1 00:00:00,000 --> 00:00:00,016 The following content is provided under a Creative 2 00:00:00,016 --> 00:00:00,022 Commons license. 3 00:00:00,022 --> 00:00:00,038 Your support will help MIT OpenCourseWare continue to 4 00:00:00,038 --> 00:00:00,054 offer high quality educational resources for free. 5 00:00:00,054 --> 00:00:00,072 To make a donation or view additional materials from 6 00:00:00,072 --> 00:00:00,088 hundreds of MIT courses, visit MIT OpenCourseWare at 7 00:00:00,088 --> 00:00:00,110 ocw.mit.edu. 8 00:00:00,110 --> 00:00:22,260 PROFESSOR: All right. 9 00:00:22,260 --> 00:00:24,870 As you're settling in, why don't you take 10 more seconds 10 00:00:24,870 --> 00:00:26,950 to answer the clicker question. 11 00:00:26,950 --> 00:00:29,470 This is the last question we'll see in class on the 12 00:00:29,470 --> 00:00:32,780 photoelectric effect, so hopefully we can have a very 13 00:00:32,780 --> 00:00:36,110 high success rate here to show we are all ready to move on 14 00:00:36,110 --> 00:00:42,410 with our lives here. 15 00:00:42,410 --> 00:00:43,250 OK, good. 16 00:00:43,250 --> 00:00:46,480 So, most of you did get the answer correct. 17 00:00:46,480 --> 00:00:50,460 For those of you that didn't, you, of course, can ask your 18 00:00:50,460 --> 00:00:52,890 TA's about this in recitation, they'll always have a copy of 19 00:00:52,890 --> 00:00:53,860 these slides. 20 00:00:53,860 --> 00:00:56,280 But just to point out the confusion can be we've 21 00:00:56,280 --> 00:00:58,660 actually switched what the question is here. 22 00:00:58,660 --> 00:01:01,950 What the information we gave was the work function, which 23 00:01:01,950 --> 00:01:04,610 is what we've been giving before, but now we gave you 24 00:01:04,610 --> 00:01:07,350 the kinetic energy of the ejected electron, so you just 25 00:01:07,350 --> 00:01:09,980 need to rearrange your equation so now you're solving 26 00:01:09,980 --> 00:01:12,190 for the incoming energy, which would mean that you need to 27 00:01:12,190 --> 00:01:13,810 add those two energies together. 28 00:01:13,810 --> 00:01:16,950 So, hopefully everyone that didn't get this right, can 29 00:01:16,950 --> 00:01:19,130 look at it again and think about asking it's just asking 30 00:01:19,130 --> 00:01:21,610 the question in a different kind of a way. 31 00:01:21,610 --> 00:01:21,940 All right. 32 00:01:21,940 --> 00:01:24,550 So, we can switch over to the class notes. 33 00:01:24,550 --> 00:01:26,630 So today, we're going to start talking about 34 00:01:26,630 --> 00:01:27,880 the hydrogen atom. 35 00:01:27,880 --> 00:01:30,500 Now that we have our Schrodinger equation for the 36 00:01:30,500 --> 00:01:33,740 hydrogen atom, we can talk about it very specifically in 37 00:01:33,740 --> 00:01:37,170 terms of binding energies and also in terms of orbitals. 38 00:01:37,170 --> 00:01:40,350 And we talked about on Wednesday the conditions that 39 00:01:40,350 --> 00:01:43,450 allowed us to use quantum mechanics, which then enable 40 00:01:43,450 --> 00:01:45,970 us to have the Schrodinger equation, which we can apply, 41 00:01:45,970 --> 00:01:48,520 and part of that is the wave particle duality 42 00:01:48,520 --> 00:01:50,020 of light and matter. 43 00:01:50,020 --> 00:01:56,450 So there was a good question in Wednesday's class about the 44 00:01:56,450 --> 00:01:58,090 de Broglie wavelength and if it can 45 00:01:58,090 --> 00:01:59,200 actually go to infinity. 46 00:01:59,200 --> 00:02:01,380 So I just wanted to address that quickly before we move 47 00:02:01,380 --> 00:02:05,610 on, and actually address another thing about dealing 48 00:02:05,610 --> 00:02:08,660 with wavelengths of particles that sometimes comes up. 49 00:02:08,660 --> 00:02:16,110 So, the question that we had in last class, was if we have 50 00:02:16,110 --> 00:02:19,370 actually a macroscopic particle, and the velocity 51 00:02:19,370 --> 00:02:22,670 let's say starts to approach zero, shouldn't we have the 52 00:02:22,670 --> 00:02:26,840 wavelength go to infinity, even if we have a magic board, 53 00:02:26,840 --> 00:02:29,660 and even if the mass is really large. 54 00:02:29,660 --> 00:02:32,880 So, in most cases, you would think that as the velocity 55 00:02:32,880 --> 00:02:38,230 gets very tiny, the mass is still going to be large enough 56 00:02:38,230 --> 00:02:41,490 to cancel it out and still make it such that the 57 00:02:41,490 --> 00:02:43,730 wavelength is going to be pretty small, right. 58 00:02:43,730 --> 00:02:47,950 Because if we think about the h, Planck's constant, here 59 00:02:47,950 --> 00:02:52,040 that's measured in 10 to the negative 34 joules per second. 60 00:02:52,040 --> 00:02:54,740 So, we would actually need a really, really, really tiny 61 00:02:54,740 --> 00:02:59,540 velocity here to actually overcome the size of the mass, 62 00:02:59,540 --> 00:03:02,195 if we're talking about macroscopic particles, to have 63 00:03:02,195 --> 00:03:04,380 a wavelength that's going to be on the order. 64 00:03:04,380 --> 00:03:07,040 So, let's say we're talking about the baseball, have a 65 00:03:07,040 --> 00:03:08,610 wavelength of the baseball that's on the 66 00:03:08,610 --> 00:03:10,060 order of the baseball. 67 00:03:10,060 --> 00:03:13,290 So, if we kind of think about the numbers we would need, we 68 00:03:13,290 --> 00:03:16,030 would actually need a velocity that approached something 69 00:03:16,030 --> 00:03:20,310 that's about 10 to the negative 30 meters per second. 70 00:03:20,310 --> 00:03:23,640 So first of all, that's pretty slow here. 71 00:03:23,640 --> 00:03:26,920 It's going to be hard to measure anyway, and in fact, 72 00:03:26,920 --> 00:03:29,640 if we're talking about something going 10 to the 73 00:03:29,640 --> 00:03:33,310 negative 30, and we're going to observe it using our eyes, 74 00:03:33,310 --> 00:03:36,640 so you using visible light to observe something going this 75 00:03:36,640 --> 00:03:39,370 slow, we're actually not going to be able to do it because 76 00:03:39,370 --> 00:03:41,880 we're limited by the wavelength of light to see how 77 00:03:41,880 --> 00:03:45,000 precise we can measure where the actual position is. 78 00:03:45,000 --> 00:03:48,290 So let's say we have the wavelength of light somewhere 79 00:03:48,290 --> 00:03:51,010 on the order of 10 to the negative 5 meters, being the 80 00:03:51,010 --> 00:03:54,030 wavelength of light, we're only going to be able to 81 00:03:54,030 --> 00:03:57,420 measure the velocity because of the uncertainty principle 82 00:03:57,420 --> 00:03:58,590 to a certain degree. 83 00:03:58,590 --> 00:04:05,070 And it turns out it's three orders of magnitude that -- 84 00:04:05,070 --> 00:04:07,460 the uncertainty is three orders of magnitude bigger 85 00:04:07,460 --> 00:04:10,060 than the velocity that we're actually trying to observe to 86 00:04:10,060 --> 00:04:12,640 get to a point where we could see the wavelength, for 87 00:04:12,640 --> 00:04:16,240 example, for even a baseball that is moving this slow? 88 00:04:16,240 --> 00:04:19,330 So that the more complete answer to the question is that 89 00:04:19,330 --> 00:04:21,960 no, we're never going to be able to observe that because 90 00:04:21,960 --> 00:04:25,165 of the uncertainty principle it's not possible to observe a 91 00:04:25,165 --> 00:04:27,680 velocity that's this slow for a macroscopic object. 92 00:04:27,680 --> 00:04:32,510 So, hopefully that kind of clears up that question. 93 00:04:32,510 --> 00:04:34,820 And, of course, when the velocity actually is zero, 94 00:04:34,820 --> 00:04:38,350 this equation that the de Broglie has put forth is valid 95 00:04:38,350 --> 00:04:40,900 for anything that has momentum, so if something does 96 00:04:40,900 --> 00:04:43,290 not have any velocity at all, it actually does not have 97 00:04:43,290 --> 00:04:46,540 momentum, so you can't apply that equation anyway. 98 00:04:46,540 --> 00:04:50,770 And another thing that came up, and it came up in 99 00:04:50,770 --> 00:04:54,140 remembering as I was writing your problem set for this 100 00:04:54,140 --> 00:04:56,510 week, which will be posted sometime this afternoon, your 101 00:04:56,510 --> 00:04:59,910 problem set 2, is when we're talking about wavelengths of 102 00:04:59,910 --> 00:05:02,550 particles, and for specifically for electrons 103 00:05:02,550 --> 00:05:05,320 sometimes, you're asked to calculate what the energy is. 104 00:05:05,320 --> 00:05:07,820 And I just want to remind everyone, so this is a 105 00:05:07,820 --> 00:05:13,550 separate thought here, that we often use the energy where 106 00:05:13,550 --> 00:05:18,210 energy is equal to h c divided by wavelength. 107 00:05:18,210 --> 00:05:21,290 So if we're talking about, for example, we know the 108 00:05:21,290 --> 00:05:23,530 wavelength of an electron and we're trying to find the 109 00:05:23,530 --> 00:05:26,300 energy or vice versa, is this an equation we 110 00:05:26,300 --> 00:05:28,640 can use to do that? 111 00:05:28,640 --> 00:05:31,390 What do you think? 