 00:05:36,260 --> 00:05:40,230 of r, and here I write r being ten angstroms. That's a good 112 00:05:40,230 --> 00:05:42,220 approximation when we're talking about atoms, because 113 00:05:42,220 --> 00:05:43,630 that's about the size of and atom. 114 00:05:43,630 --> 00:05:46,900 So, let's say we start off at the distance being ten 115 00:05:46,900 --> 00:05:49,840 angstroms. We can plug that into this differential 116 00:05:49,840 --> 00:05:53,940 equation that we'll have and solve it, and what we find out 117 00:05:53,940 --> 00:05:57,540 is that r actually goes to zero at a time that's equal to 118 00:05:57,540 --> 00:06:00,790 10 to the negative 10 seconds. 119 00:06:00,790 --> 00:06:04,130 So, let's think qualitatively for a second about what that 120 00:06:04,130 --> 00:06:06,060 means or what the real meaning of that is. 121 00:06:06,060 --> 00:06:09,440 What that is telling us is that according to Newtonian 122 00:06:09,440 --> 00:06:13,630 mechanics and Coulomb's force law, is that the electron 123 00:06:13,630 --> 00:06:16,460 should actually plummet into the nucleus in 0.1 124 00:06:16,460 --> 00:06:16,730 nanoseconds. 125 00:06:16,730 --> 00:06:22,590 So, we have a little bit of a problem here. 126 00:06:22,590 --> 00:06:26,460 And the problem that we have is that what we're figuring 127 00:06:26,460 --> 00:06:30,310 out mathematically is not exactly matching up with what 128 00:06:30,310 --> 00:06:33,060 we're observing experimentally. 129 00:06:33,060 --> 00:06:36,330 And, in fact, it's often kind of difficult to experimentally 130 00:06:36,330 --> 00:06:39,540 test your mathematical predictions -- a lot of people 131 00:06:39,540 --> 00:06:42,220 spend many, many years testing one single mathematical 132 00:06:42,220 --> 00:06:43,260 prediction. 133 00:06:43,260 --> 00:06:46,670 But, I think all of us right now can probably test this 134 00:06:46,670 --> 00:06:49,850 prediction right here, and we're observing that, in fact, 135 00:06:49,850 --> 00:06:52,960 all of us and all the atoms we can see are not immediately 136 00:06:52,960 --> 00:06:56,140 collapsing in less than a nanosecond. 137 00:06:56,140 --> 00:06:59,320 So, just, if you can take what I'm saying for a moment right 138 00:06:59,320 --> 00:07:03,140 now that in fact this should collapse in this very small 139 00:07:03,140 --> 00:07:06,290 time frame, we have to see that there's a problem with 140 00:07:06,290 --> 00:07:09,860 one of these two things, either the Coulomb force law 141 00:07:09,860 --> 00:07:12,680 or Newtonian mechanics. 142 00:07:12,680 --> 00:07:18,730 So, what do you guys think is probably the issue here? 143 00:07:18,730 --> 00:07:23,070 So, it's Newtonian mechanics, and the reason for this is 144 00:07:23,070 --> 00:07:26,510 because Newtonian mechanics does not work on this very, 145 00:07:26,510 --> 00:07:27,990 very small size scale. 146 00:07:27,990 --> 00:07:31,220 As we said, Newtonian mechanics does work in most 147 00:07:31,220 --> 00:07:34,580 cases, it does work when we're discussing things that we can 148 00:07:34,580 --> 00:07:36,920 see, it does work even on things that are 149 00:07:36,920 --> 00:07:38,090 too small to measure. 150 00:07:38,090 --> 00:07:41,570 But once we got to the atomic size scale, what happens is we 151 00:07:41,570 --> 00:07:45,880 need to be taking into account the fact that matter has these 152 00:07:45,880 --> 00:07:48,760 wave-like properties, and we'll learn more about that 153 00:07:48,760 --> 00:07:51,150 later, but essentially classical mechanics does not 154 00:07:51,150 --> 00:07:52,930 take that into account at all. 155 00:07:52,930 --> 00:07:55,330 So, we need a new kind of mechanics, which is quantum 156 00:07:55,330 --> 00:07:57,580 mechanics, which will accurately explain the 157 00:07:57,580 --> 00:08:01,590 behavior of molecules on this small scale. 158 00:08:01,590 --> 00:08:05,530 So, as I mentioned, the real key to quantum mechanics is 159 00:08:05,530 --> 00:08:08,190 that it's treating matter not just like it's a particle, 160 00:08:08,190 --> 00:08:10,680 which is what we were just doing, but also like it's a 161 00:08:10,680 --> 00:08:13,350 wave, and it treats light that way, too. 162 00:08:13,350 --> 00:08:16,340 The second important point to quantum mechanics is that it 163 00:08:16,340 --> 00:08:20,280 actually considers the fact that light consists of these 164 00:08:20,280 --> 00:08:23,590 discrete packets or particle-like pieces of 165 00:08:23,590 --> 00:08:25,570 energy, which are called photons. 166 00:08:25,570 --> 00:08:28,300 And if you think about what's actually happening here, this 167 00:08:28,300 --> 00:08:30,840 second point that light consists of photons is 168 00:08:30,840 --> 00:08:33,840 actually the same thing as saying that light shows 169 00:08:33,840 --> 00:08:37,190 particle-like properties, but that's such an important point 170 00:08:37,190 --> 00:08:41,150 that I put it separately, and we'll cover that separately as 171 00:08:41,150 --> 00:08:43,780 we go along. 172 00:08:43,780 --> 00:08:48,500 So, we now have this new way of thinking about how a 173 00:08:48,500 --> 00:08:51,520 nucleus and an electron can hang together, and this is 174 00:08:51,520 --> 00:08:54,480 quantum mechanics, and we can use this to come up with a new 175 00:08:54,480 --> 00:08:58,140 way to describe our atom and the behavior of atoms. But the 176 00:08:58,140 --> 00:09:01,080 problem is before we do this, it makes sense to take a 177 00:09:01,080 --> 00:09:03,385 little bit of a step back and actually make sure we're all 178 00:09:03,385 --> 00:09:05,690 on the same page and understanding why quantum 179 00:09:05,690 --> 00:09:09,110 mechanics is so important and how it works, and specifically 180 00:09:09,110 --> 00:09:12,210 understanding what we mean when we say that light is both 181 00:09:12,210 --> 00:09:14,770 a particle and a wave, and that matter is both a particle 182 00:09:14,770 --> 00:09:18,640 and a wave. So, we'll move on to this discussion of light as 183 00:09:18,640 --> 00:09:22,080 a wave, and we really won't pick up into going back to 184 00:09:22,080 --> 00:09:26,370 applying quantum mechanics to the atom until Friday, but in 185 00:09:26,370 --> 00:09:28,970 the meantime, we'll really get to understand the wave 186 00:09:28,970 --> 00:09:33,220 particle duality of light and of matter. 187 00:09:33,220 --> 00:09:36,640 So, we'll start with thinking about some properties of waves 188 00:09:36,640 --> 00:09:38,430 that are going to be applicable to all waves that 189 00:09:38,430 --> 00:09:40,750 we're talking about, including light waves. 190 00:09:40,750 --> 00:09:44,810 The easiest kind of waves for us to picture are ocean waves 191 00:09:44,810 --> 00:09:47,810 or water waves, because we can, in fact, see them, but 192 00:09:47,810 --> 00:09:50,110 they have similar properties to all waves. 193 00:09:50,110 --> 00:09:53,820 And those properties include that you have this periodic 194 00:09:53,820 --> 00:09:55,940 variation of some property. 195 00:09:55,940 --> 00:09:58,320 So, when we're talking about water waves, the property 196 00:09:58,320 --> 00:10:01,650 we're discussing is just the water level. 197 00:10:01,650 --> 00:10:04,780 So, for example, we have this average level, and then it can 198 00:10:04,780 --> 00:10:08,160 go high where we have the peak, or it can go very low. 199 00:10:08,160 --> 00:10:10,990 We can also discuss sound waves, so again it's just the 200 00:10:10,990 --> 00:10:14,060 periodic variation of some property -- in this case we're 201 00:10:14,060 --> 00:10:17,700 talking about density, so we have high density areas and 202 00:10:17,700 --> 00:10:20,730 low density areas. 203 00:10:20,730 --> 00:10:23,880 So, regardless of the type of wave that we're talking about, 204 00:10:23,880 --> 00:10:26,390 there's some common definitions that we want to 205 00:10:26,390 --> 00:10:28,070 make sure that we're all able to use, and 206 00:10:28,070 --> 00:10:28,920 the first is amplitude. 207 00:10:28,920 --> 00:10:32,060 And when we're talking about the amplitude of the wave, 208 00:10:32,060 --> 00:10:33,820 we're talking about the deviation from 209 00:10:33,820 --> 00:10:35,290 that average level. 210 00:10:35,290 --> 00:10:38,440 So, if we define the average level as zero, you can have 211 00:10:38,440 --> 00:10:41,760 either a positive amplitude or a negative amplitude. 