1 00:00:16,933 --> 00:00:18,335 Last week we talked about-- 2 00:00:18,335 --> 00:00:19,035 we went quantum. 3 00:00:19,035 --> 00:00:22,238 We had Dr. Quantum show us the way. 4 00:00:22,238 --> 00:00:26,943 And this week, we're going to go quantum for electrons, right? 5 00:00:26,943 --> 00:00:29,746 That's what we're going to do this week. 6 00:00:29,746 --> 00:00:32,649 These are my two favorite quantum mechanicists 7 00:00:32,649 --> 00:00:34,250 of all time. 8 00:00:34,250 --> 00:00:35,986 I believe that this sign is meant 9 00:00:35,986 --> 00:00:40,056 to teach us something about the double slit experiment. 10 00:00:40,056 --> 00:00:42,459 And just as you're leaving the lot, 11 00:00:42,459 --> 00:00:45,161 knowing that there is some chance 12 00:00:45,161 --> 00:00:48,665 that your one car could actually split into two, 13 00:00:48,665 --> 00:00:50,967 go through both exits, and recombine. 14 00:00:50,967 --> 00:00:53,336 Just like an electron does through two slits. 15 00:00:53,336 --> 00:00:55,538 And in fact, we know that that's possible now. 16 00:00:58,108 --> 00:01:02,512 And if we wanted to, you could write down-- from de Broglie-- 17 00:01:02,512 --> 00:01:06,016 you could write down like the wavelength of a car, right? 18 00:01:06,016 --> 00:01:07,984 So like in a car-- 19 00:01:07,984 --> 00:01:10,553 I don't know, your lambda of the car 20 00:01:10,553 --> 00:01:15,091 would be equal to h over mv. 21 00:01:15,091 --> 00:01:16,860 And if you plus some numbers in, this 22 00:01:16,860 --> 00:01:18,795 is going to be something like oh, you know, 23 00:01:18,795 --> 00:01:22,032 maybe 10 to the minus 37th meters. 24 00:01:22,032 --> 00:01:25,368 It's small, but it's a wave. 25 00:01:25,368 --> 00:01:28,170 Your car is a wave, you know? 26 00:01:28,170 --> 00:01:31,374 The baseball is a wave. 27 00:01:31,374 --> 00:01:34,377 The electron-- we are all waves. 28 00:01:34,377 --> 00:01:37,881 And I know, and that's what-- so the electron is a wave. 29 00:01:37,881 --> 00:01:41,116 And I know-- hashtag, we are all waves. 30 00:01:41,116 --> 00:01:43,019 Because it's a thing. 31 00:01:43,019 --> 00:01:44,253 It's really a thing. 32 00:01:44,253 --> 00:01:46,622 Because it's true. 33 00:01:46,622 --> 00:01:48,491 I am a wave. 34 00:01:48,491 --> 00:01:49,526 You are a wave. 35 00:01:49,526 --> 00:01:50,894 We are all waves. 36 00:01:50,894 --> 00:01:52,762 It's just-- our wavelengths are pretty small, 37 00:01:52,762 --> 00:01:54,330 but they're not zero. 38 00:01:54,330 --> 00:01:56,433 And so the next time you get-- oh, we're 39 00:01:56,433 --> 00:01:57,600 on the same wavelength. 40 00:01:57,600 --> 00:01:59,836 You really are. 41 00:01:59,836 --> 00:02:01,037 It's true. 42 00:02:01,037 --> 00:02:02,172 We are-- right? 43 00:02:02,172 --> 00:02:03,640 That's deep. 44 00:02:03,640 --> 00:02:05,608 We are waves. 45 00:02:05,608 --> 00:02:06,543 All of us. 46 00:02:06,543 --> 00:02:09,112 And so, the wavelength-- 47 00:02:09,112 --> 00:02:11,448 OK, the wavelength for an electron was something like 10 48 00:02:11,448 --> 00:02:13,917 to the minus 10th meters. 49 00:02:13,917 --> 00:02:18,621 Which made it a really nice way to interrogate images. 