112 00:05:31,390 --> 00:05:31,960 No. 113 00:05:31,960 --> 00:05:33,870 Hopefully you're going to say no. 114 00:05:33,870 --> 00:05:37,190 And the reason is, and this will come up on the problems 115 00:05:37,190 --> 00:05:39,670 and a lot of students end up using this equation, which is 116 00:05:39,670 --> 00:05:42,420 why I want to head it off and mention it ahead of time, we 117 00:05:42,420 --> 00:05:45,100 can't use an equation because this equation is very 118 00:05:45,100 --> 00:05:46,370 specific for light. 119 00:05:46,370 --> 00:05:50,120 We know it's very specific for light because in this equation 120 00:05:50,120 --> 00:05:52,060 is c, the speed of light. 121 00:05:52,060 --> 00:05:54,590 So any time you go to use this equation, if you're trying to 122 00:05:54,590 --> 00:05:57,870 use it for an electron, just ask yourself first, does an 123 00:05:57,870 --> 00:06:00,030 electron travel at the speed of light? 124 00:06:00,030 --> 00:06:04,160 And if your answer is no, your answer will be no, then you 125 00:06:04,160 --> 00:06:06,470 just know you can't use this equation here. 126 00:06:06,470 --> 00:06:09,660 So instead you'd have to maybe if you start with wavelength, 127 00:06:09,660 --> 00:06:12,580 go over there, and then figure out velocity and do something 128 00:06:12,580 --> 00:06:15,460 more like kinetic energy equals 1/2 n b 129 00:06:15,460 --> 00:06:16,660 squared to get there. 130 00:06:16,660 --> 00:06:18,835 So this is just a heads up for as you start your 131 00:06:18,835 --> 00:06:21,170 next problem set. 132 00:06:21,170 --> 00:06:21,500 All right. 133 00:06:21,500 --> 00:06:25,750 So jumping in to having established that, yes, 134 00:06:25,750 --> 00:06:28,570 particles have wave-like behavior, even though no, 135 00:06:28,570 --> 00:06:31,460 they're not actually photons, we can't use that equation. 136 00:06:31,460 --> 00:06:36,110 But we can use equations that describe waves to describe 137 00:06:36,110 --> 00:06:38,410 matter, and that's what we're going to be doing today. 138 00:06:38,410 --> 00:06:40,570 We're going to be looking at the solutions to the 139 00:06:40,570 --> 00:06:42,740 Schrodinger equation for a hydrogen atom, and 140 00:06:42,740 --> 00:06:45,690 specifically we'll be looking at the binding energy of the 141 00:06:45,690 --> 00:06:47,380 electron to the nucleus. 142 00:06:47,380 --> 00:06:49,640 So we'll be looking at the solution to this part of the 143 00:06:49,640 --> 00:06:52,130 Schrodinger equation where we're finding e. 144 00:06:52,130 --> 00:06:54,780 Then we'll go on, after we've made all of our predictions 145 00:06:54,780 --> 00:06:57,770 for what the energy should be, we can actually confirm 146 00:06:57,770 --> 00:07:00,200 whether or not we're correct, and we'll do this by looking 147 00:07:00,200 --> 00:07:04,490 at photon emission and photon absorption for hydrogen atoms, 148 00:07:04,490 --> 00:07:07,110 and we'll actually do a demo with that, too, so we can 149 00:07:07,110 --> 00:07:10,240 confirm it ourselves, as well as matching it with the 150 00:07:10,240 --> 00:07:12,080 observation of others. 151 00:07:12,080 --> 00:07:15,060 And if we have time, we'll move on also to talking about 152 00:07:15,060 --> 00:07:17,780 the other part of the solution to the Schrodinger equation, 153 00:07:17,780 --> 00:07:21,120 which is psi or this wave function here. 154 00:07:21,120 --> 00:07:23,420 And remember I said that wave function is just a 155 00:07:23,420 --> 00:07:26,460 representation of the particle, particularly when 156 00:07:26,460 --> 00:07:29,400 we're talking about electrons -- we're familiar with the 157 00:07:29,400 --> 00:07:34,460 term orbitals. psi is just a description of the orbital. 158 00:07:34,460 --> 00:07:36,740 So, we'll start with an introduction to that if we got 159 00:07:36,740 --> 00:07:39,270 to it at the end. 160 00:07:39,270 --> 00:07:41,450 So, to remind you, when we look at the Schrodinger 161 00:07:41,450 --> 00:07:46,110 equation here, we have two parts to it, so when we solve 162 00:07:46,110 --> 00:07:48,980 the Schrodinger equation, we're either finding psi, 163 00:07:48,980 --> 00:07:52,950 which as I said, is a wave function or an orbital. 164 00:07:52,950 --> 00:07:57,070 And in addition to finding psi, we can also solve to find 165 00:07:57,070 --> 00:08:00,960 e or to find the energy for any given psi, and these are 166 00:08:00,960 --> 00:08:04,440 the binding energies of the electron to the nucleus. 167 00:08:04,440 --> 00:08:06,840 And the most important thing about using the Schrodinger 168 00:08:06,840 --> 00:08:09,180 equation and getting out our solutions for potential 169 00:08:09,180 --> 00:08:12,170 orbitals and potential energies for an electron with 170 00:08:12,170 --> 00:08:15,050 the nucleus, is that what we find is that quantum 171 00:08:15,050 --> 00:08:17,750 mechanics, and quantum mechanics allowing us to get 172 00:08:17,750 --> 00:08:21,140 to the Schrodinger equation, allows us to correctly predict 173 00:08:21,140 --> 00:08:24,450 and confirm our observations for what we can actually 174 00:08:24,450 --> 00:08:27,620 measure are indeed the energy levels. 175 00:08:27,620 --> 00:08:29,923 Here we're talking about a hydrogen atom and that's what 176 00:08:29,923 --> 00:08:30,940 we'll focus on today. 177 00:08:30,940 --> 00:08:33,550 And it's incredibly precise and we're able to make the 178 00:08:33,550 --> 00:08:35,860 predictions and match them with experiment. 179 00:08:35,860 --> 00:08:38,270 Also, when we're looking at the Schrodinger equation, it 180 00:08:38,270 --> 00:08:42,020 allows us to explain a stable hydrogen atom, which is 181 00:08:42,020 --> 00:08:43,560 something that classical mechanics did 182 00:08:43,560 --> 00:08:46,760 not allow us to do. 183 00:08:46,760 --> 00:08:51,420 So here's the solution for a hydrogen atom, where we have 184 00:08:51,420 --> 00:08:55,040 the e term here is equal to everything written in green. 185 00:08:55,040 --> 00:08:58,260 We've got a lot of constants in this solution to the 186 00:08:58,260 --> 00:09:01,330 hydrogen atom, and we know what most of these mean. 187 00:09:01,330 --> 00:09:04,850 But remember that this whole term in green here is what is 188 00:09:04,850 --> 00:09:07,480 going to be equal to that binding energy between the 189 00:09:07,480 --> 00:09:11,230 nucleus of a hydrogen atom and the electron. 190 00:09:11,230 --> 00:09:14,430 So, let's go ahead and define our variables here, they 191 00:09:14,430 --> 00:09:17,830 should be familiar to us. 192 00:09:17,830 --> 00:09:23,570 We have the mass, first of all, m is equal to m e, so 193 00:09:23,570 --> 00:09:29,360 that's the electron mass. 194 00:09:29,360 --> 00:09:33,670 We also have e, which is going to be the 195 00:09:33,670 --> 00:09:40,010 charge on the electron. 196 00:09:40,010 --> 00:09:43,040 In addition to that, we have that epsilon nought value, 197 00:09:43,040 --> 00:09:45,820 remember that's the permittivity constant in a 198 00:09:45,820 --> 00:09:50,330 vacuum, and basically that is what we use as a conversion 199 00:09:50,330 --> 00:09:51,820 factor to get from units. 200 00:09:51,820 --> 00:09:54,260 We don't want namely coulombs to units, we want that will 201 00:09:54,260 --> 00:09:56,630 allow us to cancel out in this equation. 202 00:09:56,630 --> 00:10:00,330 And finally we have Planck's constant here, which we're all 203 00:10:00,330 --> 00:10:03,470 familiar with. 204 00:10:03,470 --> 00:10:07,140 So, what actually happens when people work with the solution 205 00:10:07,140 --> 00:10:10,440 to the Schrodinger equation for a hydrogen atom is that 206 00:10:10,440 --> 00:10:12,990 they don't always want to deal with all these constants here, 207 00:10:12,990 --> 00:10:16,500 so we can actually group them together and use them as a 208 00:10:16,500 --> 00:10:19,690 single new constant, and this new constant 209 00:10:19,690 --> 00:10:21,450 is the Rydberg constant. 210 00:10:21,450 --> 00:10:25,940 And the Rydberg constant is actually equal to 2 . 211 00:10:25,940 --> 00:10:30,410 1 8 times 10 to the negative 18 joules. 212 00:10:30,410 --> 00:10:33,050 So when we pull out all of those constants and instead 213 00:10:33,050 --> 00:10:36,270 use the Rydberg constant, what it allows us to do is really 214 00:10:36,270 --> 00:10:38,790 simplify our energy equation. 215 00:10:38,790 --> 00:10:41,890 So now we have that energy is equal to the negative of the 216 00:10:41,890 --> 00:10:46,540 Rydberg constant divided by n squared. 217 00:10:46,540 --> 00:10:49,330 So, what we have left in our equation is only one part that 218 00:10:49,330 --> 00:10:52,320 we haven't explained yet, and that is that n value. 219 00:10:52,320 --> 00:10:54,460 And it turns out that when you solve the Schrodinger 220 00:10:54,460 --> 00:10:57,700 equation, you find that there are only certain allowed 221 00:10:57,700 --> 00:10:59,470 values of this integer n. 222 00:10:59,470 --> 00:11:07,020 And those allowed values range anywhere from n equals 1, you 223 00:11:07,020 --> 00:11:10,850 can have n equal that 2, 3, and it goes all 224 00:11:10,850 --> 00:11:12,360 the way up to infinity. 