212 00:10:41,760 --> 00:10:43,930 So, sometimes people get confused when they're solving 213 00:10:43,930 --> 00:10:46,430 problems and call the amplitude this distance all 214 00:10:46,430 --> 00:10:49,760 the way from the max to the min, but it's only half of 215 00:10:49,760 --> 00:10:53,470 that because we're only going back to the average level. 216 00:10:53,470 --> 00:10:55,940 So, what we really want to talk about here is light 217 00:10:55,940 --> 00:10:59,360 waves, and light waves have the same properties as these 218 00:10:59,360 --> 00:11:02,550 other kind of waves in that they're the periodic variation 219 00:11:02,550 --> 00:11:04,080 of some property. 220 00:11:04,080 --> 00:11:06,280 So, when we're discussing light waves, what we're 221 00:11:06,280 --> 00:11:10,130 talking about is actually light or electromagnetic 222 00:11:10,130 --> 00:11:12,160 radiation, is what we'll be calling it 223 00:11:12,160 --> 00:11:13,400 throughout the course. 224 00:11:13,400 --> 00:11:15,310 And that's the periodic variation 225 00:11:15,310 --> 00:11:17,040 of an electric field. 226 00:11:17,040 --> 00:11:20,540 So, instead of having the periodic variation of water, 227 00:11:20,540 --> 00:11:24,040 or the periodic variation of air density, here we're 228 00:11:24,040 --> 00:11:25,810 talking about an electric field. 229 00:11:25,810 --> 00:11:28,940 We know what an electric field is, it's just a space through 230 00:11:28,940 --> 00:11:30,860 which a Coulomb force operates. 231 00:11:30,860 --> 00:11:32,660 And the important thing to think about when you're 232 00:11:32,660 --> 00:11:35,620 talking about the fact that it's a periodic variation, is 233 00:11:35,620 --> 00:11:38,800 if you put a charged particle somewhere into an electric 234 00:11:38,800 --> 00:11:42,270 field, it will, of course, go in a certain direction toward 235 00:11:42,270 --> 00:11:43,990 the charge it's attracted to. 236 00:11:43,990 --> 00:11:46,380 But you need to think about the difference, if you have a 237 00:11:46,380 --> 00:11:49,560 particle here on your wave, it will go in one direction. 238 00:11:49,560 --> 00:11:52,990 But remember, waves don't just have magnitude, they also do 239 00:11:52,990 --> 00:11:55,150 have direction. 240 00:11:55,150 --> 00:11:58,250 So, if instead you put your particle somewhere down here 241 00:11:58,250 --> 00:12:01,520 on the electric field, or on the wave, the electric field 242 00:12:01,520 --> 00:12:04,410 will now be in the other direction, so your particle 243 00:12:04,410 --> 00:12:06,960 will be pushed the other way. 244 00:12:06,960 --> 00:12:09,460 And from physics you know that, of course, if we have a 245 00:12:09,460 --> 00:12:12,590 propagating electric field, we also have a perpendicular 246 00:12:12,590 --> 00:12:14,970 magnetic field that's going back and forth. 247 00:12:14,970 --> 00:12:18,730 But in terms of worrying about using the concepts of a wave 248 00:12:18,730 --> 00:12:21,810 to solve chemistry problems in this course, we can actually 249 00:12:21,810 --> 00:12:26,030 put aside the fact, and only focus on the electric field 250 00:12:26,030 --> 00:12:28,210 part of things, because that's what's going to be interacting 251 00:12:28,210 --> 00:12:32,780 with our charged particles, such as our electrons. 252 00:12:32,780 --> 00:12:36,610 So, other properties of waves that you probably are all 253 00:12:36,610 --> 00:12:39,360 familiar with but I just want to review is the idea of a 254 00:12:39,360 --> 00:12:40,970 wavelength. 255 00:12:40,970 --> 00:12:43,430 If we're talking about the wavelength of a wave, we're 256 00:12:43,430 --> 00:12:45,930 just talking about the distance that there is between 257 00:12:45,930 --> 00:12:50,260 successive maxima, or of course, we can also be talking 258 00:12:50,260 --> 00:12:52,780 about the distance between successive minima. 259 00:12:52,780 --> 00:12:55,420 Basically, we can take any point on the wave, and it's 260 00:12:55,420 --> 00:12:59,090 the distance to that same point later on in the wave. 261 00:12:59,090 --> 00:13:01,580 So, that's what we call one wavelength. 262 00:13:01,580 --> 00:13:05,300 We also commonly discuss the frequency of a wave, and the 263 00:13:05,300 --> 00:13:08,270 frequency is just the number of cycles that that wave goes 264 00:13:08,270 --> 00:13:10,310 through per unit time. 265 00:13:10,310 --> 00:13:13,700 So, by a cycle we'd basically mean how many times we cycle 266 00:13:13,700 --> 00:13:15,910 through a complete wavelength. 267 00:13:15,910 --> 00:13:19,240 So, if something cycles through five wavelengths in a 268 00:13:19,240 --> 00:13:21,780 single second, we would just say that the frequency of that 269 00:13:21,780 --> 00:13:27,170 wave is five per second. 270 00:13:27,170 --> 00:13:30,110 We can also mathematically describe what's going on here 271 00:13:30,110 --> 00:13:32,260 other than just graphing it. 272 00:13:32,260 --> 00:13:35,760 So, if we want to look at the mathematical equation of a 273 00:13:35,760 --> 00:13:38,450 wave, we want to describe -- again as I mention, what we're 274 00:13:38,450 --> 00:13:40,780 describing is the electric field, we're not worrying 275 00:13:40,780 --> 00:13:46,050 about the magnetic field here, as a function of x and t 276 00:13:46,050 --> 00:13:53,540 that's equal to a cosine [ 2 pi x over wavelength, 277 00:13:53,540 --> 00:13:57,930 minus 2 pi nu t ]. 278 00:13:57,930 --> 00:13:59,260 And note this is the Greek letter nu. 279 00:13:59,260 --> 00:14:07,410 This is not a v. Where we have E, which is equal to the 280 00:14:07,410 --> 00:14:13,300 electric field, what is x? 281 00:14:13,300 --> 00:14:16,090 STUDENT: Position. 282 00:14:16,090 --> 00:14:21,610 PROFESSOR: Yup, the position of the wave. And what about t? 283 00:14:21,610 --> 00:14:26,600 Yeah, so we're talking about both position and time. 284 00:14:26,600 --> 00:14:29,383 So what we can do if we're talking about a wave is think 285 00:14:29,383 --> 00:14:31,920 of it both in terms of position time, but if we're 286 00:14:31,920 --> 00:14:34,810 trying to visualize this -- for example if we're actually 287 00:14:34,810 --> 00:14:37,760 to graph this out, the easiest thing to do is keep one of 288 00:14:37,760 --> 00:14:46,270 these two variables constant, either the x or the t, and 289 00:14:46,270 --> 00:14:49,510 then just consider the other variable. 290 00:14:49,510 --> 00:14:52,290 So, for example, if we're to hold the time constant, this 291 00:14:52,290 --> 00:14:55,270 makes it a lot simpler of an equation, because what we can 292 00:14:55,270 --> 00:14:58,070 end up doing is actually crossing out 293 00:14:58,070 --> 00:14:59,810 this whole term here. 294 00:14:59,810 --> 00:15:03,370 So what we're left with is just that the electric field 295 00:15:03,370 --> 00:15:09,630 as a function of distance is a times cosine of the argument 296 00:15:09,630 --> 00:15:13,640 there, which is now just 2 pi x over wavelength. 297 00:15:13,640 --> 00:15:15,760 So, what we want to be able to do, either when we're looking 298 00:15:15,760 --> 00:15:19,870 at the graph or looking at the equation up there, is to think 299 00:15:19,870 --> 00:15:22,020 about different properties of the wave. For example, to 300 00:15:22,020 --> 00:15:26,340 think about at what point do we have the wave where it's at 301 00:15:26,340 --> 00:15:29,740 its maximum amplitude? 302 00:15:29,740 --> 00:15:32,700 So, if we think about that, we need to have a point where 303 00:15:32,700 --> 00:15:36,020 we're making this argument of the cosine such that the 304 00:15:36,020 --> 00:15:39,120 cosine is going to all be equal to one, so all we're 305 00:15:39,120 --> 00:15:40,470 left with is that a term. 306 00:15:40,470 --> 00:15:45,340 So, we can do that basically any time that we have an 307 00:15:45,340 --> 00:15:49,430 integer variable that is either zero or an integer 308 00:15:49,430 --> 00:15:51,320 variable of the wavelength. 309 00:15:51,320 --> 00:15:53,800 So, for example, negative wavelength or positive 310 00:15:53,800 --> 00:15:56,650 wavelength are two times the wavelength, because that lets 311 00:15:56,650 --> 00:15:59,650 us cross out the term with the wavelength here, and we're 312 00:15:59,650 --> 00:16:04,760 left with some integer multiple of just pi. 313 00:16:04,760 --> 00:16:06,860 So, that's sort of the mathematically how we get to 314 00:16:06,860 --> 00:16:09,900 a, but we can also just look at the graph here, because 315 00:16:09,900 --> 00:16:12,320 every time we go one wavelength, we can see that 316 00:16:12,320 --> 00:16:14,940 we're back in a maximum. 