WEBVTT 00:00:00.090 --> 00:00:02.430 The following content is provided under a Creative 00:00:02.430 --> 00:00:03.820 Commons license. 00:00:03.820 --> 00:00:06.060 Your support will help MIT OpenCourseWare 00:00:06.060 --> 00:00:10.150 continue to offer high quality educational resources for free. 00:00:10.150 --> 00:00:12.690 To make a donation or to view additional materials 00:00:12.690 --> 00:00:16.650 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:16.650 --> 00:00:17.580 at ocw.mit.edu. 00:00:25.650 --> 00:00:27.400 CATHERINE DRENNAN: Click in your response. 00:00:51.722 --> 00:00:53.910 All right, let's just do ten seconds 00:00:53.910 --> 00:00:55.580 on the clicker question. 00:01:12.850 --> 00:01:16.150 OK, so 82%. 00:01:16.150 --> 00:01:21.250 I like it when we get into the 90s, just FYI, for these. 00:01:21.250 --> 00:01:24.580 So since this is similar to one we did last time, 00:01:24.580 --> 00:01:27.730 it's just to remind you again of the first part of problem 00:01:27.730 --> 00:01:30.130 set one where we have this material 00:01:30.130 --> 00:01:33.100 that you need to learn how to cover. 00:01:33.100 --> 00:01:36.031 So does anyone want to tell me how they got the right answer? 00:01:36.031 --> 00:01:37.780 And this is not going to be a great prize. 00:01:37.780 --> 00:01:39.446 There's going to be better prizes later. 00:01:39.446 --> 00:01:42.070 This is an American Chemical Society pen for this one, 00:01:42.070 --> 00:01:43.990 since we had a similar question last time. 00:01:46.465 --> 00:01:47.840 I should've told you it was going 00:01:47.840 --> 00:01:48.820 to be a better prize later. 00:01:48.820 --> 00:01:50.861 Now no one's going to-- everyone's going to wait. 00:01:57.150 --> 00:01:59.470 See if that's turned on. 00:01:59.470 --> 00:02:00.500 No, I guess not. 00:02:06.640 --> 00:02:08.840 AUDIENCE: So you find the limiting reactant 00:02:08.840 --> 00:02:10.690 by dividing the amount of moles for both 00:02:10.690 --> 00:02:12.340 by the molar coefficient. 00:02:12.340 --> 00:02:16.480 And you see that it's at the O. And then 00:02:16.480 --> 00:02:21.160 you just do 12 times the molar fraction, 00:02:21.160 --> 00:02:26.779 which is just one AL203 for every 3FEO and you get 4. 00:02:26.779 --> 00:02:27.820 CATHERINE DRENNAN: Great. 00:02:27.820 --> 00:02:29.740 So if you haven't practiced these yet, 00:02:29.740 --> 00:02:30.760 go ahead and practice. 00:02:30.760 --> 00:02:31.260 Yeah! 00:02:31.260 --> 00:02:34.533 [APPLAUSE] 00:02:37.240 --> 00:02:41.140 CATHERINE DRENNAN: OK, so let's think about what we 00:02:41.140 --> 00:02:42.990 were talking about on Friday. 00:02:42.990 --> 00:02:45.460 We were talking about discovery of the electron 00:02:45.460 --> 00:02:50.050 and the nucleus, and realized through the experiments 00:02:50.050 --> 00:02:52.870 that the atom is mostly empty space. 00:02:52.870 --> 00:02:56.200 But there is this concentrated small part 00:02:56.200 --> 00:03:00.370 of the nucleus that can deflect alpha particles, 00:03:00.370 --> 00:03:02.110 or ping pong balls. 00:03:02.110 --> 00:03:06.610 And this is a really small concentrated part, 00:03:06.610 --> 00:03:09.130 so that would be like the head of a pin in a room somewhat 00:03:09.130 --> 00:03:13.210 bigger than this, or a pea in the size of a sports arena. 00:03:13.210 --> 00:03:16.330 The nucleus is very tiny compared to the atom. 00:03:16.330 --> 00:03:19.150 And the atom is, again, mostly empty space. 00:03:19.150 --> 00:03:22.750 So this discovery was amazing of these subatomic particles 00:03:22.750 --> 00:03:26.470 and was really changing what people were thinking about. 00:03:26.470 --> 00:03:28.947 So at that time, they started to realize 00:03:28.947 --> 00:03:31.030 in doing these experiments and the experiments I'm 00:03:31.030 --> 00:03:33.580 going to tell you today that they needed a different way 00:03:33.580 --> 00:03:35.650 of thinking about matter. 00:03:35.650 --> 00:03:39.070 And to explain the observations that scientists 00:03:39.070 --> 00:03:42.820 were making at the time, they needed to think about the fact 00:03:42.820 --> 00:03:46.960 that radiation had both wave-like and particle-like 00:03:46.960 --> 00:03:48.010 properties. 00:03:48.010 --> 00:03:52.390 And matter had, also, wave-like and particle-like properties. 00:03:52.390 --> 00:03:55.330 And also that energy is quantized 00:03:55.330 --> 00:03:58.480 into these discrete bundles called photons. 00:03:58.480 --> 00:04:02.230 So we're going to be talking about these new discoveries 00:04:02.230 --> 00:04:04.210 and the data that didn't fit today, 00:04:04.210 --> 00:04:07.720 and how we came up with this new mechanics that 00:04:07.720 --> 00:04:11.200 helped to explain the properties that were being observed. 00:04:11.200 --> 00:04:14.890 So we're going to start today with a wave particle 00:04:14.890 --> 00:04:16.660 duality of light. 00:04:16.660 --> 00:04:19.990 So we're going to talk about light as a wave. 00:04:19.990 --> 00:04:22.330 And we're going to first talk about the characteristics 00:04:22.330 --> 00:04:24.620 of waves, which is a little review. 00:04:24.620 --> 00:04:27.560 And then we're going to talk about light as a particle 00:04:27.560 --> 00:04:30.340 and get into the photoelectric effect, which 00:04:30.340 --> 00:04:33.670 was a really important series of experiments 00:04:33.670 --> 00:04:36.830 that help scientists understand what was going on. 00:04:36.830 --> 00:04:40.480 So first we'll just have a little review about waves. 00:04:40.480 --> 00:04:44.020 So some of you come from places that probably don't have oceans 00:04:44.020 --> 00:04:45.940 nearby. 00:04:45.940 --> 00:04:49.870 You are now living in a place that does have an ocean nearby, 00:04:49.870 --> 00:04:54.100 so you can go take the blue line to Revere Beach. 00:04:54.100 --> 00:04:56.740 I always find doing a chemistry problem set is 00:04:56.740 --> 00:04:58.600 very relaxing on the beach. 00:04:58.600 --> 00:05:00.610 And you can watch the water level 00:05:00.610 --> 00:05:05.400 go up and down in this repeated periodic fashion. 00:05:05.400 --> 00:05:08.230 So if you haven't experienced water waves, 00:05:08.230 --> 00:05:11.640 you should absolutely do that. 00:05:11.640 --> 00:05:15.030 So waves have this periodic variation. 00:05:15.030 --> 00:05:16.950 So you could have average water level, 00:05:16.950 --> 00:05:19.380 the water level will go up and then go down 00:05:19.380 --> 00:05:23.430 and go up and go down from high levels to low levels. 00:05:23.430 --> 00:05:27.610 This same behavior is observed for other types of waves, 00:05:27.610 --> 00:05:29.470 such as sound waves. 00:05:29.470 --> 00:05:32.040 So here you would have the average density, 00:05:32.040 --> 00:05:35.280 and the sound wave can go to higher density, lower density, 00:05:35.280 --> 00:05:37.770 higher density, lower density. 00:05:37.770 --> 00:05:42.390 And this same periodic behavior is also observed 00:05:42.390 --> 00:05:47.370 with white light or electromagnetic radiation 00:05:47.370 --> 00:05:49.890 is also a periodic function. 00:05:49.890 --> 00:05:55.030 But here you have this periodic variation of an electric field. 