225 00:11:12,360 --> 00:11:14,970 But the important part is that there are only certain allowed 226 00:11:14,970 --> 00:11:17,640 values, so for example, you can't have 1 . 227 00:11:17,640 --> 00:11:18,720 5 or 2 . 228 00:11:18,720 --> 00:11:22,260 3, there are only these interger numbers. 229 00:11:22,260 --> 00:11:24,660 And this n here is what we call the 230 00:11:24,660 --> 00:11:34,630 principle quantum number. 231 00:11:34,630 --> 00:11:38,900 And what we find is when we apply n and plug it in to our 232 00:11:38,900 --> 00:11:42,370 energy equation, is that what we see is now we don't just 233 00:11:42,370 --> 00:11:45,810 have one distinct answer, we don't just have one possible 234 00:11:45,810 --> 00:11:48,450 binding energy of the electron to the nucleus. 235 00:11:48,450 --> 00:11:52,070 We're going to find that we actually have a whole bunch of 236 00:11:52,070 --> 00:11:55,550 possible, in fact, an infinite number of possible energy 237 00:11:55,550 --> 00:11:58,030 levels, and that's easier to see on this 238 00:11:58,030 --> 00:12:00,700 energy diagram here. 239 00:12:00,700 --> 00:12:04,090 So, let's start with n equals 1, since that's, of course, 240 00:12:04,090 --> 00:12:05,270 the simplest case. 241 00:12:05,270 --> 00:12:08,450 So, if we have n equals 1, we can plug it into our energy 242 00:12:08,450 --> 00:12:12,460 equation here, and find that the binding energy, the e sub 243 00:12:12,460 --> 00:12:15,650 n, for n equals 1, it's just going to be equal to the 244 00:12:15,650 --> 00:12:18,320 negative of the Rydberg constant, so we can actually 245 00:12:18,320 --> 00:12:21,930 graph that on an energy diagram here, and it's going 246 00:12:21,930 --> 00:12:25,010 to be down low at the bottom because that's going to be, in 247 00:12:25,010 --> 00:12:27,650 fact, the lowest or most negative energy 248 00:12:27,650 --> 00:12:30,100 when n equals 1. 249 00:12:30,100 --> 00:12:33,240 But we saw from our equation that there's more than just 250 00:12:33,240 --> 00:12:36,530 one possible value for n, so we could, for example, have n 251 00:12:36,530 --> 00:12:42,110 equals 2, n equals 3, all the way up to n equaling infinity. 252 00:12:42,110 --> 00:12:46,160 So what this tells us here is that this is not necessarily 253 00:12:46,160 --> 00:12:49,100 the binding energy of the electron in a hydrogen atom, 254 00:12:49,100 --> 00:12:51,940 it's also possible that it could, for example, have this 255 00:12:51,940 --> 00:12:54,640 energy, it could have this energy up here, it could have 256 00:12:54,640 --> 00:12:56,390 some energy way up here. 257 00:12:56,390 --> 00:12:57,840 So we have this infinite number of 258 00:12:57,840 --> 00:12:59,430 possible binding energies. 259 00:12:59,430 --> 00:13:01,110 But the really important point here is 260 00:13:01,110 --> 00:13:02,550 that they're quantized. 261 00:13:02,550 --> 00:13:05,790 So it's not a continuum of energy that we can have, it's 262 00:13:05,790 --> 00:13:08,850 only these punctuated points of energy that are possible. 263 00:13:08,850 --> 00:13:12,350 So as I tried to say on the board, we can have n equals 1, 264 00:13:12,350 --> 00:13:15,210 but since we can't have n equals 1/2, we actually can't 265 00:13:15,210 --> 00:13:19,140 have a binding energy that's anywhere in between these 266 00:13:19,140 --> 00:13:20,980 levels that are indicated here. 267 00:13:20,980 --> 00:13:23,390 And that's a really important point for something that comes 268 00:13:23,390 --> 00:13:26,750 out of solving the Schrodinger equation is this quantization 269 00:13:26,750 --> 00:13:29,130 of energy levels. 270 00:13:29,130 --> 00:13:32,620 And thanks to our equation simplified here, it's very 271 00:13:32,620 --> 00:13:35,420 easy for us to figure out what actually the allowed energy 272 00:13:35,420 --> 00:13:36,530 levels are. 273 00:13:36,530 --> 00:13:40,850 So for n equals 2, what would the binding energy be? 274 00:13:40,850 --> 00:13:41,910 Someone shout it out. 275 00:13:41,910 --> 00:13:44,590 Yup. 276 00:13:44,590 --> 00:13:48,690 So, I think the compilation of the voices that I heard was 277 00:13:48,690 --> 00:13:51,380 negative r h over 2 squared. 278 00:13:51,380 --> 00:13:54,930 We can do the same thing for 3, negative r h over 3 squared 279 00:13:54,930 --> 00:13:57,170 is going to be our binding energy. 280 00:13:57,170 --> 00:14:01,590 For 4, we can go all the way up to infinity, and actually 281 00:14:01,590 --> 00:14:05,540 when we get to the point where it's infinity, what we find is 282 00:14:05,540 --> 00:14:09,640 the binding energy at that point is going to be zero. 283 00:14:09,640 --> 00:14:13,420 And when we get to infinity, what that means is that we now 284 00:14:13,420 --> 00:14:17,620 have a free electron, so now the electron has totally 285 00:14:17,620 --> 00:14:19,600 separated from the atom. 286 00:14:19,600 --> 00:14:22,580 And that makes sense because we're at the point where 287 00:14:22,580 --> 00:14:25,640 there's no binding energy keeping it stable. 288 00:14:25,640 --> 00:14:28,470 You'll also know that all of these binding energies here 289 00:14:28,470 --> 00:14:32,050 are negative, so the negative sign indicates that it's low. 290 00:14:32,050 --> 00:14:35,430 It's a more negative energy, it's a lower energy state. 291 00:14:35,430 --> 00:14:37,800 So whenever we're thinking about energy states, it's 292 00:14:37,800 --> 00:14:41,920 always more stable to be more low in an energy well, so 293 00:14:41,920 --> 00:14:45,720 that's why it makes sense that it's favorable, in fact, to 294 00:14:45,720 --> 00:14:48,720 have an electron interacting with the nucleus that 295 00:14:48,720 --> 00:14:52,010 stabilizes and lowers the energy of that 296 00:14:52,010 --> 00:14:55,000 electron by doing so. 297 00:14:55,000 --> 00:14:58,870 So, we actually term this n equals 1 state gets a special 298 00:14:58,870 --> 00:15:02,230 name, which we call the ground state, and it's called the 299 00:15:02,230 --> 00:15:05,300 ground state because it is, in fact, the lowest to the ground 300 00:15:05,300 --> 00:15:05,950 that we can get. 301 00:15:05,950 --> 00:15:09,740 It's the most negative and most stable energy level that 302 00:15:09,740 --> 00:15:14,900 we have. And when we think about kind of in a more out 303 00:15:14,900 --> 00:15:17,980 practical sense what we mean by all of these binding 304 00:15:17,980 --> 00:15:21,460 energies, another way that we can put it is to give it some 305 00:15:21,460 --> 00:15:24,650 physical significance, and the physical significance of 306 00:15:24,650 --> 00:15:28,540 binding energies is that they're equal to the negative 307 00:15:28,540 --> 00:15:30,960 of the ionization energies. 308 00:15:30,960 --> 00:15:34,750 So, for example, in a hydrogen atom, if you take the binding 309 00:15:34,750 --> 00:15:38,100 energy, the negative of that is going to be how much energy 310 00:15:38,100 --> 00:15:41,990 you have to put in to ionize the hydrogen atom. 311 00:15:41,990 --> 00:15:45,920 So, if, for example, we were looking at a hydrogen atom in 312 00:15:45,920 --> 00:15:48,730 the case where we have the n equals 1 state, so the 313 00:15:48,730 --> 00:15:52,740 electron is in that ground state, the ionization energy, 314 00:15:52,740 --> 00:15:55,170 it makes sense, is going to be the difference between the 315 00:15:55,170 --> 00:15:58,570 ground state and the energy it takes to be a free electron. 316 00:15:58,570 --> 00:16:01,810 When we graph that on our chart here, it becomes clear 317 00:16:01,810 --> 00:16:04,420 that yes, in fact, the ionization energy is just the 318 00:16:04,420 --> 00:16:07,380 negative of the binding energy, so we can just look 319 00:16:07,380 --> 00:16:11,410 over here and figure out what our ionization energy is. 320 00:16:11,410 --> 00:16:14,160 So when we're talking about the ground state of a hydrogen 321 00:16:14,160 --> 00:16:16,930 atom, our ionization energy is just the negative of the 322 00:16:16,930 --> 00:16:19,430 Rydberg constant, so that easy, it's 2 . 323 00:16:19,430 --> 00:16:23,590 1 8 times 10 to the negative 18 joules. 324 00:16:23,590 --> 00:16:26,420 So, that should make a lot of sense intuitively, because it 325 00:16:26,420 --> 00:16:30,850 makes sense that if we need to ionize an atom, we need to put 326 00:16:30,850 --> 00:16:35,110 energy into the atom in order to eject that electron, and 327 00:16:35,110 --> 00:16:37,480 that energy we need to put in better be the difference 328 00:16:37,480 --> 00:16:40,490 between where we are now and where we have to be to be a 329 00:16:40,490 --> 00:16:44,140 free electron. 330 00:16:44,140 --> 00:16:47,830 So in most cases when we talk about ionization energy, if we 331 00:16:47,830 --> 00:16:51,080 don't say anything specific to the state we're talking about, 332 00:16:51,080 --> 00:16:53,820 you should always assume that we are, in fact, talking about 333 00:16:53,820 --> 00:16:55,330 the ground state. 334 00:16:55,330 --> 00:16:58,220 So, oftentimes you'll just be asked about ionization energy. 