317 00:16:14,940 --> 00:16:18,420 So, I mentioned we should be able to figure out where the 318 00:16:18,420 --> 00:16:19,740 maximum amplitude is. 319 00:16:19,740 --> 00:16:22,990 You should also just looking at an equation, immediately be 320 00:16:22,990 --> 00:16:26,980 able to figure out what that maximum amplitude is in terms 321 00:16:26,980 --> 00:16:30,470 of the height of it just by looking at that a-term, here 322 00:16:30,470 --> 00:16:33,200 we should also be able to know the intensity of any light 323 00:16:33,200 --> 00:16:36,780 wave, because intensity is just the amplitude squared. 324 00:16:36,780 --> 00:16:39,620 So, we should immediately be able to know how bright or how 325 00:16:39,620 --> 00:16:42,220 intense a light is just looking at the wave equation, 326 00:16:42,220 --> 00:16:47,160 or just by looking at a graph. 327 00:16:47,160 --> 00:16:49,750 We can also do a similar thing, and I'll keep my 328 00:16:49,750 --> 00:16:54,900 distance from the board, but we can instead be holding x 329 00:16:54,900 --> 00:16:58,420 constant, for example, putting x to be equal to zero, and 330 00:16:58,420 --> 00:17:01,990 then all we're doing is considering the electric field 331 00:17:01,990 --> 00:17:03,190 as a function of t. 332 00:17:03,190 --> 00:17:05,560 So, in this case we're crossing out the first term 333 00:17:05,560 --> 00:17:09,430 there, and we're left with amplitude times the cosine of 334 00:17:09,430 --> 00:17:13,120 2 pi nu times t. 335 00:17:13,120 --> 00:17:15,350 And, of course, we can do the same thing again, we can think 336 00:17:15,350 --> 00:17:18,710 about when the amplitude is going to be at its maximum, 337 00:17:18,710 --> 00:17:22,220 and it's going to be any time cosine of this term now is 338 00:17:22,220 --> 00:17:23,490 equal to one. 339 00:17:23,490 --> 00:17:26,340 So that will be at, for example, negative 1 over nu, 340 00:17:26,340 --> 00:17:28,590 or 0, or 1 over nu. 341 00:17:28,590 --> 00:17:31,090 And again, we can just look at our graph to figure that out, 342 00:17:31,090 --> 00:17:35,350 that's exactly where we're at a maximum. 343 00:17:35,350 --> 00:17:39,450 So, 1 over nu is another term we use and we call it the 344 00:17:39,450 --> 00:17:42,750 period of a wave, and the period is just the inverse of 345 00:17:42,750 --> 00:17:44,200 the frequency. 346 00:17:44,200 --> 00:17:46,450 And if we think about frequency, that's number of 347 00:17:46,450 --> 00:17:48,130 cycles per unit time. 348 00:17:48,130 --> 00:17:51,450 So, for example, number of cycles per second, whereas the 349 00:17:51,450 --> 00:17:58,660 period is how much time it takes for one cycle to occur. 350 00:17:58,660 --> 00:18:01,680 And when we talk about units of frequency, in almost every 351 00:18:01,680 --> 00:18:05,000 case, you'll be talking about number of cycles per second. 352 00:18:05,000 --> 00:18:06,900 So, you can just write inverse second, the 353 00:18:06,900 --> 00:18:07,700 cycle part is assumed. 354 00:18:07,700 --> 00:18:13,560 But you'll also frequently see it called Hertz, so, Hz here. 355 00:18:13,560 --> 00:18:15,970 So, if you're talking about five cycles per second, you 356 00:18:15,970 --> 00:18:18,740 can write five per second, or you can write five Hertz. 357 00:18:18,740 --> 00:18:21,360 The one thing you want to keep in mind though is that Hertz 358 00:18:21,360 --> 00:18:23,250 does not actually mean inverse seconds, it 359 00:18:23,250 --> 00:18:24,900 means cycles per second. 360 00:18:24,900 --> 00:18:27,760 So, if you're talking about a car going so many meters per 361 00:18:27,760 --> 00:18:31,270 second, you can't say it's going meter Hertz, you have to 362 00:18:31,270 --> 00:18:31,790 say meters per second. 363 00:18:31,790 --> 00:18:33,590 So, this really just means for frequency, 364 00:18:33,590 --> 00:18:37,090 it's a frequency label. 365 00:18:37,090 --> 00:18:38,310 Alright. 366 00:18:38,310 --> 00:18:40,920 So, since we have these terms defined, we know the frequency 367 00:18:40,920 --> 00:18:43,440 and the wavelength, it turns out we can also think about 368 00:18:43,440 --> 00:18:47,520 the speed of the wave, and specifically of a light wave, 369 00:18:47,520 --> 00:18:50,790 and speed and is just equal to the distance that's traveled 370 00:18:50,790 --> 00:18:53,370 divided by the time the elapsed. 371 00:18:53,370 --> 00:18:56,340 And because we've defined these terms, we have ways to 372 00:18:56,340 --> 00:18:57,790 describe these things. 373 00:18:57,790 --> 00:19:00,480 So, we can describe the distance that's traveled, it's 374 00:19:00,480 --> 00:19:03,070 just a wavelength here. 375 00:19:03,070 --> 00:19:06,320 And we can think about how long it takes for a wave, 376 00:19:06,320 --> 00:19:09,130 because waves are, we know not just changing in position, but 377 00:19:09,130 --> 00:19:11,700 the whole wave is moving forward with time, we can 378 00:19:11,700 --> 00:19:15,610 think about how long it takes for wave to go one wavelength. 379 00:19:15,610 --> 00:19:18,510 So, one distance that's equal to lambda. 380 00:19:18,510 --> 00:19:25,080 So, how much time would that take, does anyone know? 381 00:19:25,080 --> 00:19:29,170 So, would it take, for example, the same amount of 382 00:19:29,170 --> 00:19:33,680 time as the frequency? 383 00:19:33,680 --> 00:19:34,910 The period, that's right. 384 00:19:34,910 --> 00:19:38,470 So, it's going to take one period to move that long. 385 00:19:38,470 --> 00:19:42,280 And another way we can say period is just 1 over nu or 1 386 00:19:42,280 --> 00:19:45,860 over the frequency So, now we know both the distance 387 00:19:45,860 --> 00:19:48,140 traveled and the time the elapsed. 388 00:19:48,140 --> 00:19:49,590 So, we can just plug it in. 389 00:19:49,590 --> 00:19:53,240 Speed is equal to the distance traveled, which is lambda over 390 00:19:53,240 --> 00:19:56,950 the time elapsed, which is 1 over nu. so, we can re-write 391 00:19:56,950 --> 00:20:02,090 that as speed is equal to lambda times nu, and it turns 392 00:20:02,090 --> 00:20:04,860 out typically this is reported in meters per second or 393 00:20:04,860 --> 00:20:06,810 nanometers per second. 394 00:20:06,810 --> 00:20:09,750 So, now we have an equation where we know the relationship 395 00:20:09,750 --> 00:20:14,350 between speed and wavelength and frequency, and it turns 396 00:20:14,350 --> 00:20:17,180 out that we could take any wave, and as long as we know 397 00:20:17,180 --> 00:20:19,160 the frequency and the wavelength, we'll be able to 398 00:20:19,160 --> 00:20:20,480 figure out the speed. 399 00:20:20,480 --> 00:20:22,880 But, of course, there's something very special about 400 00:20:22,880 --> 00:20:25,190 electromagnetic waves, electromagnetic 401 00:20:25,190 --> 00:20:28,020 radiation and the speed. 402 00:20:28,020 --> 00:20:30,660 And it's not really surprising for me to tell you that 403 00:20:30,660 --> 00:20:34,240 electromagnetic radiation has a constant speed, and that 404 00:20:34,240 --> 00:20:37,760 speed is what we call the speed of light, and typically 405 00:20:37,760 --> 00:20:41,880 we abbreviate that as c, and that's from the Latin term 406 00:20:41,880 --> 00:20:45,100 celeritas, which means speed in Latin. 407 00:20:45,100 --> 00:20:47,970 That's one of four or five Latin words I remember from 408 00:20:47,970 --> 00:20:50,780 four years of high school Latin, but it comes in handy 409 00:20:50,780 --> 00:20:53,080 to remember speed of light. 410 00:20:53,080 --> 00:20:56,760 And some of you may have memorized what the speed of 411 00:20:56,760 --> 00:21:00,250 light is in high school -- it's about 3 times 10 to the 8 412 00:21:00,250 --> 00:21:01,750 meters per second. 413 00:21:01,750 --> 00:21:03,990 This is another example of a constant that you will 414 00:21:03,990 --> 00:21:06,770 accidentally memorize in this course as you use it over and 415 00:21:06,770 --> 00:21:07,310 over again. 416 00:21:07,310 --> 00:21:10,730 But again, that we will supply for you on the exam just in 417 00:21:10,730 --> 00:21:13,160 case you forget it at that moment. 418 00:21:13,160 --> 00:21:16,840 And this is a very fast speed, of course, it's about 700 419 00:21:16,840 --> 00:21:20,570 million miles per hour. 420 00:21:20,570 --> 00:21:22,980 So, one way to put that in perspective is to think about 421 00:21:22,980 --> 00:21:27,780 how long it takes for a light beam to get from 422 00:21:27,780 --> 00:21:28,640 earth to the moon. 423 00:21:28,640 --> 00:21:32,270 Does anyone have any guesses? 