00:05:55.030 --> 00:05:57.600 So we have, whether it's water waves 00:05:57.600 --> 00:06:01.200 or if we have sound waves or light waves, 00:06:01.200 --> 00:06:04.110 we always have this periodic behavior. 00:06:04.110 --> 00:06:06.570 And you can define this periodic behavior 00:06:06.570 --> 00:06:09.870 by a number of different terms, which we'll talk about now. 00:06:09.870 --> 00:06:12.300 Mostly we'll be focused on light waves today, 00:06:12.300 --> 00:06:16.860 but these terms can apply to other types of waves, as well. 00:06:16.860 --> 00:06:19.020 So we have amplitude. 00:06:19.020 --> 00:06:22.560 And that's the deviation from the average level. 00:06:22.560 --> 00:06:25.200 So you can have a positive amplitude 00:06:25.200 --> 00:06:27.630 or a negative amplitude here. 00:06:27.630 --> 00:06:32.670 So this is the height of the wave. 00:06:32.670 --> 00:06:37.530 You also have wavelength where the abbreviation is lambda. 00:06:37.530 --> 00:06:41.730 And this is the distance between successive maxima, 00:06:41.730 --> 00:06:44.910 so the distance from this maxima to this maxima 00:06:44.910 --> 00:06:48.210 is one wavelength. 00:06:48.210 --> 00:06:52.200 We also have frequency of the wave, which helps to define it. 00:06:52.200 --> 00:06:55.510 Oh, I should say wavelength can be up here or down here. 00:06:55.510 --> 00:06:58.260 They should be exactly the same. 00:06:58.260 --> 00:07:06.220 So frequency or nu is the number of cycles per unit time. 00:07:06.220 --> 00:07:11.680 So we talk about wavelength, amplitude, and frequency. 00:07:11.680 --> 00:07:14.370 And as you turn the page, we can also 00:07:14.370 --> 00:07:17.610 talk about the period of the wave. 00:07:17.610 --> 00:07:23.400 So 1 over the frequency is called the period, 00:07:23.400 --> 00:07:27.090 and it's the time it takes for one cycle to occur. 00:07:27.090 --> 00:07:30.210 So the time that you go from one maximum 00:07:30.210 --> 00:07:33.150 to the other maximum for one cycle 00:07:33.150 --> 00:07:36.240 is the period of the wave. 00:07:36.240 --> 00:07:39.870 As with most things in chemistry, there are units, 00:07:39.870 --> 00:07:43.200 always think about your units. 00:07:43.200 --> 00:07:49.200 So units of frequency are cycles per second, 00:07:49.200 --> 00:07:52.170 and that's also called a hertz. 00:07:52.170 --> 00:07:55.380 So you will often just see per second, 00:07:55.380 --> 00:07:57.620 but sometimes you'll see hertz in these problems. 00:07:57.620 --> 00:08:02.510 So those can be used interchangeably. 00:08:02.510 --> 00:08:06.890 And one other term is intensity, which is 00:08:06.890 --> 00:08:09.920 equal to the amplitude squared. 00:08:09.920 --> 00:08:11.544 So for all of these waves, there are 00:08:11.544 --> 00:08:13.460 these certain characteristics you think about. 00:08:13.460 --> 00:08:16.940 The amplitude of the wave, the wavelength, and the frequency, 00:08:16.940 --> 00:08:21.920 the period of the wave, and also the intensity of the wave. 00:08:21.920 --> 00:08:25.100 So now if we're thinking about light waves, which 00:08:25.100 --> 00:08:28.460 we will be most of the time, we can also 00:08:28.460 --> 00:08:35.030 think about the speed of that light that is traveling. 00:08:35.030 --> 00:08:38.150 And so at time 0 if we're thinking 00:08:38.150 --> 00:08:44.330 about the time it is going to take this little orange dot, 00:08:44.330 --> 00:08:47.270 to move this pink here that's labled, 00:08:47.270 --> 00:08:50.220 to move from here to here, move one wavelength. 00:08:50.220 --> 00:08:53.030 So it has moved to this second location. 00:08:53.030 --> 00:08:56.750 The time it takes to do that is going 00:08:56.750 --> 00:09:00.770 to be 1 over the frequency. 00:09:00.770 --> 00:09:04.700 If we think about then the speed at which this will happen, 00:09:04.700 --> 00:09:07.280 that it'll go from here to here at time 0 00:09:07.280 --> 00:09:12.500 to time 1 over the frequency or one period as we just defined, 00:09:12.500 --> 00:09:16.310 now we can fill out this equation. 00:09:16.310 --> 00:09:18.230 And see that the speed is going to be 00:09:18.230 --> 00:09:20.840 equal to the wavelength, lambda. 00:09:20.840 --> 00:09:23.120 So that's the distance traveled, the wave 00:09:23.120 --> 00:09:25.610 traveled one wavelength. 00:09:25.610 --> 00:09:28.490 And the time it took, the time elapsed 00:09:28.490 --> 00:09:32.300 was one period or 1 over the frequency, 00:09:32.300 --> 00:09:34.700 and then we can define one of the equations 00:09:34.700 --> 00:09:36.380 that you probably don't really need 00:09:36.380 --> 00:09:40.040 to have defined for you, which is that the speed of light 00:09:40.040 --> 00:09:43.740 is equal to the wavelength times the frequency. 00:09:43.740 --> 00:09:48.740 And this is in usually units of meters per second. 00:09:48.740 --> 00:09:54.500 So most people already know what this speed of light, 00:09:54.500 --> 00:09:58.160 we're talking again about light here, is equal to. 00:09:58.160 --> 00:10:00.860 And it has a constant speed. 00:10:00.860 --> 00:10:05.240 So electromagnetic radiation has a constant speed, 00:10:05.240 --> 00:10:07.690 the speed of light. 00:10:07.690 --> 00:10:11.500 And the speed of light is abbreviated c, 00:10:11.500 --> 00:10:14.840 equals the wavelength times the frequency, 00:10:14.840 --> 00:10:20.290 which is 2.9979 times 10 to the 8th meters per second. 00:10:20.290 --> 00:10:23.410 So most of you have seen this before 00:10:23.410 --> 00:10:25.180 and are well aware of it. 00:10:25.180 --> 00:10:28.420 This also has some of the conversions on here. 00:10:28.420 --> 00:10:31.420 Speed of light is quite fast and often 00:10:31.420 --> 00:10:34.580 people have the expression how fast [INAUDIBLE]. 00:10:34.580 --> 00:10:36.830 You're working at the speed of light. 00:10:36.830 --> 00:10:39.260 And that's a pretty valid thing to indicate 00:10:39.260 --> 00:10:41.440 that you're doing things very, very quickly, 00:10:41.440 --> 00:10:43.000 because that is fast. 00:10:43.000 --> 00:10:46.420 And in fact, if we had the earth here and the moon here, 00:10:46.420 --> 00:10:49.300 light would go like that. 00:10:49.300 --> 00:10:52.840 And it should take about 1.2 seconds to do that. 00:10:52.840 --> 00:10:55.660 So speed of light, very quickly. 00:10:55.660 --> 00:10:58.180 All right, so what's also important in thinking 00:10:58.180 --> 00:11:00.610 about this is that the speed of light 00:11:00.610 --> 00:11:04.180 is a constant, which is going to mean 00:11:04.180 --> 00:11:06.580 that these terms are related. 00:11:06.580 --> 00:11:09.790 So first before we move on, let's do a clicker question. 00:11:09.790 --> 00:11:12.310 And you can all test out that your clickers 00:11:12.310 --> 00:11:13.340 are working again. 00:11:57.140 --> 00:11:58.590 How are we doing? 00:11:58.590 --> 00:11:59.938 OK, let's do 10 more seconds. 00:12:18.760 --> 00:12:20.700 OK, 92%, that's awesome. 00:12:20.700 --> 00:12:23.610 All right, does someone want to explain 00:12:23.610 --> 00:12:29.190 how they could eliminate one and two versus three and four 00:12:29.190 --> 00:12:30.332 and get this one right? 