335 00:16:58,220 --> 00:17:01,180 If it doesn't say anything else we do mean n equals 1. 336 00:17:01,180 --> 00:17:04,280 But, in fact, we can also talk about the ionization energy of 337 00:17:04,280 --> 00:17:07,870 different states of the hydrogen atom or of any atom. 338 00:17:07,870 --> 00:17:11,560 So, for example, we could talk about the n equals 2 state, so 339 00:17:11,560 --> 00:17:14,400 that's this state here, and it's also what we could call 340 00:17:14,400 --> 00:17:15,810 the first excited state. 341 00:17:15,810 --> 00:17:18,940 So we have the ground state, and if we excite an electron 342 00:17:18,940 --> 00:17:21,380 into the next closest state, we're at the first excited 343 00:17:21,380 --> 00:17:24,620 state, or the n equals 2 state. 344 00:17:24,620 --> 00:17:27,840 So, we can now calculate the ionization energy here. it's 345 00:17:27,840 --> 00:17:30,910 an easy calculation -- we're just taking the negative of 346 00:17:30,910 --> 00:17:33,510 the binding energy, again that makes sense, because it's this 347 00:17:33,510 --> 00:17:35,610 difference in energy here. 348 00:17:35,610 --> 00:17:39,490 So what we get is that the binding energy, when it's 349 00:17:39,490 --> 00:17:42,050 negative, the ionization energy is 5 . 350 00:17:42,050 --> 00:17:46,580 4 5 times 10 to the negative 19 joules. 351 00:17:46,580 --> 00:17:49,050 So we should be able to think about these binding energies 352 00:17:49,050 --> 00:17:51,660 and figure out the ionization energy for any state that were 353 00:17:51,660 --> 00:17:52,320 asked about. 354 00:17:52,320 --> 00:17:55,920 So if we can switch over to a clicker question here and 355 00:17:55,920 --> 00:17:58,720 we'll let you do that. 356 00:17:58,720 --> 00:18:02,690 And what we're asking you to do is now tell us what the 357 00:18:02,690 --> 00:18:05,880 ionization energy is of a hydrogen atom that is in its 358 00:18:05,880 --> 00:18:21,120 third excited state. 359 00:18:21,120 --> 00:18:21,330 All right. 360 00:18:21,330 --> 00:18:36,030 Let's take 10 more seconds on that. 361 00:18:36,030 --> 00:18:36,710 OK. 362 00:18:36,710 --> 00:18:37,590 Interesting. 363 00:18:37,590 --> 00:18:40,280 Usually the majority is correct, but actually what you 364 00:18:40,280 --> 00:18:43,620 did was illustrate a point that I really wanted to stress 365 00:18:43,620 --> 00:18:45,880 and there's no better way to stress it then to get it 366 00:18:45,880 --> 00:18:48,080 incorrect, especially when it doesn't count, it 367 00:18:48,080 --> 00:18:49,860 doesn't hurt so bad. 368 00:18:49,860 --> 00:18:51,630 So, if you want to switch back over to the notes, we'll 369 00:18:51,630 --> 00:18:56,770 explain why, in fact, the correct answer is 4. 370 00:18:56,770 --> 00:19:00,580 So the key word here is that we asked you to identify the 371 00:19:00,580 --> 00:19:02,280 third excited state. 372 00:19:02,280 --> 00:19:06,630 So, what white is n equal to for the third excited state? 373 00:19:06,630 --> 00:19:07,910 4 OK. 374 00:19:07,910 --> 00:19:11,120 So that explains probably most of the confusion here and you 375 00:19:11,120 --> 00:19:13,490 just want to be careful when you're reading the problems 376 00:19:13,490 --> 00:19:15,640 that that's what you read correctly. 377 00:19:15,640 --> 00:19:18,720 I think everyone would now get the clicker question correct. 378 00:19:18,720 --> 00:19:23,160 So, the third excited state, is n equal to 4, because n 379 00:19:23,160 --> 00:19:26,670 equals 2 is first excited, 3 is second excited, 4 is third 380 00:19:26,670 --> 00:19:28,060 excited state. 381 00:19:28,060 --> 00:19:31,020 So now we can just take the negative of that binding 382 00:19:31,020 --> 00:19:34,000 energy here, and I've just rounded up here or 1 . 383 00:19:34,000 --> 00:19:37,690 4 times 10 to the negative 19 joules. 384 00:19:37,690 --> 00:19:41,220 So, I noticed that a few, a very, very small proportion of 385 00:19:41,220 --> 00:19:43,530 you, did type in selections that were 386 00:19:43,530 --> 00:19:45,650 negative ionization energies. 387 00:19:45,650 --> 00:19:48,650 And I'll just say it right now you can absolutely never have 388 00:19:48,650 --> 00:19:50,660 a negative ionization energy, so that's good 389 00:19:50,660 --> 00:19:52,180 to remember as well. 390 00:19:52,180 --> 00:19:54,240 And intuitively, it should make sense, right, because 391 00:19:54,240 --> 00:19:56,690 ionization energy is the amount of energy you need to 392 00:19:56,690 --> 00:20:00,060 put in to eject an electron from an atom. 393 00:20:00,060 --> 00:20:02,290 So you don't want to put in a negative energy, that's not 394 00:20:02,290 --> 00:20:05,010 going to help you out, you need to put in positive energy 395 00:20:05,010 --> 00:20:07,520 to get an electron out of the system. 396 00:20:07,520 --> 00:20:09,740 So that's why you'll find binding energies are always 397 00:20:09,740 --> 00:20:12,300 negative, and ionization energies are always going to 398 00:20:12,300 --> 00:20:15,040 be positive, or you could look at the equation and see it 399 00:20:15,040 --> 00:20:17,810 from there as well. 400 00:20:17,810 --> 00:20:18,240 All right. 401 00:20:18,240 --> 00:20:21,440 So, using the equation we'd initially discussed, the 402 00:20:21,440 --> 00:20:26,010 negative r sub h over n squared, we could figure out 403 00:20:26,010 --> 00:20:28,610 all of the different ionization energies and 404 00:20:28,610 --> 00:20:31,320 binding energies for a hydrogen atom, and it turns 405 00:20:31,320 --> 00:20:35,050 out if we change the equation only slightly to add a 406 00:20:35,050 --> 00:20:38,310 negative z squared in there, so, negative z squared times 407 00:20:38,310 --> 00:20:41,570 the Rydberg constant over n squared, now let's us 408 00:20:41,570 --> 00:20:46,250 calculate energy levels for absolutely any atom as long as 409 00:20:46,250 --> 00:20:48,600 this one important stipulation, it only has 1 410 00:20:48,600 --> 00:20:50,080 electron in it. 411 00:20:50,080 --> 00:20:52,540 So basically we're dealing with hydrogen atoms and then 412 00:20:52,540 --> 00:20:55,240 we're going to be dealing with ions. 413 00:20:55,240 --> 00:20:58,690 So, for example, a helium plus 1 ion has 1 414 00:20:58,690 --> 00:21:01,250 electron at z equal 2. 415 00:21:01,250 --> 00:21:06,160 A lithium 2 plus ion has 1 electron, it has z equals 3, 416 00:21:06,160 --> 00:21:08,790 so if we were to plug in, we would just do z squared up 417 00:21:08,790 --> 00:21:11,020 here, or 3 squared. 418 00:21:11,020 --> 00:21:14,610 Terbium 64 plus, another 1 electron atom. 419 00:21:14,610 --> 00:21:17,070 What is z for that? 420 00:21:17,070 --> 00:21:17,430 Yup. 421 00:21:17,430 --> 00:21:19,260 65. 422 00:21:19,260 --> 00:21:23,490 So again, terbium 64 plus, not an ion we probably will run 423 00:21:23,490 --> 00:21:27,580 into, but if we did, we could, in fact, calculate all of the 424 00:21:27,580 --> 00:21:31,030 energy levels for it using this equation here. 425 00:21:31,030 --> 00:21:33,330 And the difference between the equation, the reason that that 426 00:21:33,330 --> 00:21:37,500 z squared comes in there is because if you go back to your 427 00:21:37,500 --> 00:21:40,650 notes from Wednesday, and you look at the long written out 428 00:21:40,650 --> 00:21:43,600 form of the Schrodinger equation for a hydrogen atom, 429 00:21:43,600 --> 00:21:47,250 or any 1 electron atom, you see the last term there is a 430 00:21:47,250 --> 00:21:50,010 coulomb potential energy between the 431 00:21:50,010 --> 00:21:51,960 electron and the nucleus. 432 00:21:51,960 --> 00:21:55,120 So, of course, when we have a charge on the nucleus equal to 433 00:21:55,120 --> 00:21:58,585 1, as we do in a hydrogen atom, the z is equal to 1, so 434 00:21:58,585 --> 00:22:01,240 it drops out there, but normally we would have to 435 00:22:01,240 --> 00:22:04,390 include the full charge on the nucleus, which is equal to z 436 00:22:04,390 --> 00:22:06,940 or the atomic number times the electron. 437 00:22:06,940 --> 00:22:09,780 So even if we strip an atom of all of its electrons, we still 438 00:22:09,780 --> 00:22:11,660 have that same amount of positive 439 00:22:11,660 --> 00:22:13,680 charge in the nucleus. 440 00:22:13,680 --> 00:22:17,500 So, this allows us to look at a bunch of different atoms, of 441 00:22:17,500 --> 00:22:20,230 course, limited to the fact that it has to be 442 00:22:20,230 --> 00:22:23,790 a 1 electron atom. 443 00:22:23,790 --> 00:22:27,630 So, now that we can calculate the binding energies, we can 444 00:22:27,630 --> 00:22:31,600 think about is this, in fact, what matches up with what's 445 00:22:31,600 --> 00:22:34,280 been observed, or, in fact, could we predict what we will 446 00:22:34,280 --> 00:22:36,800 observe in different kinds of situations now that we know 447 00:22:36,800 --> 00:22:39,820 how to use the binding energy, and hopefully 448 00:22:39,820 --> 00:22:42,100 we can and we will. 449 00:22:42,100 --> 00:22:46,510 So one thing we could do is we could look at the different 450 00:22:46,510 --> 00:22:50,080 wavelengths of light that are emitted by hydrogen atoms that 451 00:22:50,080 --> 00:22:51,820 are excited to a higher state. 