50 00:02:18,621 --> 00:02:21,057 And that was my "why this matters" last week, right? 51 00:02:21,057 --> 00:02:21,858 On Friday. 52 00:02:21,858 --> 00:02:26,863 So you can take advantage of that wavelength to do things. 53 00:02:26,863 --> 00:02:31,034 Like see electron microscopy, right? 54 00:02:31,034 --> 00:02:32,535 But everyone's awake. 55 00:02:32,535 --> 00:02:36,239 That's what quantum mechanics told us. 56 00:02:36,239 --> 00:02:37,941 But what we want to do now is know 57 00:02:37,941 --> 00:02:41,845 how to represent this wave. 58 00:02:41,845 --> 00:02:43,446 So everything's waving. 59 00:02:43,446 --> 00:02:44,447 We've got that. 60 00:02:44,447 --> 00:02:46,683 But how do I describe it? 61 00:02:46,683 --> 00:02:47,216 Right? 62 00:02:47,216 --> 00:02:49,586 And that's where we left off. 63 00:02:49,586 --> 00:02:51,353 And we left off by me telling you 64 00:02:51,353 --> 00:02:55,658 that it all led to Schrodinger, who came up with the wave 65 00:02:55,658 --> 00:02:57,460 equation for quantum mechanics. 66 00:02:57,527 --> 00:03:00,630 And the wave equation of Schrodinger 67 00:03:00,630 --> 00:03:04,767 is really pretty incredible, because-- 68 00:03:04,767 --> 00:03:07,103 so I'm not going to write out Schrodinger. 69 00:03:07,103 --> 00:03:08,605 That would take me forever. 70 00:03:08,605 --> 00:03:13,076 So I'm going to write S. Eq., right? 71 00:03:13,076 --> 00:03:16,012 The Schrodinger equation, right? 72 00:03:16,012 --> 00:03:23,887 And here-- so what he had is he had the sort of wave behavior 73 00:03:23,887 --> 00:03:25,788 that was captured. 74 00:03:25,788 --> 00:03:27,690 And it was captured automatically. 75 00:03:27,690 --> 00:03:31,694 And it gave us also allowed energies, you see? 76 00:03:31,694 --> 00:03:34,664 So, allowed energies. 77 00:03:34,664 --> 00:03:40,203 And this is also the quantization. 78 00:03:40,203 --> 00:03:41,938 Ah-- I ran out of room. 79 00:03:41,938 --> 00:03:42,438 Right. 80 00:03:42,438 --> 00:03:44,941 But now, If you go back to classical-- 81 00:03:44,941 --> 00:03:49,045 so if you think about classical physics, what 82 00:03:49,045 --> 00:03:51,614 you would have is something like maybe F equals ma. 83 00:03:51,614 --> 00:03:54,517 But what that gives you-- 84 00:03:54,517 --> 00:03:56,853 well, it doesn't give you wave behavior, 85 00:03:56,853 --> 00:04:01,157 but it gives you continuous energies. 86 00:04:01,157 --> 00:04:05,361 Continuous energies. 87 00:04:05,361 --> 00:04:10,466 So the powerful point here is that from that equation-- 88 00:04:10,466 --> 00:04:13,236 and we don't need to know this equation. 89 00:04:13,236 --> 00:04:14,637 We're not going to derive it. 90 00:04:14,637 --> 00:04:15,138 Right? 91 00:04:15,138 --> 00:04:16,973 Today I'm going to tell you how it's solved, 92 00:04:16,973 --> 00:04:18,241 but you don't need to know how to solve it. 93 00:04:18,241 --> 00:04:20,543 But you need to know what the solutions mean. 94 00:04:20,543 --> 00:04:22,512 That's what we're talking about today. 