00:12:42.492 --> 00:12:44.450 AUDIENCE: Sure, well it looks like this problem 00:12:44.450 --> 00:12:46.325 is asking us to look at two different things, 00:12:46.325 --> 00:12:50.280 the wavelength of these waves and the frequency. 00:12:50.280 --> 00:12:53.800 And you can look at the distance between the two peaks 00:12:53.800 --> 00:12:58.990 in both of the waves to see how short or long the wavelength 00:12:58.990 --> 00:12:59.490 is. 00:12:59.490 --> 00:13:01.560 Wavelength A has a much shorter distance 00:13:01.560 --> 00:13:03.420 between peaks than B does. 00:13:03.420 --> 00:13:06.540 And then you're also looking for nu, the frequency. 00:13:06.540 --> 00:13:13.830 So within a period of time you can fit more waves of A than B, 00:13:13.830 --> 00:13:18.366 so it has a higher frequency. 00:13:18.366 --> 00:13:20.970 [APPLAUSE] 00:13:20.970 --> 00:13:29.220 CATHERINE DRENNAN: So, this prize here is LEGO. 00:13:29.220 --> 00:13:32.430 And LEGO has decided to make girl chemists. 00:13:32.430 --> 00:13:34.560 So this is a little LEGO girl chemist 00:13:34.560 --> 00:13:37.760 that comes with pretty colored erlenmeyer flasks. 00:13:37.760 --> 00:13:40.160 So that's very special. 00:13:42.930 --> 00:13:46.300 OK, yeah, so the trick of that question 00:13:46.300 --> 00:13:49.360 you just looked which was the longer wavelength. 00:13:49.360 --> 00:13:51.600 And then you could rule out that from the picture 00:13:51.600 --> 00:13:54.450 and also realize that there's connections because 00:13:54.450 --> 00:13:58.590 of the constant speed of light between the frequency 00:13:58.590 --> 00:14:00.250 and the wavelength. 00:14:00.250 --> 00:14:04.200 So when you're talking about wavelengths of light, 00:14:04.200 --> 00:14:06.690 c is always equal to a product of the wavelength 00:14:06.690 --> 00:14:08.110 times the frequency. 00:14:08.110 --> 00:14:10.030 So they're not independent of each other. 00:14:10.030 --> 00:14:12.210 And if you know one, you will know the other. 00:14:12.210 --> 00:14:15.060 So this is something you'll come in very handy as you're 00:14:15.060 --> 00:14:18.270 doing these problems. 00:14:18.270 --> 00:14:21.480 OK, so let's talk about light for a minute 00:14:21.480 --> 00:14:26.280 and look at these different colors of light. 00:14:26.280 --> 00:14:30.120 So we go from red at long wavelengths 00:14:30.120 --> 00:14:33.510 to violet at the shorter wavelengths. 00:14:33.510 --> 00:14:38.130 And so here the wavelength is decreasing. 00:14:38.130 --> 00:14:42.570 And then if we think about the corresponding frequencies, 00:14:42.570 --> 00:14:45.660 up here then if we have long wavelengths, 00:14:45.660 --> 00:14:49.570 what are we going to have in terms of the frequency? 00:14:49.570 --> 00:14:53.790 Yeah, so we will have lower or shorter frequencies going up 00:14:53.790 --> 00:14:56.400 to higher frequencies up here. 00:14:56.400 --> 00:14:58.440 So again, we have this relationship 00:14:58.440 --> 00:15:01.140 because the speed of light equals the wavelength 00:15:01.140 --> 00:15:03.610 times the frequency. 00:15:03.610 --> 00:15:07.290 So you are not responsible for memorizing 00:15:07.290 --> 00:15:09.600 all of the wavelengths, but you should 00:15:09.600 --> 00:15:11.940 have a sense of the order of the wavelengths 00:15:11.940 --> 00:15:15.990 and certainly the relationship between wavelength 00:15:15.990 --> 00:15:17.490 and frequency. 00:15:17.490 --> 00:15:19.890 And there's going to be a number of problems 00:15:19.890 --> 00:15:22.380 later when we're talking about colors of light that 00:15:22.380 --> 00:15:25.320 are admitted from things or colors that are absorbed where 00:15:25.320 --> 00:15:29.640 it's really convenient to have the order of wavelengths 00:15:29.640 --> 00:15:30.780 memorized. 00:15:30.780 --> 00:15:32.730 So I thought I would just help you out 00:15:32.730 --> 00:15:38.190 with this by this nice little song 00:15:38.190 --> 00:15:42.180 from They Must Be Giants in Here Comes Science's album, which 00:15:42.180 --> 00:15:45.130 should help you always remember the order of the wavelengths. 00:15:45.130 --> 00:15:47.190 So let's just see if this will play. 00:15:47.190 --> 00:15:49.933 MUSIC: R is for red. 00:15:49.933 --> 00:15:51.905 O is for orange. 00:15:51.905 --> 00:15:53.384 Y is for yellow. 00:15:53.384 --> 00:15:55.830 And G is for green. 00:15:55.830 --> 00:15:57.423 B is for blue. 00:15:57.423 --> 00:15:58.776 I for indigo. 00:15:58.776 --> 00:16:01.700 And V is for violet. 00:16:01.700 --> 00:16:05.964 And that spells Roy G. Biv. 00:16:05.964 --> 00:16:08.951 Roy G. Biv is a colorful man. 00:16:08.951 --> 00:16:13.280 And he proudly stands at the rainbow's end. 00:16:13.280 --> 00:16:18.712 Roy G. Biv is a colorful man and his name spells out 00:16:18.712 --> 00:16:20.008 the whole color spectrum. 00:16:20.008 --> 00:16:22.620 Roy G. Biv is a-- 00:16:22.620 --> 00:16:26.310 CATHERINE DRENNAN: OK, so I think you get the idea there. 00:16:26.310 --> 00:16:28.590 And it sticks in your head. 00:16:28.590 --> 00:16:32.470 And you may remember this for the rest of your life, 00:16:32.470 --> 00:16:33.910 even if you don't want to. 00:16:33.910 --> 00:16:35.430 That's a very catchy song. 00:16:35.430 --> 00:16:37.260 In fact, my six-year-old daughter 00:16:37.260 --> 00:16:39.060 learned it when she was about three, 00:16:39.060 --> 00:16:40.860 and then we get very upset if anybody 00:16:40.860 --> 00:16:44.040 drew the colors that were not in the appropriate order 00:16:44.040 --> 00:16:45.160 of the rainbow. 00:16:45.160 --> 00:16:48.990 And she would come around and correct their work. 00:16:48.990 --> 00:16:52.020 Anyway, it made her into a little bit of a holy terror 00:16:52.020 --> 00:16:54.990 but we're working on that. 00:16:54.990 --> 00:16:58.290 So in addition to the visible light, which is actually 00:16:58.290 --> 00:17:04.230 a very small part of the range of waves 00:17:04.230 --> 00:17:07.980 and so we have visual light in here, 00:17:07.980 --> 00:17:10.710 we can also think about other waves that 00:17:10.710 --> 00:17:15.810 go from then long wavelength here and low frequency 00:17:15.810 --> 00:17:18.569 to short wavelength and high frequency. 00:17:18.569 --> 00:17:23.390 So we have radio waves on the long wavelength end 00:17:23.390 --> 00:17:26.130 and we have then microwaves. 00:17:26.130 --> 00:17:30.120 Microwaves are I think college students' best friends. 00:17:30.120 --> 00:17:33.690 And as I am teaching this course, since many of you 00:17:33.690 --> 00:17:37.890 are freshmen, I feel the need to compare my many years 00:17:37.890 --> 00:17:41.860 of experience at MIT with you. 00:17:41.860 --> 00:17:46.500 Point number one, just use the popcorn button 00:17:46.500 --> 00:17:48.390 on the microwave. 00:17:48.390 --> 00:17:51.990 Don't think about how long is it-- just use the popcorn 00:17:51.990 --> 00:17:54.000 button on the microwave. 00:17:54.000 --> 00:17:57.480 I used to live in Simmons for a while. 00:17:57.480 --> 00:18:02.250 3:00 AM fire drills or fire things because someone 00:18:02.250 --> 00:18:05.400 did not push the popcorn button on the microwave 00:18:05.400 --> 00:18:06.530 while making popcorn. 