452 00:22:51,820 --> 00:22:55,130 So what we'll do in a few minutes here is 453 00:22:55,130 --> 00:22:56,650 try this with hydrogen. 454 00:22:56,650 --> 00:23:02,740 So we'll take h 2 and we'll run -- or actually we'll have 455 00:23:02,740 --> 00:23:05,880 h 2 filled in an evacuated glass tube. 456 00:23:05,880 --> 00:23:09,190 When we increase the potential between the 2 electrodes that 457 00:23:09,190 --> 00:23:12,430 we have in the tube -- we actually split the h 2 into 458 00:23:12,430 --> 00:23:16,200 the individual hydrogen atoms, and not only do that, but also 459 00:23:16,200 --> 00:23:17,600 excite the atoms. 460 00:23:17,600 --> 00:23:20,590 So when you just run across an atom in the street, you can 461 00:23:20,590 --> 00:23:22,910 assume it's going to be in its most stable ground state, 462 00:23:22,910 --> 00:23:25,290 that's where the electron would be, but when we add 463 00:23:25,290 --> 00:23:28,060 energy to the system, we can actually excite it up into all 464 00:23:28,060 --> 00:23:31,110 different sorts of higher states -- n equals 6, n equals 465 00:23:31,110 --> 00:23:33,740 10, any of those higher states. 466 00:23:33,740 --> 00:23:36,210 But that only happens momentarily, because, of 467 00:23:36,210 --> 00:23:39,080 course, if you have an energy in a higher energy level, it's 468 00:23:39,080 --> 00:23:41,890 going to want to drop back down to that lower or more 469 00:23:41,890 --> 00:23:42,890 stable level. 470 00:23:42,890 --> 00:23:46,050 And when it does that it's going to give off some energy 471 00:23:46,050 --> 00:23:48,940 equal to the difference between those two levels. 472 00:23:48,940 --> 00:23:52,000 And that will be associated with a wavelength if it 473 00:23:52,000 --> 00:23:54,210 releases the energy in terms of a photon. 474 00:23:54,210 --> 00:23:56,260 So that's what we'll look at in a few minutes. 475 00:23:56,260 --> 00:23:59,000 There's some important things to point out about what is 476 00:23:59,000 --> 00:24:00,260 happening here. 477 00:24:00,260 --> 00:24:03,000 Just to visualize exactly what we're saying, what we're 478 00:24:03,000 --> 00:24:06,280 saying is when we have an energy in a higher energy 479 00:24:06,280 --> 00:24:10,130 level, so let's say energy level, this initial level high 480 00:24:10,130 --> 00:24:14,500 up here, and it drops down to a lower final level, what we 481 00:24:14,500 --> 00:24:17,840 find is that the photon that is going to be emitted is 482 00:24:17,840 --> 00:24:21,960 going to be emitted with the exact energy, and the 483 00:24:21,960 --> 00:24:24,230 important term here is the exact. 484 00:24:24,230 --> 00:24:29,050 That is the difference between these two energy states. 485 00:24:29,050 --> 00:24:32,120 That makes sense because we're losing energy, we're going to 486 00:24:32,120 --> 00:24:34,940 a level lower level, so we can give off that extra in the 487 00:24:34,940 --> 00:24:36,630 form of light. 488 00:24:36,630 --> 00:24:38,780 And we can actually write the equation for what we would 489 00:24:38,780 --> 00:24:40,980 expect the energy for the light to be. 490 00:24:40,980 --> 00:24:44,660 So this delta energy here is very simply the energy of the 491 00:24:44,660 --> 00:24:49,560 initial state minus the energy of the final state. 492 00:24:49,560 --> 00:24:52,470 This is a little bit generic, we're not actually specifying 493 00:24:52,470 --> 00:24:55,240 the states here, but we could, we know we can calculate the 494 00:24:55,240 --> 00:24:57,020 energy from any of the states. 495 00:24:57,020 --> 00:25:00,740 So, for example, let's say we excited the hydrogen atom such 496 00:25:00,740 --> 00:25:04,790 that the electron was starting in the n equals 6 state, so 497 00:25:04,790 --> 00:25:06,130 that's our n initial. 498 00:25:06,130 --> 00:25:09,760 And we drop down to the n equals 2 state, or the first 499 00:25:09,760 --> 00:25:11,250 excited state. 500 00:25:11,250 --> 00:25:14,080 Then we would be able to change our equation to make it 501 00:25:14,080 --> 00:25:17,810 a little bit more specific and say that delta energy here is 502 00:25:17,810 --> 00:25:22,200 equal to energy of n equals 6, minus the energy of the n 503 00:25:22,200 --> 00:25:24,860 equals 2 state. 504 00:25:24,860 --> 00:25:28,060 When we talk about that frequency of light that's 505 00:25:28,060 --> 00:25:30,590 going to be emitted, it's not too commonly that we'll 506 00:25:30,590 --> 00:25:32,700 actually talk about it in terms of energy. 507 00:25:32,700 --> 00:25:35,450 A lot of times we talk about light in terms of its 508 00:25:35,450 --> 00:25:39,260 frequency or it's wavelength, but that's OK, because we know 509 00:25:39,260 --> 00:25:42,840 how to convert from energy to frequency, so we can do that 510 00:25:42,840 --> 00:25:46,700 here as well, where our frequency is just our energy 511 00:25:46,700 --> 00:25:49,610 divided by Planck's constant, and since here we're talking 512 00:25:49,610 --> 00:25:52,300 about a delta energy, we're going to talk about the 513 00:25:52,300 --> 00:25:56,690 frequency as being equal to delta energy over h. 514 00:25:56,690 --> 00:25:59,760 Or we can say the frequency is going to be equal to the 515 00:25:59,760 --> 00:26:02,350 energy initial minus the energy final all 516 00:26:02,350 --> 00:26:05,090 over Planck's constant. 517 00:26:05,090 --> 00:26:07,660 So this means that we can go directly from the energy 518 00:26:07,660 --> 00:26:10,880 between two levels to the frequency of the photon that's 519 00:26:10,880 --> 00:26:14,230 emitted when you go between those levels. 520 00:26:14,230 --> 00:26:17,590 What we can also do is say something about the wavelength 521 00:26:17,590 --> 00:26:20,150 as well because we know the relationship between energy 522 00:26:20,150 --> 00:26:22,640 and frequency and wavelength. 523 00:26:22,640 --> 00:26:25,300 So, in the first case here, let's say we go from a high 524 00:26:25,300 --> 00:26:29,340 level to a low level, let's say we go from five to one. 525 00:26:29,340 --> 00:26:32,660 If we have a large energy difference here, are we going 526 00:26:32,660 --> 00:26:36,530 to have a high or low frequency? 527 00:26:36,530 --> 00:26:36,920 Good. 528 00:26:36,920 --> 00:26:38,360 A high frequency. 529 00:26:38,360 --> 00:26:40,830 If we have a high frequency, what about the wavelength, 530 00:26:40,830 --> 00:26:43,380 long or short? 531 00:26:43,380 --> 00:26:43,720 All right. 532 00:26:43,720 --> 00:26:44,080 Good. 533 00:26:44,080 --> 00:26:45,780 So we should always be able to keep these 534 00:26:45,780 --> 00:26:47,390 relationships in mind. 535 00:26:47,390 --> 00:26:50,550 So, similarly in a case where instead we have a small energy 536 00:26:50,550 --> 00:26:54,360 difference, we're going to have a low frequency, which 537 00:26:54,360 --> 00:27:01,410 means that we're going to have a long wavelength here. 538 00:27:01,410 --> 00:27:04,600 So now we can go ahead and try observing 539 00:27:04,600 --> 00:27:06,140 some of this ourselves. 540 00:27:06,140 --> 00:27:09,870 So what we're actually going to do is this experiment that 541 00:27:09,870 --> 00:27:13,760 I explained here where we're going to excite hydrogen atoms 542 00:27:13,760 --> 00:27:17,040 such that they're electrons go into these higher energy 543 00:27:17,040 --> 00:27:20,340 levels, and then we're going to see if we can actually see 544 00:27:20,340 --> 00:27:23,610 individual wavelengths that come out of that that 545 00:27:23,610 --> 00:27:25,840 correspond with the energy difference. 546 00:27:25,840 --> 00:27:30,330 So, our detection devices are a little bit limited here 547 00:27:30,330 --> 00:27:33,420 today, we're actually only going to be using our eyes, so 548 00:27:33,420 --> 00:27:36,120 that means that we need to stick with the visible range 549 00:27:36,120 --> 00:27:38,080 of the electromagnetic spectrum. 550 00:27:38,080 --> 00:27:40,200 Actually that simplifies things, because that really 551 00:27:40,200 --> 00:27:42,435 cuts down on the number of wavelengths that we're going 552 00:27:42,435 --> 00:27:44,300 to be trying to observe here. 553 00:27:44,300 --> 00:27:47,770 So it turns out that in the visible range, when you figure 554 00:27:47,770 --> 00:27:50,520 out the differences between energy levels, in hydrogen 555 00:27:50,520 --> 00:27:53,470 atoms, there's only 4 wavelengths that fall in the 556 00:27:53,470 --> 00:27:55,080 visible range of the spectrum. 557 00:27:55,080 --> 00:27:58,120 So hopefully, when we turn out the lights, we're going to 558 00:27:58,120 --> 00:28:03,320 turn on this lamp here, which has hydrogen in it and we're 559 00:28:03,320 --> 00:28:05,140 going to excite that hydrogen. 560 00:28:05,140 --> 00:28:08,280 You'll see light coming out, but it's, of course, going to 561 00:28:08,280 --> 00:28:11,060 be bulk light -- you're not going to be able to tell the 562 00:28:11,060 --> 00:28:12,220 individual wavelengths. 