95 00:04:22,512 --> 00:04:29,052 But that equation-- what it does is it sets up the energies 96 00:04:29,052 --> 00:04:30,987 as a function of the wave. 97 00:04:30,987 --> 00:04:36,192 Psi-- that function, psi-- is the wave function, OK? 98 00:04:36,192 --> 00:04:39,128 And so you get waves by default, because that's what you're 99 00:04:39,128 --> 00:04:40,897 solving for-- these waves. 100 00:04:40,897 --> 00:04:42,665 And then you have a minus second-- 101 00:04:42,665 --> 00:04:44,701 oh, there's an h bar. 102 00:04:44,701 --> 00:04:46,803 That's an h over 2 pi. 103 00:04:49,239 --> 00:04:49,739 Right? 104 00:04:49,739 --> 00:04:52,642 But it's like the same Planck's constant. 105 00:04:52,642 --> 00:04:53,142 OK. 106 00:04:53,142 --> 00:04:56,179 But the wave behavior gives you-- 107 00:04:56,179 --> 00:04:58,748 because there's only certain energies that 108 00:04:58,748 --> 00:04:59,782 solve that equation. 109 00:04:59,782 --> 00:05:03,720 So quantization falls out naturally. 110 00:05:03,720 --> 00:05:05,655 You don't have to put it in anymore. 111 00:05:05,655 --> 00:05:09,659 It is a direct result of solving this equation. 112 00:05:09,659 --> 00:05:11,828 If I take a wave-- 113 00:05:11,828 --> 00:05:12,862 think about this, right. 114 00:05:12,862 --> 00:05:16,266 If you take a wave and you put it in a box, 115 00:05:16,266 --> 00:05:19,569 then it can only have certain solutions. 116 00:05:19,569 --> 00:05:23,506 Once you define the box, if you throw a wave in it, 117 00:05:23,506 --> 00:05:27,043 well, that's where those things are on the right are. 118 00:05:27,043 --> 00:05:28,511 Maybe it's a standing wave. 119 00:05:28,511 --> 00:05:30,913 And so it's going to look-- 120 00:05:30,913 --> 00:05:35,752 no-- it's going to be like this. 121 00:05:35,752 --> 00:05:37,754 One solution. 122 00:05:37,754 --> 00:05:41,624 And some energy. 123 00:05:41,624 --> 00:05:44,193 Or maybe it's going to look-- 124 00:05:44,193 --> 00:05:46,162 I didn't leave myself any room-- 125 00:05:46,162 --> 00:05:48,464 like this. 126 00:05:48,464 --> 00:05:51,501 And it's going to have some other energy, right? 127 00:05:51,501 --> 00:05:52,902 1, 2. 128 00:05:52,902 --> 00:05:53,403 That's it. 129 00:05:53,403 --> 00:05:54,937 If you throw a wave in a box-- like, 130 00:05:54,937 --> 00:05:56,539 here's the first one, second one. 131 00:05:56,539 --> 00:05:59,642 But there are only certain ones that are going to work. 132 00:05:59,642 --> 00:06:01,844 All right, and you can get that sense. 133 00:06:01,844 --> 00:06:04,013 Because otherwise it's not going to line up and then 134 00:06:04,013 --> 00:06:06,616 be able to wave and keep going. 135 00:06:06,616 --> 00:06:08,651 It's not going to be a standing wave. 136 00:06:08,651 --> 00:06:09,552 Right? 137 00:06:09,552 --> 00:06:12,422 So you get this sense right away of quantization. 138 00:06:12,422 --> 00:06:15,358 Only certain waves, and only certain energies, 139 00:06:15,358 --> 00:06:16,559 will solve this equation. 140 00:06:16,559 --> 00:06:20,830 Now, here's the key, is this-- 141 00:06:20,830 --> 00:06:24,400 we're going to throw an electron into this equation, right? 142 00:06:24,400 --> 00:06:27,637 But we're going to throw it into the right potential. 143 00:06:27,637 --> 00:06:31,207 And that is the potential that we know it sits in, in an atom. 144 00:06:31,207 --> 00:06:34,377 Which is simply a Coulomb potential. 