00:18:06.530 --> 00:18:10.890 Anyway, life lesson number one, microwaves. 00:18:10.890 --> 00:18:15.930 So molecules behave differently in these different kinds 00:18:15.930 --> 00:18:16.550 of waves. 00:18:16.550 --> 00:18:20.360 So you can rotate infrared, you're looking at vibrations. 00:18:20.360 --> 00:18:22.620 Of course here, visible light. 00:18:22.620 --> 00:18:24.690 We also have UV light. 00:18:24.690 --> 00:18:27.780 So when you go to the beach on the green line 00:18:27.780 --> 00:18:30.384 this weekend to do prom set number two 00:18:30.384 --> 00:18:31.800 and look at the waves, you'll want 00:18:31.800 --> 00:18:36.230 to wear your sunscreen because UV is, in fact, dangerous. 00:18:36.230 --> 00:18:40.640 So wear sunscreen, advice number two. 00:18:40.640 --> 00:18:43.230 Then we have x-rays. 00:18:43.230 --> 00:18:45.660 Hopefully most of you do not know one of the uses 00:18:45.660 --> 00:18:47.790 to detect broken bones. 00:18:47.790 --> 00:18:49.830 And as you'll hear later on, x-rays 00:18:49.830 --> 00:18:53.190 can also be used to solve structures of molecules 00:18:53.190 --> 00:18:54.840 at atomic resolution. 00:18:54.840 --> 00:18:57.440 And then on the very short wavelength, 00:18:57.440 --> 00:18:59.830 then, we have gamma rays as well. 00:18:59.830 --> 00:19:02.460 So again, you're not responsible for memorizing 00:19:02.460 --> 00:19:04.350 all of these numbers, but you should 00:19:04.350 --> 00:19:09.330 have a sense of the order of these different types of rays 00:19:09.330 --> 00:19:13.110 of the electromagnetic spectrum, what's at short, 00:19:13.110 --> 00:19:15.510 what's at long wavelengths. 00:19:15.510 --> 00:19:18.130 All right, so waves have other properties. 00:19:18.130 --> 00:19:21.120 And one of the most important properties of waves 00:19:21.120 --> 00:19:24.330 is that they can superimpose. 00:19:24.330 --> 00:19:28.020 So if you have two waves, one drawn up here, 00:19:28.020 --> 00:19:32.650 and one drawn down here, that are in phase with each other, 00:19:32.650 --> 00:19:35.610 which means that their troughs are at the same place, 00:19:35.610 --> 00:19:37.910 their peaks are at the same place, 00:19:37.910 --> 00:19:41.130 you can get constructive interference 00:19:41.130 --> 00:19:43.560 and that would look like this. 00:19:43.560 --> 00:19:48.120 So you have these waves come together in phase 00:19:48.120 --> 00:19:52.380 and you get this much larger constructive interference. 00:19:52.380 --> 00:19:55.230 This property can be very important 00:19:55.230 --> 00:19:59.110 as we'll talk a little bit more about later. 00:19:59.110 --> 00:20:03.810 You can also have what's called destructive interference, 00:20:03.810 --> 00:20:07.130 so when you have out of phase waves. 00:20:07.130 --> 00:20:10.940 And the clicker, you can tell me what that should look like. 00:20:33.020 --> 00:20:34.010 OK, ten seconds. 00:20:38.630 --> 00:20:40.710 Now looks like it's back to being a darker color 00:20:40.710 --> 00:20:43.820 box in the corner. 00:20:43.820 --> 00:20:45.960 Just likes to vary it up on its own. 00:20:45.960 --> 00:20:47.126 OK, that's one second. 00:20:50.040 --> 00:20:51.370 Woo! 00:20:51.370 --> 00:20:53.420 All right, 98%. 00:20:53.420 --> 00:20:55.430 We don't have to explain that one. 00:20:55.430 --> 00:20:57.830 That one was pretty clear. 00:20:57.830 --> 00:21:01.410 So here you had they were completely out of phase. 00:21:01.410 --> 00:21:04.170 So you had total destructive interference. 00:21:04.170 --> 00:21:09.860 So that just looks like a straight line. 00:21:09.860 --> 00:21:12.680 So the combination of constructive and destructive 00:21:12.680 --> 00:21:15.020 interference actually has a number 00:21:15.020 --> 00:21:18.830 of practical applications. 00:21:18.830 --> 00:21:21.300 So people who are very interested 00:21:21.300 --> 00:21:24.250 in constructive and destructive interference 00:21:24.250 --> 00:21:29.880 include people who are designing symphony halls or classrooms. 00:21:29.880 --> 00:21:31.950 Actually, this is one of the better classrooms 00:21:31.950 --> 00:21:33.830 in terms of the acoustics. 00:21:33.830 --> 00:21:36.750 And the Boston Symphony is actually, supposedly, 00:21:36.750 --> 00:21:39.680 the third best in the world in terms of acoustics. 00:21:39.680 --> 00:21:43.290 MIT students get nice discounts, go check it out. 00:21:43.290 --> 00:21:47.160 Another practical application was 00:21:47.160 --> 00:21:50.550 in designing noise canceling headphones. 00:21:50.550 --> 00:21:53.220 I brought a pair if some of you have never tried them 00:21:53.220 --> 00:21:57.150 and you want to come down after class, you can give them a try 00:21:57.150 --> 00:21:59.730 and see what you think. 00:21:59.730 --> 00:22:03.130 These headphones, the Bose headphones, 00:22:03.130 --> 00:22:05.490 were developed by a former MIT professor. 00:22:05.490 --> 00:22:07.230 He passed away last year. 00:22:07.230 --> 00:22:10.710 He taught at MIT, taught acoustics, for many years. 00:22:10.710 --> 00:22:14.160 And he was riding on an airplane once and it was just so loud. 00:22:14.160 --> 00:22:17.070 And he was thinking, wow, I was wondering if there a way 00:22:17.070 --> 00:22:19.800 I can design some good headphones to cancel 00:22:19.800 --> 00:22:21.140 this noise. 00:22:21.140 --> 00:22:24.090 And he did and many billions and billions and billions 00:22:24.090 --> 00:22:25.660 of dollars later. 00:22:25.660 --> 00:22:30.060 So as you are an MIT student, you 00:22:30.060 --> 00:22:31.862 get a discount on these headphones. 00:22:31.862 --> 00:22:34.320 So if you're going to buy them, buy them while you're here. 00:22:34.320 --> 00:22:40.260 Also, when he died, the majority share of his stock went to MIT. 00:22:40.260 --> 00:22:42.600 So you will buy them, get a discount, 00:22:42.600 --> 00:22:44.490 and you'll also be giving MIT money 00:22:44.490 --> 00:22:48.390 by buying these because we get a lot of money for this. 00:22:48.390 --> 00:22:52.006 So I feel like this brings up a really important point 00:22:52.006 --> 00:22:53.130 that I just want to stress. 00:22:53.130 --> 00:22:54.546 And I'll probably mention a couple 00:22:54.546 --> 00:22:57.960 of times that the material that you learn in your classes 00:22:57.960 --> 00:23:00.200 here at MIT, and in this class, you 00:23:00.200 --> 00:23:02.520 will learn a lot of really useful things. 00:23:02.520 --> 00:23:04.800 Some of that will lead to money. 00:23:04.800 --> 00:23:08.430 And as you make lots of money, you 00:23:08.430 --> 00:23:13.110 should remember where you learned that and know that I 00:23:13.110 --> 00:23:15.155 take both cash and checks. 00:23:18.000 --> 00:23:21.630 Another practical application is actually in my own research. 00:23:21.630 --> 00:23:23.250 So we have a series that I'm going 00:23:23.250 --> 00:23:26.184 to be using I mentioned to bring some different faces in. 00:23:26.184 --> 00:23:28.350 The first video I'm going to show you in this series 00:23:28.350 --> 00:23:29.190 is actually me. 00:23:29.190 --> 00:23:30.810 So it's not a different face. 00:23:30.810 --> 00:23:33.300 But when I asked other people to make videos 00:23:33.300 --> 00:23:34.800 about how they were using chemical 00:23:34.800 --> 00:23:36.869 principles in their research, they said OK, 00:23:36.869 --> 00:23:38.785 but you're going to do one, too, right, Cathy? 