563 00:28:12,220 --> 00:28:15,150 So what our TAs, actually if they can come down now, are 564 00:28:15,150 --> 00:28:19,360 going to pass out to you is these either defraction 565 00:28:19,360 --> 00:28:23,230 goggles, or just a little plate, and you're going to be 566 00:28:23,230 --> 00:28:26,870 splitting that light into its individual wavelengths. 567 00:28:26,870 --> 00:28:30,960 And the glasses, there aren't enough to go around for all of 568 00:28:30,960 --> 00:28:32,460 you, so that's why there's plates. 569 00:28:32,460 --> 00:28:35,070 And though glasses do look way cooler, the plates work a 570 00:28:35,070 --> 00:28:37,470 little better, so either you or your neighbor should try to 571 00:28:37,470 --> 00:28:39,070 have one of the plates in case one of you 572 00:28:39,070 --> 00:28:40,300 can't see all the lines. 573 00:28:40,300 --> 00:28:49,920 So our TAs will pass these around for us. 574 00:28:49,920 --> 00:28:53,390 And I also want to point out, it's guaranteed pretty much 575 00:28:53,390 --> 00:28:56,040 you'll be able to see these three here in the visible 576 00:28:56,040 --> 00:28:58,860 range -- you may or may not be able to see, sometimes it's 577 00:28:58,860 --> 00:29:03,550 hard to see that one that's getting near the UV end of our 578 00:29:03,550 --> 00:29:04,550 visible spectrum. 579 00:29:04,550 --> 00:29:14,490 So we won't worry if we can't see that. 580 00:29:14,490 --> 00:29:24,590 I'll take one actually. 581 00:29:24,590 --> 00:29:53,330 Can you raise your hand if you if you still need one? 582 00:29:53,330 --> 00:29:56,350 All right, so TA's walk carefully now, I'm going to 583 00:29:56,350 --> 00:29:58,210 shut the lights down here. 584 00:29:58,210 --> 00:30:10,140 All right, so we do still have some little bits of ambient 585 00:30:10,140 --> 00:30:12,360 light, so you might see a slight 586 00:30:12,360 --> 00:30:14,290 amount of the full continuum. 587 00:30:14,290 --> 00:30:17,370 But if you look through your plate, and actually especially 588 00:30:17,370 --> 00:30:20,810 if you kind of look off to the side, hopefully you'll be able 589 00:30:20,810 --> 00:30:25,240 to see the individual lines of the spectrum. 590 00:30:25,240 --> 00:30:27,480 Is everyone seeing that? 591 00:30:27,480 --> 00:30:28,390 Yeah, pretty much. 592 00:30:28,390 --> 00:30:29,730 OK. 593 00:30:29,730 --> 00:30:30,880 Can anyone not see it? 594 00:30:30,880 --> 00:30:32,850 Does anyone need -- actually I can't even tell if 595 00:30:32,850 --> 00:30:33,480 you raise your hand. 596 00:30:33,480 --> 00:30:36,380 So ask your neighbor if you can't see it and get one of 597 00:30:36,380 --> 00:30:37,680 the plates if you're having trouble 598 00:30:37,680 --> 00:30:39,470 seeing with the glasses. 599 00:30:39,470 --> 00:30:42,980 So this should match up with the spectrum that we saw. 600 00:30:42,980 --> 00:30:46,380 And actually keep those glasses with you. 601 00:30:46,380 --> 00:30:49,710 We'll turn the light back on for a second here. 602 00:30:49,710 --> 00:30:53,400 And hydrogen atom is what we're learning about, so 603 00:30:53,400 --> 00:30:54,740 that's the most relevant here. 604 00:30:54,740 --> 00:30:58,580 But just to show you that each atom does have its own set of 605 00:30:58,580 --> 00:31:02,990 spectral lines, just for fun we'll look at neon also so you 606 00:31:02,990 --> 00:31:17,280 can have a comparison point. 607 00:31:17,280 --> 00:31:17,690 All right. 608 00:31:17,690 --> 00:31:20,320 So, this is probably a familiar color having seen 609 00:31:20,320 --> 00:31:28,720 many neon lights around everywhere. 610 00:31:28,720 --> 00:31:31,780 So you see with the neon is there's just a lot more lines 611 00:31:31,780 --> 00:31:35,700 in that orange part of the spectrum then compared to the 612 00:31:35,700 --> 00:31:39,980 hydrogen, and that's really what gives you that neon color 613 00:31:39,980 --> 00:31:41,480 in the neon signs. 614 00:31:41,480 --> 00:31:45,160 That's the true color of a neon being excited, sometimes 615 00:31:45,160 --> 00:31:49,060 neon signs are painted with other compounds. 616 00:31:49,060 --> 00:31:50,970 All right, does everyone have their fill of 617 00:31:50,970 --> 00:31:51,890 seeing the neon lines? 618 00:31:51,890 --> 00:31:53,950 STUDENT: No. 619 00:31:53,950 --> 00:31:56,490 PROFESSOR: All right, let's take two more seconds to look 620 00:31:56,490 --> 00:32:01,920 at neon then. 621 00:32:01,920 --> 00:32:02,350 All right. 622 00:32:02,350 --> 00:32:08,350 So our special effects portion of the class is over. 623 00:32:08,350 --> 00:32:10,850 And what you see when we see it with our eye, which is all 624 00:32:10,850 --> 00:32:13,580 the wavelengths, of course, mixed together, is whichever 625 00:32:13,580 --> 00:32:15,900 those wavelengths is most intense. 626 00:32:15,900 --> 00:32:18,290 So, when we looked at the individual neon lines, it was 627 00:32:18,290 --> 00:32:21,560 the orange colors that was most intense, which is why we 628 00:32:21,560 --> 00:32:25,330 were seeing kind of a general orange glow with the neon, 629 00:32:25,330 --> 00:32:29,290 which is different from what we see with the hydrogen. 630 00:32:29,290 --> 00:32:35,400 All right, so we can, in fact, observe individual lines. 631 00:32:35,400 --> 00:32:37,860 There's nothing more exciting to see with your glasses on, 632 00:32:37,860 --> 00:32:38,590 while you look nice. 633 00:32:38,590 --> 00:32:42,690 You can take those off if you wish to, or you can try to 634 00:32:42,690 --> 00:32:46,490 just be splitting the light in the room until the TAs grab 635 00:32:46,490 --> 00:32:48,360 your glasses, either is fine. 636 00:32:48,360 --> 00:32:51,130 It turns out that we are far from the first people, 637 00:32:51,130 --> 00:32:53,950 although it felt exciting, we did not discover this for the 638 00:32:53,950 --> 00:32:56,570 first time here today. 639 00:32:56,570 --> 00:33:01,930 In fact, J.J. Balmer, who was a school teacher in the 1800s, 640 00:33:01,930 --> 00:33:05,810 was the first to describe these lines that could be seen 641 00:33:05,810 --> 00:33:07,130 from hydrogen. 642 00:33:07,130 --> 00:33:11,060 And he saw the same lines that we saw here today, and 643 00:33:11,060 --> 00:33:16,200 although he could not explain, even start to explain why you 644 00:33:16,200 --> 00:33:19,090 saw only these specific lines and not a whole 645 00:33:19,090 --> 00:33:20,310 continuum of the light. 646 00:33:20,310 --> 00:33:22,600 Right, we already have an idea because we just talked about 647 00:33:22,600 --> 00:33:24,860 energy levels, we know there's only certain allowed energy 648 00:33:24,860 --> 00:33:27,540 levels, but at the time there's no reason J.J. Balmer 649 00:33:27,540 --> 00:33:30,410 should have known this, and in fact he didn't, but he still 650 00:33:30,410 --> 00:33:33,750 came up with a quantitative way to describe 651 00:33:33,750 --> 00:33:34,920 what was going on. 652 00:33:34,920 --> 00:33:38,720 He came up with this equation here where what he found was 653 00:33:38,720 --> 00:33:42,180 that he could explain the wavelengths of these different 654 00:33:42,180 --> 00:33:48,040 lines by multiplying 1 over 4 minus 1 over some integer n, 655 00:33:48,040 --> 00:33:51,140 and multiplying it by this number, 3 . 656 00:33:51,140 --> 00:33:55,300 29 times 10 to the 15 Hertz, and he found that this was 657 00:33:55,300 --> 00:33:57,510 true where n was some integer value -- 658 00:33:57,510 --> 00:34:00,900 3, 4, 5, or 6. 659 00:34:00,900 --> 00:34:11,990 So he could explain it quantitatively in terms of 660 00:34:11,990 --> 00:34:14,100 putting an equation with it, but he couldn't explain what 661 00:34:14,100 --> 00:34:15,780 was actually going on. 662 00:34:15,780 --> 00:34:19,310 But we, having learned about energy levels, having had the 663 00:34:19,310 --> 00:34:22,670 Schrodinger equation solved for us to understand what's 664 00:34:22,670 --> 00:34:26,420 going on, can, in fact, explain what happened when we 665 00:34:26,420 --> 00:34:28,420 saw these different colors. 666 00:34:28,420 --> 00:34:30,440 So, what we know is happening is that were having 667 00:34:30,440 --> 00:34:36,590 transitions from some excited states to a more relaxed 668 00:34:36,590 --> 00:34:39,360 lower, more stable state in the hydrogen atom. 669 00:34:39,360 --> 00:34:43,630 And it turns out what we can detect visibly with our eyes 670 00:34:43,630 --> 00:34:46,930 is in the visible range, and that means that the final 671 00:34:46,930 --> 00:34:49,630 state is n equals 2. 672 00:34:49,630 --> 00:34:52,830 Because you see how n equals 1 is so much further away, and 673 00:34:52,830 --> 00:34:55,060 actually that's not to scale, it's actually much, much 674 00:34:55,060 --> 00:34:58,570 further down in the energy well, such that the energy of 675 00:34:58,570 --> 00:35:01,500 the light is so great that it's going to be in 676 00:35:01,500 --> 00:35:04,630 ultraviolet very high energy, high frequency range. 677 00:35:04,630 --> 00:35:07,600 So we can't actually see any of that, it's too high energy 678 00:35:07,600 --> 00:35:08,560 for us to see. 679 00:35:08,560 --> 00:35:11,940 So everything we see is going to be where we have the final 680 00:35:11,940 --> 00:35:15,210 energy state being n equals 2. 