145 00:06:34,377 --> 00:06:36,245 So this is how we get there, right? 146 00:06:36,245 --> 00:06:39,549 We take Schrodinger's equation of quantum mechanics. 147 00:06:39,549 --> 00:06:45,855 And we solve it for an electron waving in the presence 148 00:06:45,855 --> 00:06:49,225 of the potential of the atom. 149 00:06:49,225 --> 00:06:51,527 Which is a positive potential. 150 00:06:51,527 --> 00:06:52,695 And you can see, this is a-- 151 00:06:52,695 --> 00:06:54,497 OK, V is a potential. 152 00:06:54,497 --> 00:06:56,999 And that's an attractive potential, right? 153 00:06:56,999 --> 00:06:58,735 That's an attractive potential. 154 00:06:58,735 --> 00:07:00,069 So what happens when we do that? 155 00:07:00,069 --> 00:07:01,437 So that's what we're going to do. 156 00:07:01,437 --> 00:07:03,072 I'm going to leave this for-- 157 00:07:03,072 --> 00:07:03,906 so. 158 00:07:03,906 --> 00:07:04,440 What happens? 159 00:07:04,440 --> 00:07:07,810 So if we take a hydrogen atom-- 160 00:07:07,810 --> 00:07:14,517 or as I've written it here, a "Hatom," then you would have-- 161 00:07:14,517 --> 00:07:15,017 Let's see. 162 00:07:15,017 --> 00:07:16,085 What do you get from this? 163 00:07:16,085 --> 00:07:20,757 Well, you get that the potential is going to be minus 1 over r. 164 00:07:20,757 --> 00:07:21,257 Yeah. 165 00:07:21,257 --> 00:07:22,625 It goes as minus 1-- 166 00:07:22,625 --> 00:07:26,095 an e and an over-permittivity of space and stuff like that. 167 00:07:26,095 --> 00:07:28,898 But it goes as minus 1 over r. 168 00:07:28,898 --> 00:07:31,134 That's the Coulomb potential. 169 00:07:31,134 --> 00:07:32,168 Right? 170 00:07:32,168 --> 00:07:39,242 A plus charge is sitting outside of a minus charge. 171 00:07:39,242 --> 00:07:41,344 Ah! 172 00:07:41,344 --> 00:07:42,779 That was a close call. 173 00:07:42,779 --> 00:07:47,016 The electron is sitting out here, and there's the nucleus. 174 00:07:47,016 --> 00:07:49,152 And the potential feels is a Coulomb potential. 175 00:07:49,152 --> 00:07:50,486 OK, so that's point 1. 176 00:07:50,486 --> 00:07:56,558 Point 2 is that we're going to apply the-- 177 00:07:56,558 --> 00:07:59,662 oh, I'm saving myself so much time. 178 00:07:59,662 --> 00:08:02,064 I love it, when you're efficient like that-- 179 00:08:02,064 --> 00:08:02,832 S. Eq. 180 00:08:02,832 --> 00:08:04,801 Schrodinger equation. 181 00:08:04,801 --> 00:08:06,569 The Schrodinger equation. 182 00:08:06,569 --> 00:08:09,972 But the way that we're going to do this is in spherical 183 00:08:09,972 --> 00:08:13,109 coordinates. 184 00:08:13,109 --> 00:08:17,680 Spherical coords. 185 00:08:17,680 --> 00:08:20,283 And all that means is that I'm going 186 00:08:20,283 --> 00:08:29,091 to write psi as a function of r, theta, and phi. 187 00:08:32,462 --> 00:08:35,264 And the last thing that I'm going to do 188 00:08:35,264 --> 00:08:39,635 is I'm going to separate the variables. 189 00:08:39,635 --> 00:08:42,772 And that's just a standard way to solve 190 00:08:42,772 --> 00:08:43,940 mathematical equations. 191 00:08:43,940 --> 00:08:45,575 So I'm going to separate the variables. 192 00:08:45,575 --> 00:08:47,076 So separate. 