00:23:38.785 --> 00:23:41.010 So I was like, yes, I guess I'm going to do one. 00:23:41.010 --> 00:23:42.750 And that just happens to be the first one 00:23:42.750 --> 00:23:43.990 that I'm going to show. 00:23:43.990 --> 00:23:48.560 So another practical use of constructive and destructive 00:23:48.560 --> 00:23:50.760 interference has to do with x-rays. 00:23:50.760 --> 00:23:53.880 And you can use constructive and destructive interference 00:23:53.880 --> 00:23:56.520 to determine the structures of very tiny things, protein 00:23:56.520 --> 00:23:59.240 molecules or nucleic acids in your body. 00:23:59.240 --> 00:24:00.990 So I'm going to try to run this movie now. 00:24:00.990 --> 00:24:02.600 We'll see, this as a demo. 00:24:02.600 --> 00:24:07.590 Good to try it out with me and see how this is going to work. 00:24:13.325 --> 00:24:15.450 CATHERINE DRENNAN (VIDEO): My name is Cathy Drennan 00:24:15.450 --> 00:24:18.720 and I'm a Professor of Chemistry and Biology at MIT. 00:24:18.720 --> 00:24:21.210 And I'm also a Professor and Investigator with the Howard 00:24:21.210 --> 00:24:22.580 Hughes Medical Institute. 00:24:22.580 --> 00:24:27.660 And my lab uses the principles of diffraction in our research. 00:24:27.660 --> 00:24:29.790 A wave shoots through some kind of grating. 00:24:29.790 --> 00:24:32.640 You can have light, say light waves, shooting through. 00:24:32.640 --> 00:24:36.080 And when the light waves hit the metal lattice, 00:24:36.080 --> 00:24:37.450 they'll be diffracted. 00:24:37.450 --> 00:24:40.320 And some of those waves will be in phase with each other 00:24:40.320 --> 00:24:42.030 and will constructively interfere 00:24:42.030 --> 00:24:45.150 and you get a bright spot in a diffraction pattern. 00:24:45.150 --> 00:24:48.000 Other waves will be out of phase and they'll destructively 00:24:48.000 --> 00:24:50.760 interfere and you'll see nothing as a result of those waves. 00:24:54.450 --> 00:24:57.240 From this pattern of spots and no spots, 00:24:57.240 --> 00:24:59.370 you can understand something about the structure 00:24:59.370 --> 00:25:01.900 of the grating that it went through. 00:25:01.900 --> 00:25:03.510 So if I had two different gratings, 00:25:03.510 --> 00:25:05.760 the diffraction patterns would be different for these. 00:25:05.760 --> 00:25:07.718 And so from looking at the diffraction pattern, 00:25:07.718 --> 00:25:12.430 you can figure out how the metal or whatever was arranged 00:25:12.430 --> 00:25:14.850 that generated that pattern. 00:25:14.850 --> 00:25:17.040 This property works whether it's a metal 00:25:17.040 --> 00:25:22.260 grating or a lattice that's made up of protein molecules. 00:25:22.260 --> 00:25:24.100 Because the protein molecules are small 00:25:24.100 --> 00:25:26.290 and crystals are small, we use x-rays 00:25:26.290 --> 00:25:28.380 and short wavelength, high energy. 00:25:28.380 --> 00:25:30.240 But because everything is really tiny, 00:25:30.240 --> 00:25:33.450 we need really bright x-rays to do this. 00:25:33.450 --> 00:25:38.050 And I don't mean high energy bright, I mean intensity. 00:25:38.050 --> 00:25:41.364 So we need more photons per second. 00:25:41.364 --> 00:25:42.780 So we have to go to a place called 00:25:42.780 --> 00:25:44.880 the synchrotron, a research facility, that 00:25:44.880 --> 00:25:47.130 has really intense x-rays. 00:25:47.130 --> 00:25:49.490 And then we shoot those x-rays through our crystal, 00:25:49.490 --> 00:25:51.610 collect this diffraction pattern, 00:25:51.610 --> 00:25:54.310 and then figure out what the shapes of these molecules are. 00:25:57.070 --> 00:25:59.830 The structure can tell you so much. 00:25:59.830 --> 00:26:01.747 I mean, there can be big questions of field 00:26:01.747 --> 00:26:02.830 about how something works. 00:26:02.830 --> 00:26:05.204 And all of a sudden, you see what the molecule looks like 00:26:05.204 --> 00:26:07.600 and you're like, ha, of course. 00:26:07.600 --> 00:26:09.730 Sometimes there's a problem with the DNA 00:26:09.730 --> 00:26:13.360 that then gets translated into a defect in the protein. 00:26:13.360 --> 00:26:15.760 But people often don't know why does 00:26:15.760 --> 00:26:18.790 it matter, why does it matter that the protein is 00:26:18.790 --> 00:26:20.070 this or that? 00:26:20.070 --> 00:26:22.270 But we can look at it and figure it out. 00:26:22.270 --> 00:26:25.360 So we can compare what the protein structure looks 00:26:25.360 --> 00:26:28.360 like for a healthy individual with the protein structure 00:26:28.360 --> 00:26:29.890 from someone who has a mutation. 00:26:29.890 --> 00:26:31.540 All of a sudden you might see, wow, 00:26:31.540 --> 00:26:34.480 the vitamin that this protein needs can't bind anymore. 00:26:34.480 --> 00:26:36.340 So we can have a sense of what's wrong. 00:26:36.340 --> 00:26:37.881 And then sometimes you can figure out 00:26:37.881 --> 00:26:40.674 how to treat it once you know what the problem is. 00:26:40.674 --> 00:26:42.340 Sometimes there'll be a protein molecule 00:26:42.340 --> 00:26:43.720 that everyone knows is important. 00:26:43.720 --> 00:26:46.080 Everyone wants to know what it looks like. 00:26:46.080 --> 00:26:48.040 But you might be the one who does it. 00:26:48.040 --> 00:26:50.480 You might be the one to figure out what it looks like. 00:26:50.480 --> 00:26:52.130 And you'll be the first one. 00:26:52.130 --> 00:26:54.380 You'll see these patterns, these diffraction patterns, 00:26:54.380 --> 00:26:56.629 and you'll build this model and all of a sudden you'll 00:26:56.629 --> 00:26:59.170 be like wow, that's not what people expected. 00:26:59.170 --> 00:27:01.210 And it'll just be this incredible discovery. 00:27:01.210 --> 00:27:04.420 So you're an explorer of the molecular world 00:27:04.420 --> 00:27:05.986 when you're a crystallographer. 00:27:09.880 --> 00:27:11.152 [APPLAUSE] 00:27:11.152 --> 00:27:12.360 CATHERINE DRENNAN: Thank you! 00:27:18.470 --> 00:27:21.760 OK, so that's the first in the series. 00:27:21.760 --> 00:27:24.616 We're going to have another one this week, 00:27:24.616 --> 00:27:26.365 as well, because we have a lot of history. 00:27:26.365 --> 00:27:29.560 So we've got to counter it with a lot of current research. 00:27:29.560 --> 00:27:33.760 And so you'll be learning about quantum dots also this week. 00:27:33.760 --> 00:27:38.140 OK, so those are some of the characteristics of waves 00:27:38.140 --> 00:27:42.190 that are really important and we talked about light as a wave. 00:27:42.190 --> 00:27:45.060 Now we're going to talk about light as a particle. 00:27:45.060 --> 00:27:47.740 Light as a wave is a little bit easier to grasp. 00:27:47.740 --> 00:27:51.530 Light as a particle is a little bit more confusing. 00:27:51.530 --> 00:27:54.910 And it took a while for people to really appreciate 00:27:54.910 --> 00:27:57.170 that light had particle-like properties, i.e. 00:27:57.170 --> 00:27:58.840 It was quantized. 00:27:58.840 --> 00:28:02.320 And this really came out of the photoelectric effect. 