681 00:35:15,210 --> 00:35:19,310 So if we think about, for example, this red line here, 682 00:35:19,310 --> 00:35:23,980 which energy state or which principle quantum number do 683 00:35:23,980 --> 00:35:30,450 you think that our electron started in? 684 00:35:30,450 --> 00:35:30,910 STUDENT: Three. 685 00:35:30,910 --> 00:35:31,230 PROFESSOR: Good. 686 00:35:31,230 --> 00:35:33,540 So, it's going to be in 3, because that's the shortest 687 00:35:33,540 --> 00:35:37,960 energy difference we can have, and the red is the longest 688 00:35:37,960 --> 00:35:40,960 wavelength we can see -- those 2 are inversely related, so it 689 00:35:40,960 --> 00:35:42,960 must be n equals 3. 690 00:35:42,960 --> 00:35:47,640 What about the kind of cyan-ish, blue-green one? 691 00:35:47,640 --> 00:35:50,440 Yup. so n equals 4 for that one. 692 00:35:50,440 --> 00:35:53,240 Similarly we can go on, match up the others. 693 00:35:53,240 --> 00:35:56,630 So n equals 5 for the bluish-purple and the violet 694 00:35:56,630 --> 00:35:58,250 is n equals 6. 695 00:35:58,250 --> 00:36:01,230 And again, that matches up, because the violet, or getting 696 00:36:01,230 --> 00:36:05,750 really close to the UV range here has the longest energy, 697 00:36:05,750 --> 00:36:08,510 so the highest frequency, and that's going to be the 698 00:36:08,510 --> 00:36:11,170 shortest wavelength and we can see here it is, in fact, the 699 00:36:11,170 --> 00:36:15,470 shortest wavelength that we can actually see. 700 00:36:15,470 --> 00:36:19,670 So, we can see if we can come up with the same equation that 701 00:36:19,670 --> 00:36:23,700 J.J. Balmer came up with by actually starting with what we 702 00:36:23,700 --> 00:36:26,830 know and working our way that way instead of coming up from 703 00:36:26,830 --> 00:36:29,880 the other direction, which he did, which was just to explain 704 00:36:29,880 --> 00:36:31,070 what he saw. 705 00:36:31,070 --> 00:36:33,830 So, if we start instead with talking about the energy 706 00:36:33,830 --> 00:36:36,850 levels, we can relate these to frequency, because we already 707 00:36:36,850 --> 00:36:40,050 said that frequency is related to, or it's equal to the 708 00:36:40,050 --> 00:36:43,840 initial energy level here minus the final energy level 709 00:36:43,840 --> 00:36:47,540 there over Planck's constant to get us to frequency. 710 00:36:47,540 --> 00:36:51,480 And we also have the equation that comes out of Schrodinger 711 00:36:51,480 --> 00:36:55,420 equation that tell us exactly what that binding energy is, 712 00:36:55,420 --> 00:36:57,260 that binding energy is just equal to the negative of the 713 00:36:57,260 --> 00:37:01,800 Rydberg constant over n squared. 714 00:37:01,800 --> 00:37:05,060 So that means that our frequency is going to equal, 715 00:37:05,060 --> 00:37:10,250 if we plug in e n into the initial and final energy here, 716 00:37:10,250 --> 00:37:14,690 1 over Planck's constant times negative r h over n initial 717 00:37:14,690 --> 00:37:19,890 squared, minus negative r h over n final squared. 718 00:37:19,890 --> 00:37:22,990 So we have an equation that should relate how we can 719 00:37:22,990 --> 00:37:26,630 actually calculate the frequency to 720 00:37:26,630 --> 00:37:29,180 what J.J. Balmer observed. 721 00:37:29,180 --> 00:37:32,055 We can simplify this equation by pulling up the r h and 722 00:37:32,055 --> 00:37:35,450 getting rid of some of these negatives here by saying the 723 00:37:35,450 --> 00:37:38,560 frequency is going to be equal to the Rydberg constant 724 00:37:38,560 --> 00:37:43,120 divided by Planck's constant all times 1 over n final 725 00:37:43,120 --> 00:37:46,120 squared -- this is just to switch the signs around and 726 00:37:46,120 --> 00:37:48,460 get rid of some negatives -- minus 1 727 00:37:48,460 --> 00:37:53,130 over n initial squared. 728 00:37:53,130 --> 00:37:56,760 We can plug this in further when we're talking about the 729 00:37:56,760 --> 00:38:00,170 visible part of the light spectrum, because we know that 730 00:38:00,170 --> 00:38:04,160 for n final equals 2, then that would mean we plug in 2 731 00:38:04,160 --> 00:38:06,940 squared here, so what we get is 1 over 4. 732 00:38:06,940 --> 00:38:10,570 So this is our final equation, and this is actually called 733 00:38:10,570 --> 00:38:13,590 the Balmer series, which was named after Balmer, and this 734 00:38:13,590 --> 00:38:18,010 tells us the frequency of any of the lights where we start 735 00:38:18,010 --> 00:38:20,490 with an electron in some higher energy level and we 736 00:38:20,490 --> 00:38:23,300 drop down to an n final that's equal to 2. 737 00:38:23,300 --> 00:38:25,690 So it's a more specific version of the equation where 738 00:38:25,690 --> 00:38:28,980 we have the n final equal to 2. 739 00:38:28,980 --> 00:38:31,930 And it turns out that actually we find that this matches up 740 00:38:31,930 --> 00:38:36,420 perfectly with Balmer's equation, because the value of 741 00:38:36,420 --> 00:38:39,460 r h, the Rydberg constant divided by the Planck's 742 00:38:39,460 --> 00:38:42,950 constant is actually -- it's also another constant, so we 743 00:38:42,950 --> 00:38:44,370 can write it as this kind of strange 744 00:38:44,370 --> 00:38:46,430 looking cursive r here. 745 00:38:46,430 --> 00:38:49,630 Unfortunately, this is also call the Rydberg constant, so 746 00:38:49,630 --> 00:38:50,800 it's a little bit confusing. 747 00:38:50,800 --> 00:38:55,560 But really it means the Rydberg constant divided by h, 748 00:38:55,560 --> 00:38:57,250 and that's equal to 3 . 749 00:38:57,250 --> 00:38:59,970 29 times 10 to the 15 per second. 750 00:38:59,970 --> 00:39:04,140 So if you remember what the equation Balmer found was this 751 00:39:04,140 --> 00:39:06,470 number multiplied by this here. 752 00:39:06,470 --> 00:39:09,830 So, we found the exact same equation, but just now 753 00:39:09,830 --> 00:39:11,730 starting from understanding the difference 754 00:39:11,730 --> 00:39:14,000 between energy levels. 755 00:39:14,000 --> 00:39:17,740 So, sometimes you'll find the Rydberg constant in different 756 00:39:17,740 --> 00:39:21,010 forms, but just make sure you pay attention to units because 757 00:39:21,010 --> 00:39:23,350 then you won't mess them up, because this is in inverse 758 00:39:23,350 --> 00:39:26,230 seconds here, the other Rydberg constant is in joules, 759 00:39:26,230 --> 00:39:29,470 so you'll be able to use what you need depending on how 760 00:39:29,470 --> 00:39:33,230 you're using that constant. 761 00:39:33,230 --> 00:39:37,570 So in talking about the hydrogen atom, they actually 762 00:39:37,570 --> 00:39:42,440 have different names for different series, which means 763 00:39:42,440 --> 00:39:46,000 in terms of different n values that we end in. 764 00:39:46,000 --> 00:39:48,930 So we talked about what we could see with visible light, 765 00:39:48,930 --> 00:39:51,250 we said that's actually the Balmer series. 766 00:39:51,250 --> 00:39:54,750 So anything that goes from a higher energy level to 2 is 767 00:39:54,750 --> 00:39:57,960 going to be falling within the Balmer series, which is in the 768 00:39:57,960 --> 00:40:00,610 visible range of the spectrum. 769 00:40:00,610 --> 00:40:03,830 We can think about the Lyman series, which is 770 00:40:03,830 --> 00:40:05,280 where n equals 1. 771 00:40:05,280 --> 00:40:08,570 We know that that's going to be a higher energy difference, 772 00:40:08,570 --> 00:40:12,660 so that means that we're going to be in the UV range. 773 00:40:12,660 --> 00:40:15,140 We can also go in the opposite direction. 774 00:40:15,140 --> 00:40:18,690 So, for example, when n equals 3, that's called the Paschen 775 00:40:18,690 --> 00:40:21,430 series, and these are named after basically the people 776 00:40:21,430 --> 00:40:24,650 that first discovered these different lines and 777 00:40:24,650 --> 00:40:27,790 characterized them, and this is in the near IR range. 778 00:40:27,790 --> 00:40:31,680 And again, the n equals 4 is the Brackett series, and 779 00:40:31,680 --> 00:40:33,270 that's an IR range. 780 00:40:33,270 --> 00:40:36,530 I think there's names for even a few more levels up. 781 00:40:36,530 --> 00:40:39,370 You don't need to know those, but just because it's a 782 00:40:39,370 --> 00:40:41,880 special case with the hydrogen atom, they do tend to be named 783 00:40:41,880 --> 00:40:44,970 -- the most important, of course, tends to be the Balmer 784 00:40:44,970 --> 00:40:47,670 series because that's what we can actually see being emitted 785 00:40:47,670 --> 00:40:51,060 from the hydrogen atom. 786 00:40:51,060 --> 00:40:55,900 So, now we should be able to relate what we know about 787 00:40:55,900 --> 00:41:00,220 different frequencies and different wavelengths, so 788 00:41:00,220 --> 00:41:06,190 Darcy can you switch us over to a clicker question here? 789 00:41:06,190 --> 00:41:09,940 And we can also talk about the difference between what's 790 00:41:09,940 --> 00:41:13,110 happening when we have emission, and we're going to 791 00:41:13,110 --> 00:41:14,190 switch over to absorption. 