193 00:08:47,076 --> 00:08:54,317 And so what that means is that psi can be written as one 194 00:08:54,317 --> 00:08:56,919 function-- let's call it r-- 195 00:08:56,919 --> 00:09:03,726 of the radius, times another function, p, of the theta, 196 00:09:03,726 --> 00:09:06,262 times another function f of phi. 197 00:09:06,262 --> 00:09:09,932 So that's my separation of variables, OK? 198 00:09:09,932 --> 00:09:13,703 Again, I'm not all about having you know 199 00:09:13,703 --> 00:09:16,706 how to solve this equation. 200 00:09:16,706 --> 00:09:17,540 OK? 201 00:09:17,540 --> 00:09:19,942 That you can learn in quantum mechanics. 202 00:09:19,942 --> 00:09:23,779 But what I'm all about is what that quantum mechanics solution 203 00:09:23,779 --> 00:09:26,415 means for us here in chemistry. 204 00:09:26,415 --> 00:09:28,351 And this is deep. 205 00:09:28,351 --> 00:09:29,585 This is deep, because-- 206 00:09:29,585 --> 00:09:30,319 why? 207 00:09:30,319 --> 00:09:35,057 Because this whole thing is quantized, right? 208 00:09:35,057 --> 00:09:43,199 So just like before, there's only certain allowed values 209 00:09:43,199 --> 00:09:44,500 for the wave function. 210 00:09:44,500 --> 00:09:50,473 There's only certain allowed values for these variables. 211 00:09:50,473 --> 00:09:53,242 Each one of them is quantized. 212 00:09:53,242 --> 00:09:55,144 Each one of them. 213 00:09:55,144 --> 00:09:56,078 OK? 214 00:09:56,078 --> 00:09:58,347 And that's what we need to learn about today, 215 00:09:58,347 --> 00:10:00,716 is what that means for chemistry. 216 00:10:00,716 --> 00:10:01,951 All right. 217 00:10:01,951 --> 00:10:08,357 So now we're going to go through the quantum numbers 218 00:10:08,357 --> 00:10:09,325 and see what they mean. 219 00:10:09,325 --> 00:10:12,295 And we're going to start with this first one, 220 00:10:12,295 --> 00:10:14,997 the radial function. 221 00:10:14,997 --> 00:10:19,402 So radial, and then two angular functions. 222 00:10:19,402 --> 00:10:20,069 OK. 223 00:10:20,069 --> 00:10:22,438 Now the radial-- so what do we get? 224 00:10:22,438 --> 00:10:26,075 Well, the radial function-- 225 00:10:26,075 --> 00:10:28,544 I'm using a word here, I got to tell you why. 226 00:10:28,544 --> 00:10:31,547 Orbital of hydrogen, right? 227 00:10:31,547 --> 00:10:32,682 So I've solved this now. 228 00:10:32,682 --> 00:10:38,688 I've solved this equation, and I'm plotting this orbital 229 00:10:38,688 --> 00:10:42,825 for first quantization-- n equals 1, n equals 2, 230 00:10:42,825 --> 00:10:43,759 n equals 3. 231 00:10:43,759 --> 00:10:45,728 We've got to talk about this, right? 232 00:10:45,728 --> 00:10:49,832 But I'm just plotting what that function looks like. 233 00:10:49,832 --> 00:10:51,233 Well, let's compare. 234 00:10:51,233 --> 00:10:56,339 Because if I'm Bohr, then what I have is this. 235 00:10:56,339 --> 00:10:56,906 Remember this? 236 00:10:56,906 --> 00:10:58,407 I've got like this-- 237 00:10:58,407 --> 00:11:01,744 OK, there's 1, and it's going around, 238 00:11:01,744 --> 00:11:04,347 and it's very happy in an orbit. 239 00:11:08,784 --> 00:11:12,355 But see, we don't call these orbits anymore. 