00:28:02.320 --> 00:28:03.700 So what were people doing? 00:28:03.700 --> 00:28:06.250 And this is around the time of the discovery of the electron 00:28:06.250 --> 00:28:07.530 and the nucleus. 00:28:07.530 --> 00:28:09.880 And what scientists were having fun doing 00:28:09.880 --> 00:28:13.990 were taking beams of UV light and hitting metal surfaces, 00:28:13.990 --> 00:28:16.335 and seeing if they could inject electrons, 00:28:16.335 --> 00:28:17.460 which have been discovered. 00:28:17.460 --> 00:28:19.150 It's like, let's get some electrons out 00:28:19.150 --> 00:28:20.590 of those metal surfaces. 00:28:20.590 --> 00:28:24.130 We know they're there, let's see them come off and characterize 00:28:24.130 --> 00:28:25.770 their properties. 00:28:25.770 --> 00:28:32.110 So they found that if they had some UV light and the frequency 00:28:32.110 --> 00:28:35.770 of that UV light was below something, below a threshold 00:28:35.770 --> 00:28:39.810 that they referred to as the threshold frequency. 00:28:39.810 --> 00:28:42.850 So we have a new zero here. 00:28:42.850 --> 00:28:46.450 If the frequency was lower than this magic number 00:28:46.450 --> 00:28:50.230 for frequency, nothing would happen. 00:28:50.230 --> 00:28:52.930 But if they increased the frequency, 00:28:52.930 --> 00:28:57.610 if it was greater than or equal to this threshold frequency, 00:28:57.610 --> 00:28:59.950 then all of a sudden they would see something. 00:28:59.950 --> 00:29:03.100 They would see an electron being ejected. 00:29:03.100 --> 00:29:05.410 And the electron would come off with a certain amount 00:29:05.410 --> 00:29:08.740 of kinetic energy, K.E. And kinetic energy 00:29:08.740 --> 00:29:13.690 is equal to a half times mass times the velocity squared. 00:29:13.690 --> 00:29:16.830 All right, so they decided let's characterize this. 00:29:16.830 --> 00:29:21.560 Lets very some parameters and see what happens. 00:29:21.560 --> 00:29:25.150 So they looked at constant intensity of this light 00:29:25.150 --> 00:29:28.000 and they changed the frequency. 00:29:28.000 --> 00:29:30.490 And then they looked at the number of electrons 00:29:30.490 --> 00:29:32.650 that were coming off. 00:29:32.650 --> 00:29:36.190 And so below this threshold frequency, 00:29:36.190 --> 00:29:37.960 no electrons came off. 00:29:37.960 --> 00:29:40.180 I just told you about that. 00:29:40.180 --> 00:29:42.700 Then when they were at the threshold, 00:29:42.700 --> 00:29:45.400 they saw electrons coming off and then they 00:29:45.400 --> 00:29:47.920 increased the frequency even more, 00:29:47.920 --> 00:29:51.560 but they weren't getting any more electrons. 00:29:51.560 --> 00:29:52.560 Hm. 00:29:52.560 --> 00:29:54.980 OK, this was interesting. 00:29:54.980 --> 00:29:57.520 So they thought what else can we measure here. 00:29:57.520 --> 00:29:59.560 And they knew how to measure the kinetic energy. 00:29:59.560 --> 00:30:01.150 So it's like, let's start measuring 00:30:01.150 --> 00:30:06.430 the kinetic energy of these electrons that are coming off. 00:30:06.430 --> 00:30:10.750 So they plotted kinetic energy of the ejected electrons 00:30:10.750 --> 00:30:14.980 as a function of the frequency of the incoming light. 00:30:14.980 --> 00:30:18.640 And again, below the threshold, they saw nothing. 00:30:18.640 --> 00:30:23.090 But above the threshold, they saw the kinetic energy increase 00:30:23.090 --> 00:30:28.270 proportionally to the increase in the frequency of the light. 00:30:28.270 --> 00:30:30.130 And this didn't really make any sense 00:30:30.130 --> 00:30:32.380 from what they knew at the time. 00:30:32.380 --> 00:30:36.910 They didn't have a way to relate kinetic energy and frequency. 00:30:36.910 --> 00:30:40.560 So they really weren't sure what this was about, 00:30:40.560 --> 00:30:42.490 but they were having fun doing experiments. 00:30:42.490 --> 00:30:48.310 It's like, let's keep going, let's vary more properties. 00:30:48.310 --> 00:30:52.630 So then they decided to look at how 00:30:52.630 --> 00:30:55.360 the kinetic energy of the electron 00:30:55.360 --> 00:30:58.240 was affected by changing the intensity of the light. 00:30:58.240 --> 00:31:00.790 And they thought that if you increase the intensity, 00:31:00.790 --> 00:31:03.060 you'd have more energy in your system, 00:31:03.060 --> 00:31:06.130 you should have more kinetic energy. 00:31:06.130 --> 00:31:10.510 But that did not seem to be the case. 00:31:10.510 --> 00:31:13.960 They increased the intensity, the kinetic energy 00:31:13.960 --> 00:31:15.970 stayed the same. 00:31:15.970 --> 00:31:18.430 They were having trouble wrapping their head around it. 00:31:18.430 --> 00:31:23.290 But they said, all right, well let's collect some more data. 00:31:23.290 --> 00:31:28.540 So now they decided to look at the number of ejected electrons 00:31:28.540 --> 00:31:31.264 as a function of the intensity. 00:31:31.264 --> 00:31:32.680 And they really didn't think there 00:31:32.680 --> 00:31:33.980 should be much difference. 00:31:33.980 --> 00:31:36.640 Increase the intensity, number of electrons 00:31:36.640 --> 00:31:37.810 should be the same. 00:31:37.810 --> 00:31:41.950 But experiments showed otherwise. 00:31:41.950 --> 00:31:45.160 So when they increased the intensity, 00:31:45.160 --> 00:31:49.010 more electrons came off. 00:31:49.010 --> 00:31:51.029 And this is where they were in the field. 00:31:51.029 --> 00:31:52.570 It almost seemed like everything they 00:31:52.570 --> 00:31:55.270 did was opposite of what they expected. 00:31:55.270 --> 00:31:57.910 It's a pretty exciting time actually in science 00:31:57.910 --> 00:32:00.530 when you're getting results that are unexpected. 00:32:00.530 --> 00:32:03.430 And some of this data sat around for a while. 00:32:03.430 --> 00:32:06.070 And then Einstein decided to take a little look at it 00:32:06.070 --> 00:32:09.026 and see what he thought of this data. 00:32:09.026 --> 00:32:10.900 And people were studying all sorts of things. 00:32:10.900 --> 00:32:13.580 They're taking different metals, you have a different metal, 00:32:13.580 --> 00:32:15.850 you have a different threshold frequency. 00:32:15.850 --> 00:32:20.080 And so people were characterizing different metals 00:32:20.080 --> 00:32:21.980 and figuring out the threshold frequency 00:32:21.980 --> 00:32:23.590 for all the different metals. 00:32:23.590 --> 00:32:27.310 And then plotting the kinetic energy of the ejected 00:32:27.310 --> 00:32:30.640 electrons as a function of the frequency. 00:32:30.640 --> 00:32:34.300 And you look at this, you realize huh, 00:32:34.300 --> 00:32:36.260 there's different threshold frequencies 00:32:36.260 --> 00:32:38.620 for the different metals, but they all 00:32:38.620 --> 00:32:41.290 seem to have these straight lines that all 00:32:41.290 --> 00:32:43.964 seem to have the same slope. 00:32:43.964 --> 00:32:45.880 And sometimes when you look at the discoveries 00:32:45.880 --> 00:32:48.610 of really amazing people like Einstein, 00:32:48.610 --> 00:32:52.160 you're thinking well, basically what 00:32:52.160 --> 00:32:55.010 he did was solve the equation for a straight line. 00:32:55.010 --> 00:32:59.000 You realize hey, maybe I can contribute to science, as well. 00:32:59.000 --> 00:33:04.010 So we had a whole lot of straight lines here. 00:33:04.010 --> 00:33:07.910 And when you have that, you can solve for the slope. 