424 00:21:32,270 --> 00:21:33,980 Eight seconds, that sounds good. 425 00:21:33,980 --> 00:21:37,170 Anyone else? 426 00:21:37,170 --> 00:21:39,810 These are all really good guesses, so it actually takes 427 00:21:39,810 --> 00:21:42,500 1.2 seconds for light to travel from the 428 00:21:42,500 --> 00:21:43,360 earth to the moon. 429 00:21:43,360 --> 00:21:46,750 So, we're talking pretty fast, so that's nice to 430 00:21:46,750 --> 00:21:48,930 appreciate in itself. 431 00:21:48,930 --> 00:21:53,560 But other than that point, we can also think about the fact 432 00:21:53,560 --> 00:22:00,520 that frequency and wavelength are related in a way that now 433 00:22:00,520 --> 00:22:03,260 since we know the speed of light, if we know one we can 434 00:22:03,260 --> 00:22:03,950 tell the other. 435 00:22:03,950 --> 00:22:06,090 So, you can go ahead and switch us to our clicker 436 00:22:06,090 --> 00:22:08,720 question here. 437 00:22:08,720 --> 00:22:13,110 So, we should be able to look at different types of waves 438 00:22:13,110 --> 00:22:16,460 and be able to figure out something about both their 439 00:22:16,460 --> 00:22:18,670 frequency and their wavelength, and know the 440 00:22:18,670 --> 00:22:20,570 relationship between the two. 441 00:22:20,570 --> 00:22:23,880 So, it's up on this screen here now, so we'll work 442 00:22:23,880 --> 00:22:25,120 on the other one. 443 00:22:25,120 --> 00:22:28,590 If you can identify which of these statements is correct 444 00:22:28,590 --> 00:22:30,940 based on what you know about the relationship between 445 00:22:30,940 --> 00:22:32,880 frequency and wavelength and also just 446 00:22:32,880 --> 00:22:42,400 looking at the waves. 447 00:22:42,400 --> 00:22:42,670 Alright. 448 00:22:42,670 --> 00:22:49,550 So, let's give ten more seconds on that. 449 00:22:49,550 --> 00:23:06,670 So, ten seconds on that. 450 00:23:06,670 --> 00:23:07,170 Alright. 451 00:23:07,170 --> 00:23:08,320 So, good job. 452 00:23:08,320 --> 00:23:11,920 So, most people could recognize that light wave a 453 00:23:11,920 --> 00:23:13,340 has the shorter wavelength. 454 00:23:13,340 --> 00:23:18,240 We can see that just by looking at the graph itself -- 455 00:23:18,240 --> 00:23:20,950 we can see, certainly, this is shorter from maxima to maxima. 456 00:23:20,950 --> 00:23:22,810 This we can't even see the next maxima, 457 00:23:22,810 --> 00:23:24,010 so it's much longer. 458 00:23:24,010 --> 00:23:26,640 And then, we also know that means that it has the higher 459 00:23:26,640 --> 00:23:29,430 frequency, because our relationship between 460 00:23:29,430 --> 00:23:32,450 wavelength and frequency are inversely related. 461 00:23:32,450 --> 00:23:35,190 And also, we know the speed of light. 462 00:23:35,190 --> 00:23:38,410 So, if we think about if it's a shorter wavelength, we'll be 463 00:23:38,410 --> 00:23:40,840 able to get a lot more wavelengths in, in a given 464 00:23:40,840 --> 00:23:43,450 time, than we would for a longer wavelength. 465 00:23:43,450 --> 00:23:47,400 So, we can switch back to the notes and think about what 466 00:23:47,400 --> 00:23:50,230 this means, and what this means when we're talking about 467 00:23:50,230 --> 00:23:52,670 all the different kinds of light waves we have, and I've 468 00:23:52,670 --> 00:23:56,930 shown a bunch here, is that if we have the wavelength, we 469 00:23:56,930 --> 00:23:59,670 also know the frequency of these wavelengths. 470 00:23:59,670 --> 00:24:03,070 So, for example, radio waves, which have very long 471 00:24:03,070 --> 00:24:07,620 wavelengths have very low frequencies. 472 00:24:07,620 --> 00:24:12,620 Whereas where we go to waves that have very short 473 00:24:12,620 --> 00:24:16,630 wavelengths, such a x-rays or cosmic rays, they, in turn, 474 00:24:16,630 --> 00:24:19,660 have very high frequencies. 475 00:24:19,660 --> 00:24:22,210 So, it's important to get a little bit of a sense of what 476 00:24:22,210 --> 00:24:24,510 all these different kinds of lights do. 477 00:24:24,510 --> 00:24:27,610 You're absolutely not responsible to memorize what 478 00:24:27,610 --> 00:24:29,950 the wavelengths of the different types of lights are, 479 00:24:29,950 --> 00:24:32,870 but you do want to be able to know the 480 00:24:32,870 --> 00:24:34,260 general order of them. 481 00:24:34,260 --> 00:24:37,700 So, if someone tells you they're using UV light versus 482 00:24:37,700 --> 00:24:40,770 x-ray light, you know that the x-ray light is, in fact, at a 483 00:24:40,770 --> 00:24:41,760 higher frequency. 484 00:24:41,760 --> 00:24:43,330 So that's the important take-away 485 00:24:43,330 --> 00:24:44,810 message from this slide. 486 00:24:44,810 --> 00:24:47,150 If we think about these different types of lights, 487 00:24:47,150 --> 00:24:50,420 microwave light, if it's absorbed by a molecule, is a 488 00:24:50,420 --> 00:24:53,650 sufficient amount of frequency and energy to get those 489 00:24:53,650 --> 00:24:55,370 molecules to rotate. 490 00:24:55,370 --> 00:24:57,200 That, of course, generates heat, so that's how your 491 00:24:57,200 --> 00:24:58,300 microwaves work. 492 00:24:58,300 --> 00:25:02,530 If we talk about infrared light, which is at a higher 493 00:25:02,530 --> 00:25:06,610 frequency here and a shorter wavelength, infrared light 494 00:25:06,610 --> 00:25:08,950 when it's absorbed by molecules actually is enough 495 00:25:08,950 --> 00:25:12,050 to cause molecules now to vibrate. 496 00:25:12,050 --> 00:25:15,570 If we move up to the more high-frequency and divisible 497 00:25:15,570 --> 00:25:19,350 light and all the way into UV light, if you shine UV light 498 00:25:19,350 --> 00:25:21,830 at certain molecules, it's going to have enough energy to 499 00:25:21,830 --> 00:25:25,430 actually pop those electrons in that molecule up to a 500 00:25:25,430 --> 00:25:28,210 higher energy level, which will make more sense once we 501 00:25:28,210 --> 00:25:31,790 talk about energy levels in atoms, but that's what UV 502 00:25:31,790 --> 00:25:32,910 light can do. 503 00:25:32,910 --> 00:25:35,130 And actually, that's responsible for fluorescence 504 00:25:35,130 --> 00:25:37,850 and phosphorescence that you see where typically 505 00:25:37,850 --> 00:25:39,780 UV light comes in. 506 00:25:39,780 --> 00:25:42,000 So, if you use a black lamp or something and you excite 507 00:25:42,000 --> 00:25:44,140 something up to a higher energy level and then it 508 00:25:44,140 --> 00:25:47,490 relaxes back down to its lower energy state, it's going to 509 00:25:47,490 --> 00:25:50,540 emit a new wavelength of light, which is going to be 510 00:25:50,540 --> 00:25:51,920 visible to you. 511 00:25:51,920 --> 00:25:55,610 X-rays are at even a higher frequency, and those are 512 00:25:55,610 --> 00:25:59,365 sufficient to actually be absorbed by a molecule and pop 513 00:25:59,365 --> 00:26:01,450 an electron all the way out of that molecule. 514 00:26:01,450 --> 00:26:04,580 You can see how that would be damaging to the integrity of 515 00:26:04,580 --> 00:26:08,090 that molecule, that's why x-rays are so damaging -- you 516 00:26:08,090 --> 00:26:11,040 don't want to have electrons disappearing for no good 517 00:26:11,040 --> 00:26:13,140 reason from your molecules that can cause the kind of 518 00:26:13,140 --> 00:26:16,770 mutations we don't want to be seeing in ourselves. 519 00:26:16,770 --> 00:26:18,930 And then also as we go higher, we have gamma 520 00:26:18,930 --> 00:26:21,580 rays and cosmic rays. 521 00:26:21,580 --> 00:26:25,400 Within the visible range of what we can see, you also want 522 00:26:25,400 --> 00:26:29,200 to know this relative order that's pretty easy -- most of 523 00:26:29,200 --> 00:26:30,850 us have memorized that in kindergarten, so 524 00:26:30,850 --> 00:26:32,260 that should be fine. 525 00:26:32,260 --> 00:26:36,140 Just remembering that violet is the end that actually has 526 00:26:36,140 --> 00:26:39,670 the shortest wavelength, which means that it also has, of 527 00:26:39,670 --> 00:26:42,100 course, the highest frequency. 528 00:26:42,100 --> 00:26:45,560 So, just an interesting fact about this set of light, which 529 00:26:45,560 --> 00:26:48,830 we're most familiar with, if we think about our vision, it 530 00:26:48,830 --> 00:26:51,330 turns out that our vision's actually logarithmic and it's 531 00:26:51,330 --> 00:26:54,150 centered around this green frequency. 