792 00:41:14,190 --> 00:41:17,850 So, we just talked about emission, so before we head 793 00:41:17,850 --> 00:41:20,360 into absorption, if you can answer this clicker question 794 00:41:20,360 --> 00:41:23,580 in terms of what do you think absorption means having just 795 00:41:23,580 --> 00:41:27,610 discussed hydrogen emission here? 796 00:41:27,610 --> 00:41:31,030 So we have four choices in terms of initial and final 797 00:41:31,030 --> 00:41:33,276 energy levels, and also what it means in terms of the 798 00:41:33,276 --> 00:41:36,320 electron -- whether it's gaining energy or whether it's 799 00:41:36,320 --> 00:41:39,940 going to be emitting energy? 800 00:41:39,940 --> 00:41:42,440 So, why do you take 10 seconds on that, we'll 801 00:41:42,440 --> 00:41:54,500 make it a quick one. 802 00:41:54,500 --> 00:41:55,100 All right, great. 803 00:41:55,100 --> 00:41:58,510 So already just from knowing the emission part, we can 804 00:41:58,510 --> 00:42:00,470 figure out what absorption probably means. 805 00:42:00,470 --> 00:42:03,590 Absorption is just the opposite of emission, so 806 00:42:03,590 --> 00:42:10,220 instead of starting at a high energy level and dropping 807 00:42:10,220 --> 00:42:13,800 down, when we absorb light we start low and we absorb energy 808 00:42:13,800 --> 00:42:17,750 to bring ourselves up to an n final that's higher. 809 00:42:17,750 --> 00:42:21,100 And instead of having the electron giving off energy as 810 00:42:21,100 --> 00:42:23,920 a photon, instead now the electron is going to take in 811 00:42:23,920 --> 00:42:29,800 energy from light and move up to that higher level. 812 00:42:29,800 --> 00:42:32,390 So now we're going to be talking briefly about photon 813 00:42:32,390 --> 00:42:33,780 absorption here. 814 00:42:33,780 --> 00:42:37,260 So again, this is just stating the same thing, and it could 815 00:42:37,260 --> 00:42:40,880 take in a long wavelength light, which would give it 816 00:42:40,880 --> 00:42:43,980 just a little bit of energy, maybe just enough to head up 817 00:42:43,980 --> 00:42:48,550 one energy level or two, or we could take in a high energy 818 00:42:48,550 --> 00:42:51,800 photon, and that means that the electron is going to get 819 00:42:51,800 --> 00:42:56,690 to move up to an even higher energy level. 820 00:42:56,690 --> 00:43:00,110 And again, we can talk about the same relationship here, so 821 00:43:00,110 --> 00:43:02,670 it's a very similar equation to the Rydberg equation that 822 00:43:02,670 --> 00:43:06,450 we saw earlier, except now what you see is the n initial 823 00:43:06,450 --> 00:43:08,810 and the n final are swapped places. 824 00:43:08,810 --> 00:43:12,620 So instead now we have r h over Planck's constant times 1 825 00:43:12,620 --> 00:43:17,470 over n initial squared minus n final squared. 826 00:43:17,470 --> 00:43:20,570 And what you want to keep in mind is that whatever you're 827 00:43:20,570 --> 00:43:23,230 dealing with, whether it's absorption or emission, the 828 00:43:23,230 --> 00:43:25,340 frequency of the light is always going to be a positive 829 00:43:25,340 --> 00:43:27,760 number, so you always want to make sure what's inside these 830 00:43:27,760 --> 00:43:29,780 brackets here turns out to be positive. 831 00:43:29,780 --> 00:43:32,540 So that's just a little bit of a check for yourself, and it 832 00:43:32,540 --> 00:43:36,080 should make sense because what you're doing is you're 833 00:43:36,080 --> 00:43:39,160 calculating the difference between energy levels, so you 834 00:43:39,160 --> 00:43:42,620 just need to flip around which you put first to end up with a 835 00:43:42,620 --> 00:43:44,770 positive number here, and that's a little bit of a check 836 00:43:44,770 --> 00:43:48,250 that you can do what yourself. 837 00:43:48,250 --> 00:43:51,300 So let's do a sample calculation now using this 838 00:43:51,300 --> 00:43:55,050 Rydberg formula, and we'll switch back to emission, and 839 00:43:55,050 --> 00:43:57,490 the reason that we'll do that is because it would be nice to 840 00:43:57,490 --> 00:44:01,450 actually approve what we just saw here and calculate the 841 00:44:01,450 --> 00:44:04,140 frequency of one of our lines in the wavelength of one of 842 00:44:04,140 --> 00:44:05,850 the lines we saw. 843 00:44:05,850 --> 00:44:09,340 So what we'll do is this problem here, which is let's 844 00:44:09,340 --> 00:44:11,870 calculate out what the wavelength of radiation would 845 00:44:11,870 --> 00:44:16,520 be emitted from a hydrogen atom if we start at the n 846 00:44:16,520 --> 00:44:22,750 equals 3 level and we go down to the n equals 2 level. 847 00:44:22,750 --> 00:44:29,990 So what we need to do here is use the Rydberg formula, and 848 00:44:29,990 --> 00:44:32,670 actually you'll be given the Rydberg formulas in both 849 00:44:32,670 --> 00:44:37,530 forms, both or absorption and emission on the exams. if you 850 00:44:37,530 --> 00:44:41,020 don't want to use that, you can also derive it as we did 851 00:44:41,020 --> 00:44:42,950 every time, it should intuitively make 852 00:44:42,950 --> 00:44:44,360 sense how we got there. 853 00:44:44,360 --> 00:44:47,010 But the exams are pretty short, so we don't want you 854 00:44:47,010 --> 00:44:49,420 doing that every time, so we'll save the 2 minutes and 855 00:44:49,420 --> 00:44:51,230 give you the equations directly, but it's still 856 00:44:51,230 --> 00:44:53,980 important to know how to use them. 857 00:44:53,980 --> 00:44:56,980 So, we can get from these energy differences to 858 00:44:56,980 --> 00:45:02,730 frequency by frequency is equal to r sub h over Planck's 859 00:45:02,730 --> 00:45:07,960 constant times 1 over n final squared minus 1 860 00:45:07,960 --> 00:45:12,710 over n initial squared. 861 00:45:12,710 --> 00:45:16,090 So let's actually just simplify this to the other 862 00:45:16,090 --> 00:45:17,970 version of the Rydberg constant, since we 863 00:45:17,970 --> 00:45:19,300 can use that here. 864 00:45:19,300 --> 00:45:23,500 So kind of that strange cursive r, and our n final is 865 00:45:23,500 --> 00:45:30,830 2, so 1 over 2 squared minus n initial, so 1 over 3 squared. 866 00:45:30,830 --> 00:45:35,660 So, our frequency of light is going to be equal to r 867 00:45:35,660 --> 00:45:40,980 times 5 over 36. 868 00:45:40,980 --> 00:45:43,790 But when we were actually looking at our different 869 00:45:43,790 --> 00:45:46,630 wavelengths, what we associate mostly with color is the wave 870 00:45:46,630 --> 00:45:49,770 length of the light and not the frequency of the light, so 871 00:45:49,770 --> 00:45:52,110 let's look at wavelength instead. 872 00:45:52,110 --> 00:45:57,100 We know that wavelength is equal to c over nu. 873 00:45:57,100 --> 00:46:02,140 We can plug in what we have for nu, so we have 36 c 874 00:46:02,140 --> 00:46:08,360 divided by 5, and that cursivey Rydberg constant, and 875 00:46:08,360 --> 00:46:12,540 that gives us 36 times the speed of light, 2 . 876 00:46:12,540 --> 00:46:23,500 998 times 10 the 8 meters per second, all over 5 times 3 . 877 00:46:23,500 --> 00:46:31,400 29 times 10 to the 15 per second. 878 00:46:31,400 --> 00:46:34,570 So, what we end up getting when we do this calculation is 879 00:46:34,570 --> 00:46:39,070 the wavelength of light, which is equal to 6 . 880 00:46:39,070 --> 00:46:45,130 57 times 10 to the negative 7 meters, or if we convert that 881 00:46:45,130 --> 00:46:49,580 to nanometers, we have 657 nanometers. 882 00:46:49,580 --> 00:46:52,560 So does anyone remember what range of light 657 883 00:46:52,560 --> 00:46:55,390 nanometers falls in? 884 00:46:55,390 --> 00:46:56,080 What color? 885 00:46:56,080 --> 00:46:57,370 STUDENT: Red. 886 00:46:57,370 --> 00:46:59,240 PROFESSOR: Yeah, it's in the red range. 887 00:46:59,240 --> 00:47:00,430 So that's promising. 888 00:47:00,430 --> 00:47:05,050 We did, in fact, see red in our spectrum, and it turns out 889 00:47:05,050 --> 00:47:07,970 that that's exactly the wavelength that we see is that 890 00:47:07,970 --> 00:47:10,790 we're at 657 nanometers. 891 00:47:10,790 --> 00:47:15,330 So it turns out that we can, in fact, use the energy levels 892 00:47:15,330 --> 00:47:18,290 to predict, and we could if we wanted to do them for all of 893 00:47:18,290 --> 00:47:20,650 the different wavelengths of light that we observed, and 894 00:47:20,650 --> 00:47:22,390 also all the different wavelengths of light that can 895 00:47:22,390 --> 00:47:26,810 be detected, even if we can't observe them. 896 00:47:26,810 --> 00:47:29,490 All right, so that's what we're going to cover in terms 897 00:47:29,490 --> 00:47:32,290 of the energy portion of the Schrodinger equation. 898 00:47:32,290 --> 00:47:36,400 I mentioned that we can also solve for psi here, which is 899 00:47:36,400 --> 00:47:39,700 the wave function, and we're running a little short on 900 00:47:39,700 --> 00:47:42,880 time, so we'll start on Monday with solving 901 00:47:42,880 --> 00:47:44,670 for the wave function.