00:33:07.910 --> 00:33:10.540 So that's what he did, he solved for the slope. 00:33:10.540 --> 00:33:14.380 And he got this number, 6.626 times 10 00:33:14.380 --> 00:33:18.640 to the -34th Joule seconds. 00:33:18.640 --> 00:33:21.190 And he saw that number and he's like, I've 00:33:21.190 --> 00:33:24.550 heard that number before. 00:33:24.550 --> 00:33:28.730 Planck came up with that number when he was studying black body 00:33:28.730 --> 00:33:30.740 radiation. 00:33:30.740 --> 00:33:33.220 So totally different phenomenon, but yet 00:33:33.220 --> 00:33:35.050 the number comes up again, Planck's 00:33:35.050 --> 00:33:38.990 constant, also known as h. 00:33:38.990 --> 00:33:43.150 Now that seemed like a really strange coincidence. 00:33:43.150 --> 00:33:47.290 So there must be something to this number. 00:33:47.290 --> 00:33:49.490 So if you look at this plot, we can also 00:33:49.490 --> 00:33:53.380 think about what the y-axis is. 00:33:53.380 --> 00:33:59.590 So the y-intercept is minus Planck's constant times 00:33:59.590 --> 00:34:02.570 that threshold frequency. 00:34:02.570 --> 00:34:04.490 And when you have all of this, you 00:34:04.490 --> 00:34:09.020 can now write the equation for the straight line in terms 00:34:09.020 --> 00:34:12.020 of all of these variables. 00:34:12.020 --> 00:34:15.850 And so y-axis here is kinetic energy. 00:34:15.850 --> 00:34:20.770 So we'll solve that equation now in terms of kinetic energy. 00:34:20.770 --> 00:34:24.110 So kinetic energy is going to be equal. 00:34:24.110 --> 00:34:26.050 We have our x-axis here. 00:34:26.050 --> 00:34:28.630 The x-axis is frequency. 00:34:28.630 --> 00:34:31.600 And again, now, the slope of the line we know 00:34:31.600 --> 00:34:35.080 is Planck's constant, so that's h. 00:34:35.080 --> 00:34:41.139 And the y-intercept, or b, was -h 00:34:41.139 --> 00:34:45.820 times the threshold frequency. 00:34:45.820 --> 00:34:49.270 And this is a very important equation. 00:34:49.270 --> 00:34:52.179 So just to define those terms again, 00:34:52.179 --> 00:34:56.290 we have the frequency here, Planck's constant. 00:34:56.290 --> 00:35:01.660 Planck's constant times the frequency is an energy. 00:35:01.660 --> 00:35:04.010 It is the energy of the incident light 00:35:04.010 --> 00:35:08.240 or the incoming light, e sub i. 00:35:08.240 --> 00:35:12.610 And on this side over here, we have that threshold frequency 00:35:12.610 --> 00:35:13.420 again. 00:35:13.420 --> 00:35:15.370 We also have Planck's constant. 00:35:15.370 --> 00:35:19.660 So Planck's constant times a threshold frequency 00:35:19.660 --> 00:35:23.350 is another energy term, which is called the threshold 00:35:23.350 --> 00:35:28.490 energy, or more commonly a work function. 00:35:28.490 --> 00:35:32.950 So the kinetic energy equals the incident energy, 00:35:32.950 --> 00:35:38.470 the energy of the incoming light minus the work function, 00:35:38.470 --> 00:35:40.780 which has to do with the threshold frequency which 00:35:40.780 --> 00:35:43.780 depends on the metal in question. 00:35:43.780 --> 00:35:47.800 So this was a really important equation. 00:35:47.800 --> 00:35:52.270 And Einstein realized that the energy of light 00:35:52.270 --> 00:35:56.560 is proportional to its frequency and it's proportional 00:35:56.560 --> 00:35:58.220 by Planck's constant. 00:35:58.220 --> 00:35:59.890 And this really changed how people 00:35:59.890 --> 00:36:02.660 had been thinking about energy. 00:36:02.660 --> 00:36:06.200 And all of a sudden, a lot of those observations made sense. 00:36:06.200 --> 00:36:10.870 Now, Einstein of course had many important discoveries 00:36:10.870 --> 00:36:12.340 in his career. 00:36:12.340 --> 00:36:15.410 But this one was the one that he personally felt 00:36:15.410 --> 00:36:17.800 was the most revolutionary. 00:36:17.800 --> 00:36:18.659 I don't know. 00:36:18.659 --> 00:36:20.200 People are always their worst critic, 00:36:20.200 --> 00:36:24.990 but even he realized that this was important. 00:36:24.990 --> 00:36:29.730 And in terms of units, because units are always important. 00:36:29.730 --> 00:36:33.770 Notice usually you'll see energy in joules or kilojoules. 00:36:33.770 --> 00:36:37.830 And Planck's constant has the units of joule seconds. 00:36:37.830 --> 00:36:41.390 And frequency is per seconds or hertz. 00:36:41.390 --> 00:36:46.640 So in this equation, your units work out. 00:36:46.640 --> 00:36:50.160 So from this idea then we have this notion 00:36:50.160 --> 00:36:52.920 that light is made up of these energy packets which 00:36:52.920 --> 00:36:57.750 people call photons where the energy of that photon 00:36:57.750 --> 00:37:01.840 depends on its frequency. 00:37:01.840 --> 00:37:04.310 So we can go back to the photoelectric effect 00:37:04.310 --> 00:37:07.580 now and start thinking about those observations 00:37:07.580 --> 00:37:12.770 and try to rationalize now what we had been seeing. 00:37:12.770 --> 00:37:17.010 So here's this new model for the photoelectric effect 00:37:17.010 --> 00:37:20.430 where we can think about the energy of that incoming photon, 00:37:20.430 --> 00:37:23.870 or that incident photon. 00:37:23.870 --> 00:37:26.430 If it's greater than the work function, 00:37:26.430 --> 00:37:32.660 then you'll eject an electron from the metal. 00:37:32.660 --> 00:37:36.600 And any left over energy is the kinetic energy 00:37:36.600 --> 00:37:38.550 of that ejected electron. 00:37:38.550 --> 00:37:40.470 So we can think about that here. 00:37:40.470 --> 00:37:43.260 That here we have the energy coming in 00:37:43.260 --> 00:37:45.660 of the incident photon. 00:37:45.660 --> 00:37:48.000 We have to get over that threshold frequency 00:37:48.000 --> 00:37:50.040 or overcome that work function. 00:37:50.040 --> 00:37:53.580 So you have this minus this, and the leftover 00:37:53.580 --> 00:37:55.470 is the kinetic energy. 00:37:55.470 --> 00:37:57.540 So we can also write it this way, 00:37:57.540 --> 00:38:00.080 that the kinetic energy equals the incident 00:38:00.080 --> 00:38:05.010 energy minus the work function. 00:38:05.010 --> 00:38:08.660 So if you just have enough energy to do this, 00:38:08.660 --> 00:38:10.290 you have very small kinetic energy. 00:38:10.290 --> 00:38:12.810 But if you have a lot of extra energy 00:38:12.810 --> 00:38:14.540 once you overcome the work function, 00:38:14.540 --> 00:38:17.470 you'll have more kinetic energy. 00:38:17.470 --> 00:38:20.040 We can also write the equation this way, 00:38:20.040 --> 00:38:23.250 that the incident energy equals the kinetic energy 00:38:23.250 --> 00:38:26.730 plus the work function. 00:38:26.730 --> 00:38:30.146 OK, so let's just try a clicker question on this. 00:38:30.146 --> 00:38:32.270 And we're going to go back and look at those graphs 00:38:32.270 --> 00:38:33.561 and think about what they mean. 00:39:26.035 --> 00:39:27.576 All right, let's do ten more seconds. 