532 00:26:54,150 --> 00:26:57,520 So, if instead of a red laser pointer here, I had a green 533 00:26:57,520 --> 00:27:00,370 one, you'd actually, to our eyes, it would seem like the 534 00:27:00,370 --> 00:27:04,110 green one was brighter, even if the intensity was the same, 535 00:27:04,110 --> 00:27:06,740 and that's just because our eyes are centered and 536 00:27:06,740 --> 00:27:11,710 logarithmic around this green frequency set. 537 00:27:11,710 --> 00:27:15,780 So, using the relationship between frequency and 538 00:27:15,780 --> 00:27:18,450 wavelength, we can actually understand a lot about what's 539 00:27:18,450 --> 00:27:20,330 going on, and pretty soon we'll also draw the 540 00:27:20,330 --> 00:27:22,830 relationship very soon to energy, so it will be even 541 00:27:22,830 --> 00:27:24,300 more informative then. 542 00:27:24,300 --> 00:27:27,370 But I just want to point out one of the many, many groups 543 00:27:27,370 --> 00:27:31,850 at MIT that works with different fluorescing types of 544 00:27:31,850 --> 00:27:34,940 molecules, and this is Professor Bawendi's laboratory 545 00:27:34,940 --> 00:27:38,250 at MIT, and he works with quantum dots. 546 00:27:38,250 --> 00:27:42,950 And quantum dots are these just very tiny, tiny crystals 547 00:27:42,950 --> 00:27:44,780 of semiconductor material. 548 00:27:44,780 --> 00:27:48,640 They're on the order of one to ten nanometers, and these can 549 00:27:48,640 --> 00:27:51,040 be shined on with UV light -- they have a lot of different 550 00:27:51,040 --> 00:27:53,100 interesting properties, but one I'll mention is that if 551 00:27:53,100 --> 00:27:56,740 you excite them with UV light, they will have some of the 552 00:27:56,740 --> 00:28:00,140 electrons move to a higher energy state, and when they 553 00:28:00,140 --> 00:28:04,300 drop back down, they actually emit light with a wavelength 554 00:28:04,300 --> 00:28:09,820 that corresponds with the size of the actual quantum dot. 555 00:28:09,820 --> 00:28:13,240 So, from what we know so far, we should be able to look at 556 00:28:13,240 --> 00:28:15,460 any of these quantum dots, which are depicted as a 557 00:28:15,460 --> 00:28:18,680 cartoon here, but here we have an actual picture of the 558 00:28:18,680 --> 00:28:24,390 quantum dots suspended in some sort of solution and shone on 559 00:28:24,390 --> 00:28:27,450 with UV light, and you can see that you can achieve this 560 00:28:27,450 --> 00:28:31,710 whole beautiful range of colors just by modulating the 561 00:28:31,710 --> 00:28:33,510 size of the different dots. 562 00:28:33,510 --> 00:28:36,660 And we should be able to know if we're looking at a red dot 563 00:28:36,660 --> 00:28:41,040 -- is a red dot, it's going to have a longer wavelength, so 564 00:28:41,040 --> 00:28:44,200 is this a higher or lower frequency? 565 00:28:44,200 --> 00:28:47,020 Yeah, and similarly, if someone tells us that their 566 00:28:47,020 --> 00:28:49,670 dot is blue-shifted, that should automatically in our 567 00:28:49,670 --> 00:28:52,980 heads tell us, oh it shifted to a higher frequency. 568 00:28:52,980 --> 00:28:55,740 And these dots are really interesting in that you can, 569 00:28:55,740 --> 00:28:58,450 I'm sure by looking at this picture, already imagine just 570 00:28:58,450 --> 00:29:01,330 a whole slew of different biological or sensing 571 00:29:01,330 --> 00:29:02,830 applications that you could think of. 572 00:29:02,830 --> 00:29:04,800 For example, if you were trying to study different 573 00:29:04,800 --> 00:29:07,600 protein interactions, you could think about labeling 574 00:29:07,600 --> 00:29:09,930 them with different colored dots, or there's also a bunch 575 00:29:09,930 --> 00:29:12,240 of different fluorescent techniques that you could 576 00:29:12,240 --> 00:29:14,970 apply using these dots, or you could think of in-vivo 577 00:29:14,970 --> 00:29:18,080 sensing, how useful these could be if you could think of 578 00:29:18,080 --> 00:29:21,780 a way to get them into your body without being too toxic, 579 00:29:21,780 --> 00:29:22,420 for example. 580 00:29:22,420 --> 00:29:25,410 These are all things that the Bawendi group is working on. 581 00:29:25,410 --> 00:29:28,470 What they are real experts in is synthesizing many different 582 00:29:28,470 --> 00:29:31,100 kinds of these dots, and they have a synthetic scheme that's 583 00:29:31,100 --> 00:29:33,760 used by research groups around the world. 584 00:29:33,760 --> 00:29:37,610 The Bawendi group also collaborates with people, both 585 00:29:37,610 --> 00:29:39,330 at different schools and at MIT. 586 00:29:39,330 --> 00:29:43,590 One example, on some of their biochemistry applications is 587 00:29:43,590 --> 00:29:47,640 with another Professor at MIT, Alice Ting and her lab. 588 00:29:47,640 --> 00:29:51,640 So really what I want to point out here is as we get more 589 00:29:51,640 --> 00:29:54,890 into describing quantum mechanics, these quantum dots 590 00:29:54,890 --> 00:29:57,640 are one really good example where a lot of the properties 591 00:29:57,640 --> 00:29:59,460 of quantum mechanics apply directly. 592 00:29:59,460 --> 00:30:02,780 So, if you're interested, I put the Bawendi lab research 593 00:30:02,780 --> 00:30:04,960 website onto your notes. 594 00:30:04,960 --> 00:30:08,050 And also, Professor Bawendi recently did an interview with 595 00:30:08,050 --> 00:30:11,890 "The Tech." Did anyone see that interview in the paper? 596 00:30:11,890 --> 00:30:16,510 So, three or four -- a few of you read the paper last week. 597 00:30:16,510 --> 00:30:18,960 So, you can either pick up an old issue or I put the link on 598 00:30:18,960 --> 00:30:19,820 the website, too. 599 00:30:19,820 --> 00:30:23,710 And that's not just about his research, it's also about some 600 00:30:23,710 --> 00:30:26,560 of his memories as a student and advice to all of you. 601 00:30:26,560 --> 00:30:29,320 So, it's interesting to read and get to know some of these 602 00:30:29,320 --> 00:30:32,440 Professors at MIT a little bit better. 603 00:30:32,440 --> 00:30:35,830 So, one property that was important we talked about with 604 00:30:35,830 --> 00:30:38,920 waves is the relationship between frequency and 605 00:30:38,920 --> 00:30:39,680 wavelength. 606 00:30:39,680 --> 00:30:42,540 Another very important property of waves that's true 607 00:30:42,540 --> 00:30:45,660 of all waves, is that you can have superposition or 608 00:30:45,660 --> 00:30:48,530 interference between two waves. 609 00:30:48,530 --> 00:30:52,490 So, if we're looking at waves and they're in-phase, and when 610 00:30:52,490 --> 00:30:55,730 I talk about in-phase, what I mean is that they're lined up, 611 00:30:55,730 --> 00:30:58,560 so that the maxima are in the same position and the minima 612 00:30:58,560 --> 00:31:01,650 are in the same position, what we can have a something called 613 00:31:01,650 --> 00:31:03,840 constructive interference. 614 00:31:03,840 --> 00:31:06,310 And all we mean by constructive interference is 615 00:31:06,310 --> 00:31:09,040 that literally those two waves add together, such as the 616 00:31:09,040 --> 00:31:12,240 maxima are now twice as high, and the minima are 617 00:31:12,240 --> 00:31:13,560 now twice as low. 618 00:31:13,560 --> 00:31:17,540 So, you can also imagine a situation where instead of 619 00:31:17,540 --> 00:31:21,910 being perfectly lined up, now we have the minima being lined 620 00:31:21,910 --> 00:31:23,470 up with the maxima here. 621 00:31:23,470 --> 00:31:27,980 So, if we switch over to a clicker question maybe on this 622 00:31:27,980 --> 00:31:41,090 screen -- okay, can it be done up there to switch? 623 00:31:41,090 --> 00:31:44,430 So, we're still settling in with the renovations 624 00:31:44,430 --> 00:31:46,070 here in this room. 625 00:31:46,070 --> 00:31:48,940 So, why don't you all go ahead and tell me what happens if 626 00:31:48,940 --> 00:31:56,060 you combine these two waves, which are now out of phase? 627 00:31:56,060 --> 00:32:07,610 So, let's -- okay, so, why don't you all think about 628 00:32:07,610 --> 00:32:10,880 would happen -- we'll start with the thought exercise. 629 00:32:10,880 --> 00:32:12,602 You can switch back to my lecture notes then if this 630 00:32:12,602 --> 00:32:18,130 isn't going. 631 00:32:18,130 --> 00:32:18,480 Alright. 632 00:32:18,480 --> 00:32:21,770 So, hopefully what everyone came up with is the straight 633 00:32:21,770 --> 00:32:23,300 line, is that what you answered? 634 00:32:23,300 --> 00:32:24,560 STUDENT: Yeah. 635 00:32:24,560 --> 00:32:25,170 PROFESSOR: OK, very good. 636 00:32:25,170 --> 00:32:28,510 And I didn't make you try to draw the added, the 637 00:32:28,510 --> 00:32:33,810 superimposed positive construction in your notes, 638 00:32:33,810 --> 00:32:35,120 but I think everyone can handle 639 00:32:35,120 --> 00:32:36,470 drawing a straight line. 640 00:32:36,470 --> 00:32:39,670 So, you can go ahead and draw what happens when we have 641 00:32:39,670 --> 00:32:42,270 destructive interference. 642 00:32:42,270 --> 00:32:44,790 And destructive interference, of course, is the extreme, but 643 00:32:44,790 --> 00:32:47,370 you can picture also a case where you have waves that are 644 00:32:47,370 --> 00:32:50,010 not quite lined up, but they're also not completely 645 00:32:50,010 --> 00:32:50,930 out of phase. 646 00:32:50,930 --> 00:32:53,260 So in that case, you're either going to have the wave get a 647 00:32:53,260 --> 00:32:55,360 little bigger, but not twice as big or 648 00:32:55,360 --> 00:32:56,700 a little bit smaller. 649 00:32:56,700 --> 00:32:59,690 So, I think the easiest way to think about interference is 650 00:32:59,690 --> 00:33:01,810 not actually with light, but sometimes it's easiest to 651 00:33:01,810 --> 00:33:04,180 think about with sound, especially when you're dealing 652 00:33:04,180 --> 00:33:07,350 with times where you have destructive interference. 653 00:33:07,350 --> 00:33:10,280 Has anyone here ever been in a concert hall where they feel 654 00:33:10,280 --> 00:33:13,620 like they're kind of in a dead spot, or you don't quite hear 655 00:33:13,620 --> 00:33:16,520 as well, and if you move down just two seats all of a sudden 656 00:33:16,520 --> 00:33:19,270 it's just blasting at you -- hopefully not in this room. 657 00:33:19,270 --> 00:33:22,350 But have people experienced that before? 658 00:33:22,350 --> 00:33:24,830 Yeah, I definitely experienced it, too. 659 00:33:24,830 --> 00:33:26,910 And really, all you're experiencing there is 660 00:33:26,910 --> 00:33:30,560 destructive interference in a very bad way. 661 00:33:30,560 --> 00:33:33,890 Halls, they try to design halls such that that doesn't 662 00:33:33,890 --> 00:33:38,050 happen, and I show an example of a concert hall here -- this 663 00:33:38,050 --> 00:33:41,430 is Symphony Hall in Boston, and I can pretty much 664 00:33:41,430 --> 00:33:43,470 guarantee you if you do go to this Symphony Hall, you will 665 00:33:43,470 --> 00:33:46,710 not experience a bad seat or a dead seat. 666 00:33:46,710 --> 00:33:50,720 This is described as actually one of the top two or three 667 00:33:50,720 --> 00:33:53,850 acoustic concert halls in the whole world. 668 00:33:53,850 --> 00:33:57,450 So, it's very well designed such that they've minimized 669 00:33:57,450 --> 00:34:01,230 any of these destructive interference dead sounds. 670 00:34:01,230 --> 00:34:03,500 So, it's nice, on a student budget you can go and get the 671 00:34:03,500 --> 00:34:05,710 worst seat in the house and you can hear just as well as 672 00:34:05,710 --> 00:34:08,780 they can hear up front, even if you can't actually see 673 00:34:08,780 --> 00:34:11,630 what's going on. 674 00:34:11,630 --> 00:34:14,240 So, another example of destructive interference is 675 00:34:14,240 --> 00:34:16,240 just with the Bose headphones. 676 00:34:16,240 --> 00:34:18,520 I've never actually tried these on, but you see people 677 00:34:18,520 --> 00:34:21,590 with them, and what happens here is it's supposed to be 678 00:34:21,590 --> 00:34:24,070 those noise cancellation headphones. 679 00:34:24,070 --> 00:34:26,680 All they do is they take in the ambient noise that's 680 00:34:26,680 --> 00:34:28,200 around it, and there's actually battery in the 681 00:34:28,200 --> 00:34:31,890 headphones, that then produces waves that are going to 682 00:34:31,890 --> 00:34:34,150 destructively interfere with that ambient noise. 683 00:34:34,150 --> 00:34:37,700 And that's how it actually gets to be so quiet when you 684 00:34:37,700 --> 00:34:43,350 have on, supposedly, these quite expensive headphones. 685 00:34:43,350 --> 00:34:46,860 So, that's light as a wave, and the reason -- well, that 686 00:34:46,860 --> 00:34:49,820 was sound as a wave, but light as a wave is the same idea. 687 00:34:49,820 --> 00:34:53,650 And it was really established by the early 1900s that, in 688 00:34:53,650 --> 00:34:57,040 fact, light behaved as a wave. And the reason that it was so 689 00:34:57,040 --> 00:34:59,570 certain that light was a wave was because we could observe 690 00:34:59,570 --> 00:35:01,860 these things -- we could see, for example, that light 691 00:35:01,860 --> 00:35:04,630 defracted, and we could see that light constructively or 692 00:35:04,630 --> 00:35:08,880 destructively could interfere with other light waves, and 693 00:35:08,880 --> 00:35:12,300 this was all confirmed and visualized. 694 00:35:12,300 --> 00:35:17,080 But also, around the time that Thomson was discovering the 695 00:35:17,080 --> 00:35:19,710 electron, there were some other observations that were 696 00:35:19,710 --> 00:35:23,740 going on, and the most disturbing to kind of the 697 00:35:23,740 --> 00:35:26,500 understanding of the universe was the fact that there were 698 00:35:26,500 --> 00:35:29,590 some observations about light that didn't make sense with 699 00:35:29,590 --> 00:35:32,600 this idea that light is a particle. 700 00:35:32,600 --> 00:35:35,720 And the photoelectric effect is maybe the most clear 701 00:35:35,720 --> 00:35:37,320 example of this. 702 00:35:37,320 --> 00:35:41,180 So, the photoelectric effect is the effect that if you have 703 00:35:41,180 --> 00:35:43,550 some metal, and you can pick essentially any metal you 704 00:35:43,550 --> 00:35:47,380 want, and you shine light of a certain frequency onto that 705 00:35:47,380 --> 00:35:52,110 metal, you can actually pop off an electron, and you can 706 00:35:52,110 --> 00:35:54,110 go ahead and measure what the kinetic energy of that 707 00:35:54,110 --> 00:35:57,110 electron that comes off is, because we can measure the 708 00:35:57,110 --> 00:36:00,530 velocity and we know that kinetic energy equals 1/2 m b 709 00:36:00,530 --> 00:36:02,720 squared, and thanks to Thomson we also know 710 00:36:02,720 --> 00:36:05,150 the mass of an electron. 711 00:36:05,150 --> 00:36:09,140 So, this is an interesting observation, and in itself not 712 00:36:09,140 --> 00:36:13,790 too disturbing, yet but the important thing to point out 713 00:36:13,790 --> 00:36:18,170 is that there's this threshold frequency that is of the 714 00:36:18,170 --> 00:36:20,360 metal, and each metal has a different threshold frequency, 715 00:36:20,360 --> 00:36:23,680 such as if you shine light on the metal where the frequency 716 00:36:23,680 --> 00:36:27,680 of the light is less than the threshold frequency, nothing 717 00:36:27,680 --> 00:36:31,900 will happen -- no electron will pop off of that metal. 718 00:36:31,900 --> 00:36:34,450 However, if you shine a light with a frequency that's 719 00:36:34,450 --> 00:36:37,470 greater than the threshold frequency, you will be able to 720 00:36:37,470 --> 00:36:39,320 pop off an electron. 721 00:36:39,320 --> 00:36:42,080 So, people were making this observation, but this wasn't 722 00:36:42,080 --> 00:36:44,570 making any sense at all because there was nothing in 723 00:36:44,570 --> 00:36:46,890 classical physics that described any sort of 724 00:36:46,890 --> 00:36:51,510 relationship between the frequency of light and the 725 00:36:51,510 --> 00:36:55,310 energy, much less the energy of an electron that would get 726 00:36:55,310 --> 00:37:01,030 popped off of a metal that would basically come off only 727 00:37:01,030 --> 00:37:03,820 when we're hitting this threshold frequency. 728 00:37:03,820 --> 00:37:07,050 So, what they could do was actually graph what was 729 00:37:07,050 --> 00:37:10,050 happening here, so we can also graph what was happening, and 730 00:37:10,050 --> 00:37:13,590 what they found was that if we were at any point below the 731 00:37:13,590 --> 00:37:16,460 threshold frequency and we were counting the numbers of 732 00:37:16,460 --> 00:37:20,000 electrons that were popping off of our metal, we weren't 733 00:37:20,000 --> 00:37:21,810 seeing anything at all. 734 00:37:21,810 --> 00:37:25,650 But if you go up the threshold frequency, suddenly you see 735 00:37:25,650 --> 00:37:28,420 that there's some number of electrons that comes off, and 736 00:37:28,420 --> 00:37:31,110 amazingly, the number of electrons actually had no 737 00:37:31,110 --> 00:37:35,240 relationship at all to the frequency of the light. 