00:39:45.850 --> 00:39:48.530 Yeah, OK. 00:39:48.530 --> 00:39:53.010 So here the trick was to think about what the work function is 00:39:53.010 --> 00:39:56.370 and how much energy was coming in of the photon. 00:39:56.370 --> 00:40:01.350 But here the energy is lower than the threshold needed, 00:40:01.350 --> 00:40:05.660 so you're not going to get any electrons ejected. 00:40:05.660 --> 00:40:06.642 Let's try one more. 00:40:06.642 --> 00:40:08.100 Let's see if you can get up to 90%. 00:40:13.110 --> 00:40:15.760 So now we've changed the energies. 00:40:15.760 --> 00:40:18.908 Or the energy, but not the threshold energy. 00:40:39.700 --> 00:40:40.747 OK, ten more seconds. 00:40:57.570 --> 00:40:59.280 Yeah, 98%. 00:40:59.280 --> 00:41:02.920 Yeah, so now we're over the threshold energy. 00:41:02.920 --> 00:41:06.090 So we need to subtract the threshold energy 00:41:06.090 --> 00:41:08.800 and the remaining is the kinetic energy. 00:41:08.800 --> 00:41:12.340 OK, so these are the kinds of questions we have on this. 00:41:12.340 --> 00:41:16.420 And now let's go back and think about these plots again. 00:41:16.420 --> 00:41:18.970 So we don't have these a second time in your notes, 00:41:18.970 --> 00:41:20.480 but you have them one time. 00:41:20.480 --> 00:41:24.220 And let's just think about how this makes sense now 00:41:24.220 --> 00:41:28.750 with the new equations that Einstein helped us achieve. 00:41:28.750 --> 00:41:33.570 So in the top here, we have the surprising observation 00:41:33.570 --> 00:41:36.550 that when you increase the frequency of the light 00:41:36.550 --> 00:41:38.800 that the kinetic energy increase. 00:41:38.800 --> 00:41:41.470 Well, now this makes sense, because if you're 00:41:41.470 --> 00:41:43.720 increasing the frequency of the light, 00:41:43.720 --> 00:41:47.800 you're increasing the incident energy of the photons coming 00:41:47.800 --> 00:41:48.400 in. 00:41:48.400 --> 00:41:52.260 And so if you're increasing this frequency, 00:41:52.260 --> 00:41:54.520 so you're increasing the incident energy. 00:41:54.520 --> 00:41:57.480 And once you're above the threshold energy, 00:41:57.480 --> 00:42:01.780 you'll have more extra kinetic energy coming off 00:42:01.780 --> 00:42:05.710 as the frequency, or the energy of the incident light comes up. 00:42:05.710 --> 00:42:07.190 So that makes sense. 00:42:07.190 --> 00:42:09.190 All right, what about intensity? 00:42:09.190 --> 00:42:11.870 We haven't really talked so much about intensity. 00:42:11.870 --> 00:42:14.500 So let's consider intensity for a minute 00:42:14.500 --> 00:42:18.230 and think about the number of electrons, as well. 00:42:18.230 --> 00:42:20.900 So both of these are about intensity. 00:42:20.900 --> 00:42:23.280 So let's think about the number of electrons 00:42:23.280 --> 00:42:24.814 ejected from a metal surface. 00:42:24.814 --> 00:42:26.980 We're going to come back to those plots in a minute, 00:42:26.980 --> 00:42:30.010 sorry to make you go back and forth in your notes. 00:42:30.010 --> 00:42:31.930 And that's going to be proportional 00:42:31.930 --> 00:42:33.740 to the number of photons. 00:42:33.740 --> 00:42:37.170 So the more photons you have coming in, 00:42:37.170 --> 00:42:39.670 the more electrons are going to have coming out. 00:42:39.670 --> 00:42:44.320 That is, if the photons have the appropriate amount, 00:42:44.320 --> 00:42:49.750 if they're over the threshold frequency over the threshold 00:42:49.750 --> 00:42:52.990 energy, then you're going to have an electron ejected 00:42:52.990 --> 00:42:54.360 from the metal surface. 00:42:54.360 --> 00:42:59.110 So for each photon that has greater incident 00:42:59.110 --> 00:43:01.150 energy than the threshold, you'll 00:43:01.150 --> 00:43:03.610 have an electron being ejected. 00:43:03.610 --> 00:43:05.470 So what is intensity? 00:43:05.470 --> 00:43:10.190 Well, the intensity is really the photons per second. 00:43:10.190 --> 00:43:13.240 So it's proportional to the number of photons being 00:43:13.240 --> 00:43:15.610 absorbed by the metal, and therefore, 00:43:15.610 --> 00:43:20.080 the number of electrons coming out of the metal. 00:43:20.080 --> 00:43:23.070 So intensity's units are often in watts. 00:43:23.070 --> 00:43:27.380 You also can do a conversion in joules per second. 00:43:27.380 --> 00:43:31.780 So the higher the intensity, the more 00:43:31.780 --> 00:43:36.160 photons with the appropriate amount of energy 00:43:36.160 --> 00:43:40.860 to overcome that work function, the more electrons coming off. 00:43:40.860 --> 00:43:44.980 So now we can go back and think about these plots again. 00:43:44.980 --> 00:43:49.720 So here the relationship between intensity and kinetic energy 00:43:49.720 --> 00:43:50.440 was flat. 00:43:50.440 --> 00:43:52.270 And that was unexpected. 00:43:52.270 --> 00:43:55.630 But the kinetic energy doesn't change here 00:43:55.630 --> 00:44:00.760 since the intensity means more photons per second, not 00:44:00.760 --> 00:44:03.150 more energy per photon. 00:44:03.150 --> 00:44:06.280 So you're just increasing the number of photons. 00:44:06.280 --> 00:44:09.550 If none of the photons have the appropriate energy, 00:44:09.550 --> 00:44:12.880 you're not going to have any electrons coming off. 00:44:12.880 --> 00:44:18.610 But if you have more photons per second, 00:44:18.610 --> 00:44:21.900 and they have the appropriate amount of energy, 00:44:21.900 --> 00:44:26.530 then you are going to see these electrons coming off. 00:44:26.530 --> 00:44:29.400 So the number of electrons admitted 00:44:29.400 --> 00:44:33.400 does change since high intensity means more photons. 00:44:33.400 --> 00:44:37.150 More photons, more electrons. 00:44:37.150 --> 00:44:40.840 So these things that Einstein helped us with, 00:44:40.840 --> 00:44:44.730 these equations, now made sense of the data 00:44:44.730 --> 00:44:46.190 that was being observed. 00:44:46.190 --> 00:44:48.520 So the photoelectric effect was really 00:44:48.520 --> 00:44:51.970 important in helping derive these relationships 00:44:51.970 --> 00:44:54.250 between energy and frequency. 00:44:54.250 --> 00:44:57.630 And so in particular, the really important points 00:44:57.630 --> 00:45:00.880 here is that light is made up of these photons, 00:45:00.880 --> 00:45:03.820 these discrete energy packages. 00:45:03.820 --> 00:45:08.230 And each one of those photons has to have enough energy in it 00:45:08.230 --> 00:45:11.500 to overcome the threshold to emit an electron. 00:45:11.500 --> 00:45:14.710 So energy is proportional to frequency, 00:45:14.710 --> 00:45:18.100 which was a really new and exciting idea at the time. 00:45:18.100 --> 00:45:21.480 E equals Planck's constant times frequency. 00:45:21.480 --> 00:45:24.420 And the intensity of light has to do with the number 00:45:24.420 --> 00:45:26.540 of photons hitting per second. 00:45:26.540 --> 00:45:28.590 And if you keep these things in mind, 00:45:28.590 --> 00:45:31.900 you'll do really well finishing up a number of the problems 00:45:31.900 --> 00:45:36.340 on the photoelectric effect, which are in problem set one. 00:45:36.340 --> 00:45:37.860 OK, see you on Wednesday. 00:45:37.860 --> 00:45:41.820 We're going to do a demo of the photoelectric effect.