738 00:37:35,240 --> 00:37:38,040 And this didn't make a lot of sense to people at the time 739 00:37:38,040 --> 00:37:42,710 because they thought that the frequency should be related to 740 00:37:42,710 --> 00:37:44,880 the number of electrons that are coming off, because you 741 00:37:44,880 --> 00:37:48,340 have more frequency coming in, you'd expect more electrons 742 00:37:48,340 --> 00:37:49,510 that are coming off -- this wasn't 743 00:37:49,510 --> 00:37:50,860 what people were seeing. 744 00:37:50,860 --> 00:37:53,270 So, what they decided to do is just study absolutely 745 00:37:53,270 --> 00:37:56,100 everything they could about the photoelectric effect and 746 00:37:56,100 --> 00:37:58,300 hope, at some point, someone would piece something together 747 00:37:58,300 --> 00:38:00,660 that could explain what's going on or shed some light on 748 00:38:00,660 --> 00:38:02,440 this effect. 749 00:38:02,440 --> 00:38:04,620 So, one thing they did, because it was so easy to 750 00:38:04,620 --> 00:38:08,630 measure kinetic energy of electrons, is plot the 751 00:38:08,630 --> 00:38:11,600 frequency of the light against the kinetic energy of the 752 00:38:11,600 --> 00:38:13,860 electron that's coming off here. 753 00:38:13,860 --> 00:38:16,040 And in your notes and on these slides here, just for your 754 00:38:16,040 --> 00:38:18,090 reference, I'm just pointing out what's going to be 755 00:38:18,090 --> 00:38:19,930 predicted from classical physics. 756 00:38:19,930 --> 00:38:22,060 You're not responsible for that and we won't really 757 00:38:22,060 --> 00:38:24,290 discuss it, but it just gives you the contrast of the 758 00:38:24,290 --> 00:38:26,700 surprise that comes up when people make these 759 00:38:26,700 --> 00:38:27,840 observations. 760 00:38:27,840 --> 00:38:30,800 And the first observation was that the frequency of the 761 00:38:30,800 --> 00:38:34,190 light had a linear relationship to the kinetic 762 00:38:34,190 --> 00:38:38,620 energy of the electrons that are ejected here. 763 00:38:38,620 --> 00:38:42,040 This made no sense at all to people, and again they saw 764 00:38:42,040 --> 00:38:44,620 this effect where if you were below that threshold 765 00:38:44,620 --> 00:38:48,900 frequency, you saw nothing at all. 766 00:38:48,900 --> 00:38:51,800 So, that was frequency with kinetic energy. 767 00:38:51,800 --> 00:38:54,350 The next thing that they wanted to look at was the 768 00:38:54,350 --> 00:38:57,870 actual intensity of the light and see what the relationship 769 00:38:57,870 --> 00:39:00,610 of intensity to kinetic energy is. 770 00:39:00,610 --> 00:39:03,640 So, what we would expect is that there is a relationship 771 00:39:03,640 --> 00:39:06,380 between intensity in kinetic energy, because it was 772 00:39:06,380 --> 00:39:08,790 understood that however intense the light was, if you 773 00:39:08,790 --> 00:39:10,810 had a more intense light, it was a higher 774 00:39:10,810 --> 00:39:12,270 energy light beam. 775 00:39:12,270 --> 00:39:14,940 So that should mean that the energy that's transferred to 776 00:39:14,940 --> 00:39:18,000 the electron should be greater, but that's not what 777 00:39:18,000 --> 00:39:20,830 you saw at all, and what you saw is that if you kept the 778 00:39:20,830 --> 00:39:25,390 frequency constant, there was absolutely no change in the 779 00:39:25,390 --> 00:39:28,490 kinetic energy of the electrons, no matter how high 780 00:39:28,490 --> 00:39:30,980 up you had the intensity of the light go. 781 00:39:30,980 --> 00:39:33,650 You could keep increasing the intensity and nothing was 782 00:39:33,650 --> 00:39:36,790 going to happen. 783 00:39:36,790 --> 00:39:40,040 So, we could also plot the number of electrons that are 784 00:39:40,040 --> 00:39:43,930 ejected as a relationship to the intensity, so that was yet 785 00:39:43,930 --> 00:39:46,330 another experiment they could do. 786 00:39:46,330 --> 00:39:48,790 And this is what they had expected that there would be 787 00:39:48,790 --> 00:39:53,380 no relationship, but instead here they saw that there was a 788 00:39:53,380 --> 00:39:56,820 linear relationship not to the intensity and the kinetic 789 00:39:56,820 --> 00:39:59,340 energy of the electrons, but to the intensity and the 790 00:39:59,340 --> 00:40:00,610 number of electrons. 791 00:40:00,610 --> 00:40:03,920 So, none of these observations made sense to any scientists 792 00:40:03,920 --> 00:40:06,780 at the time, and really all of these observations were made 793 00:40:06,780 --> 00:40:10,040 and somewhat put aside for several years before someone 794 00:40:10,040 --> 00:40:12,970 that could kind of process everything that was going on 795 00:40:12,970 --> 00:40:17,620 at once came along, and that person was Einstein, 796 00:40:17,620 --> 00:40:19,930 conveniently enough -- if anyone could put it together, 797 00:40:19,930 --> 00:40:22,730 we would hope that he could, and he did. 798 00:40:22,730 --> 00:40:26,340 And what he did in a way that made sense when all of us look 799 00:40:26,340 --> 00:40:30,190 at it, is he plotted all of these different metals on the 800 00:40:30,190 --> 00:40:32,310 same graph and made some observations. 801 00:40:32,310 --> 00:40:35,760 So, for example, here we're showing rubidium and potassium 802 00:40:35,760 --> 00:40:40,190 and sodium plotted where we're plotting the frequency -- 803 00:40:40,190 --> 00:40:43,920 that's the frequency of that light that's coming into the 804 00:40:43,920 --> 00:40:47,820 metal versus the kinetic energy of the electron that's 805 00:40:47,820 --> 00:40:50,980 ejected from the surface of the metal. 806 00:40:50,980 --> 00:40:53,980 And what he found here, which is what you can see and we can 807 00:40:53,980 --> 00:40:57,390 all see pretty clearly, is the slope of all of these lines is 808 00:40:57,390 --> 00:41:01,040 the same regardless of what the type of metal is. 809 00:41:01,040 --> 00:41:05,270 So, he fit all these to the equation of the line, and what 810 00:41:05,270 --> 00:41:08,000 he noticed was the slope was specifically this number, 811 00:41:08,000 --> 00:41:13,530 6.626 times 10 to the negative 34, joules times seconds. 812 00:41:13,530 --> 00:41:18,290 And he also found that the y intercept for each one of 813 00:41:18,290 --> 00:41:23,990 these metals was equal to basically this number here, 814 00:41:23,990 --> 00:41:31,820 which was the slope times the minimum frequency required of 815 00:41:31,820 --> 00:41:37,160 each specific metal, so that's of the threshold frequency. 816 00:41:37,160 --> 00:41:40,960 And he actually knew that this number had popped up before, 817 00:41:40,960 --> 00:41:44,070 and a lot of you are familiar with this number also, and 818 00:41:44,070 --> 00:41:45,620 this is Planck's constant. 819 00:41:45,620 --> 00:41:48,440 Planck had observed this number as a fitting constant 820 00:41:48,440 --> 00:41:51,060 years earlier when he looked at some phenomena, and you can 821 00:41:51,060 --> 00:41:53,810 read about in your book, such as black body radiation. 822 00:41:53,810 --> 00:41:57,680 And what he found was he needed this constant to fit 823 00:41:57,680 --> 00:42:00,210 his data to what was observed. 824 00:42:00,210 --> 00:42:02,700 And this is the same thing that Einstein was observing, 825 00:42:02,700 --> 00:42:07,170 that he needed this fitting constant, that this constant 826 00:42:07,170 --> 00:42:09,360 was just falling right out of, for example, this slope and 827 00:42:09,360 --> 00:42:11,110 also the y intercept. 828 00:42:11,110 --> 00:42:15,720 So he decided to go ahead and define exactly what it is, 829 00:42:15,720 --> 00:42:19,760 this line, in terms of these new constants, this constant 830 00:42:19,760 --> 00:42:22,560 he's calling h, which is Planck's constant. 831 00:42:22,560 --> 00:42:25,650 So, on the y axis we have kinetic energy, so we 832 00:42:25,650 --> 00:42:27,460 can plug that in. 833 00:42:27,460 --> 00:42:29,980 If we talk about what the x axis is, that's just the 834 00:42:29,980 --> 00:42:32,200 frequency of the light that's coming in. 835 00:42:32,200 --> 00:42:36,420 We know what m is, m is equal to h. 836 00:42:36,420 --> 00:42:41,900 And then we can plug in what b is, the y intercept, because 837 00:42:41,900 --> 00:42:45,140 that's just the negative of h times 838 00:42:45,140 --> 00:42:47,090 that threshold frequency. 839 00:42:47,090 --> 00:42:50,520 So we have this new equation here when we're considering 840 00:42:50,520 --> 00:42:53,250 this photoelectric effect, which is that the kinetic 841 00:42:53,250 --> 00:42:59,180 energy is equal to h nu minus h nu threshold of the metal. 842 00:42:59,180 --> 00:43:03,210 And what Einstein concluded and observed is that well, 843 00:43:03,210 --> 00:43:07,160 kinetic energy, of course, that's an energy term, and h 844 00:43:07,160 --> 00:43:10,170 times nu, well that has to be energy also, because energy 845 00:43:10,170 --> 00:43:13,280 has to be equal to energy -- there's no other way about it. 846 00:43:13,280 --> 00:43:15,740 And this worked out with units as well because we're talking 847 00:43:15,740 --> 00:43:18,510 about joules for kinetic energy, and when we're talking 848 00:43:18,510 --> 00:43:20,880 about h times nu, we're talking about joules times 849 00:43:20,880 --> 00:43:23,490 second times inverse seconds. 850 00:43:23,490 --> 00:43:26,320 So, the very important conclusion that Einstein made 851 00:43:26,320 --> 00:43:32,000 here is that energy is equal to h times nu, or that h times 852 00:43:32,000 --> 00:43:35,280 nu is an actual energy term. 853 00:43:35,280 --> 00:43:39,690 And this kind of went along with two observations. 854 00:43:39,690 --> 00:43:41,940 The first is that energy of a photon is 855 00:43:41,940 --> 00:43:43,850 proportional to its frequency. 856 00:43:43,850 --> 00:43:47,300 So this was never recognized before that if we know the 857 00:43:47,300 --> 00:43:52,450 frequency of a photon or a wave of light, we can know the 858 00:43:52,450 --> 00:43:54,230 energy of that light. 859 00:43:54,230 --> 00:43:57,060 So, since we know that there's relationship also between 860 00:43:57,060 --> 00:43:59,560 frequency and wavelength, we can do the same thing -- if we 861 00:43:59,560 --> 00:44:02,650 know the wavelength, we can know the energy of the light. 862 00:44:02,650 --> 00:44:05,480 And I use the term photon here, and that's because he 863 00:44:05,480 --> 00:44:08,500 also concluded that light must be made up of these energy 864 00:44:08,500 --> 00:44:11,250 packets, and each packet has that h, that Planck's 865 00:44:11,250 --> 00:44:15,210 constant's worth of energy in it, so that's why you have to 866 00:44:15,210 --> 00:44:17,940 multiply Planck's constant times the frequency. 867 00:44:17,940 --> 00:44:21,620 Any frequency can't have an energy, you have to -- you 868 00:44:21,620 --> 00:44:24,900 don't have a continuum of frequencies that are of a 869 00:44:24,900 --> 00:44:28,900 certain energy, it's actually punctuated into these packets 870 00:44:28,900 --> 00:44:30,430 that are called photons. 871 00:44:30,430 --> 00:44:33,330 And, as you know, Einstein made many, many, many very 872 00:44:33,330 --> 00:44:36,870 important contributions to science and relativity, but he 873 00:44:36,870 --> 00:44:41,660 called this his one single most important contribution to 874 00:44:41,660 --> 00:44:45,740 science, the relationship between energy and frequency 875 00:44:45,740 --> 00:44:48,660 and the idea of photons. 876 00:44:48,660 --> 00:44:52,030 So this means we now have a new way of thinking about the 877 00:44:52,030 --> 00:44:57,400 photoelectric effect, and that is the idea that h times nu is 878 00:44:57,400 --> 00:44:59,130 actually an energy. 879 00:44:59,130 --> 00:45:02,060 So, it's the energy of an incident photon if we're 880 00:45:02,060 --> 00:45:04,760 talking about nu where we're talking about the energy of 881 00:45:04,760 --> 00:45:08,890 the photon going in, so we can abbreviate that as e sub i, 882 00:45:08,890 --> 00:45:11,050 energy of the incident photon. 883 00:45:11,050 --> 00:45:16,170 We can talk about also h times nu nought, which is that 884 00:45:16,170 --> 00:45:17,840 threshold frequency. 885 00:45:17,840 --> 00:45:20,380 So this is a term we're going to see a lot, especially in 886 00:45:20,380 --> 00:45:23,620 your problem sets, it's called the work function, and the 887 00:45:23,620 --> 00:45:27,410 work function is the same thing as the threshold 888 00:45:27,410 --> 00:45:29,320 frequency of a metal, except, of course, that it's 889 00:45:29,320 --> 00:45:31,280 multiplied by Planck's constant. 890 00:45:31,280 --> 00:45:34,910 So, it's the minimum energy that a certain metal requires 891 00:45:34,910 --> 00:45:36,700 in order to pop a photon out of it -- in order to eject an 892 00:45:36,700 --> 00:45:38,100 electron from the surface of that metal. 893 00:45:38,100 --> 00:45:46,160 So this is our new kind of schematic way that we can 894 00:45:46,160 --> 00:45:50,240 think about looking at the photoelectric effect, so if 895 00:45:50,240 --> 00:45:53,580 this is the total amount of energy that we put into the 896 00:45:53,580 --> 00:45:57,430 system, where here we have the energy of a free electron. 897 00:45:57,430 --> 00:46:01,660 We have this much energy going in, the metal itself requires 898 00:46:01,660 --> 00:46:04,540 this much energy, the work function, in 899 00:46:04,540 --> 00:46:06,280 order to eject an electron. 900 00:46:06,280 --> 00:46:08,720 So that much energy is going to be used up 901 00:46:08,720 --> 00:46:09,620 just ejecting it. 902 00:46:09,620 --> 00:46:12,840 And what we have left over is this amount of energy here, 903 00:46:12,840 --> 00:46:15,320 which is going to be the kinetic energy 904 00:46:15,320 --> 00:46:17,600 of the ejected electron. 905 00:46:17,600 --> 00:46:20,650 So, therefore, we can rewrite our equation in two ways. 906 00:46:20,650 --> 00:46:24,410 One is just talking about it in terms only of energy where 907 00:46:24,410 --> 00:46:27,580 our kinetic energy here is going to be equal to the total 908 00:46:27,580 --> 00:46:32,220 energy going in -- the energy initial minus this energy of 909 00:46:32,220 --> 00:46:34,210 the work function here. 910 00:46:34,210 --> 00:46:38,880 We can also talk about it in terms of if we want to solve, 911 00:46:38,880 --> 00:46:41,120 if we, for example, we want to find out what that initial 912 00:46:41,120 --> 00:46:44,370 energy was, we can just rearrange our equation, or we 913 00:46:44,370 --> 00:46:48,110 can look at this here where the initial energy is equal to 914 00:46:48,110 --> 00:46:50,800 kinetic energy plus the work function. 915 00:46:50,800 --> 00:46:54,640 So before we go we'll try to see if we can do a clicker 916 00:46:54,640 --> 00:46:58,610 question for you on this, and we can, very good. 917 00:46:58,610 --> 00:47:01,610 So, everyone take those clickers back out and tell me, 918 00:47:01,610 --> 00:47:03,770 if a beam of light with a certain energy, and we're 919 00:47:03,770 --> 00:47:07,900 going to say four electron volts strikes a gold surface, 920 00:47:07,900 --> 00:47:11,015 and here we're saying that the gold surface has a work 921 00:47:11,015 --> 00:47:15,990 function of 5.1 electron volts, what is the maximum 922 00:47:15,990 --> 00:47:31,490 kinetic energy of the electron that is ejected? 923 00:47:31,490 --> 00:47:37,370 So why don't you go ahead and take ten seconds on that. 924 00:47:37,370 --> 00:47:40,500 And if you don't know, that's okay, just type in an answer 925 00:47:40,500 --> 00:47:44,370 and give it your best shot. 926 00:47:44,370 --> 00:47:47,220 And let's see what we come up with here. 927 00:47:47,220 --> 00:47:47,600 Alright. 928 00:47:47,600 --> 00:47:52,270 So, it looks like some of you were tricked, but many of you 929 00:47:52,270 --> 00:47:55,060 were not, so no electrons will be ejected. 930 00:47:55,060 --> 00:47:59,110 The reason for that is because this is the minimum amount of 931 00:47:59,110 --> 00:48:01,790 energy -- hold off a sec on the packing up, so in case 932 00:48:01,790 --> 00:48:03,920 someone doesn't understand -- this is the minimum amount of 933 00:48:03,920 --> 00:48:07,550 energy that's required from the energy going in in order 934 00:48:07,550 --> 00:48:08,900 to eject an electron. 935 00:48:08,900 --> 00:48:12,490 So if the incident energy is less than the energy that's 936 00:48:12,490 --> 00:48:14,370 required, absolutely nothing will happen. 937 00:48:14,370 --> 00:48:15,870 That's the same thing we were talking about 938 00:48:15,870 --> 00:48:17,260 with threshold frequency. 939 00:48:17,260 --> 00:48:18,580 All right, now you can pack up and 940 00:48:18,580 --> 00:48:20,430 we'll see you on Wednesday.