240 00:11:12,355 --> 00:11:14,724 And it's going to be clear as we talk about this picture, 241 00:11:14,724 --> 00:11:18,728 because these aren't distinct orbits, right? 242 00:11:18,728 --> 00:11:26,068 So now in quantum what you have-- 243 00:11:26,068 --> 00:11:29,238 I'm just going to take that n equals 1 solution. 244 00:11:29,238 --> 00:11:34,443 That's the first solution to the radial part, right? 245 00:11:34,443 --> 00:11:36,879 That's not a fixed distance. 246 00:11:36,879 --> 00:11:38,914 That's not a fixed distance, right? 247 00:11:38,914 --> 00:11:44,153 So now I'm just looking at the radial distribution 248 00:11:44,153 --> 00:11:46,455 of the probability. 249 00:11:46,455 --> 00:11:49,759 The probability of finding the electron. 250 00:11:49,759 --> 00:11:53,129 That's how we speak when we speak quantum. 251 00:11:53,129 --> 00:11:55,998 We don't say it's here, right? 252 00:11:55,998 --> 00:11:58,034 We say it could be here. 253 00:11:58,034 --> 00:11:58,567 I don't know. 254 00:11:58,567 --> 00:12:00,336 But there's a probability that it's there. 255 00:12:00,336 --> 00:12:05,975 So now it sort of has a probability cloud. 256 00:12:05,975 --> 00:12:09,245 Now it looks like it gets a little less-- 257 00:12:09,245 --> 00:12:11,213 why am I drawing spirals? 258 00:12:11,213 --> 00:12:13,549 It looks like it gets a little less probable 259 00:12:13,549 --> 00:12:15,551 as you go further out, right? 260 00:12:15,551 --> 00:12:17,753 So maybe the density of probability-- because look, 261 00:12:17,753 --> 00:12:18,254 right? 262 00:12:18,254 --> 00:12:19,889 It's got a peak there. 263 00:12:19,889 --> 00:12:25,261 But even if I just plot that first orbital, 264 00:12:25,261 --> 00:12:30,232 even as I go all the way out to here, it is non-0, right? 265 00:12:30,232 --> 00:12:32,468 So this is probability. 266 00:12:37,139 --> 00:12:39,241 And this would be n equals 1. 267 00:12:39,241 --> 00:12:41,977 So it's a totally different story. 268 00:12:41,977 --> 00:12:46,949 That electron isn't in one place, but it is. 269 00:12:46,949 --> 00:12:48,451 But it's not. 270 00:12:48,451 --> 00:12:49,585 It could be anywhere. 271 00:12:49,585 --> 00:12:51,854 It could be-- if I'm a hydrogen atom, 272 00:12:51,854 --> 00:12:54,457 my electron could literally be across the room. 273 00:12:54,457 --> 00:12:57,693 There is a finite probability that that's true. 274 00:12:57,693 --> 00:13:01,430 And we know that since we are all waves, 275 00:13:01,430 --> 00:13:04,567 and we can all be defined by the equations of quantum 276 00:13:04,567 --> 00:13:08,137 mechanics-- and in fact, that is the way to define the world-- 277 00:13:08,137 --> 00:13:11,040 that we also have probabilities. 278 00:13:11,040 --> 00:13:13,375 They're small, you know. 279 00:13:13,375 --> 00:13:16,178 But I could be over there right now. 280 00:13:16,178 --> 00:13:17,346 There's a chance. 281 00:13:17,346 --> 00:13:20,216 My weight function is not exactly 0 282 00:13:20,216 --> 00:13:21,317 all the way over there. 283 00:13:21,317 --> 00:13:22,451 It's close. 284 00:13:22,451 --> 00:13:26,155 But it's not exact, right? 285 00:13:26,155 --> 00:13:30,793 That is a very different picture of an electron in an orbit-- 286 00:13:30,793 --> 00:13:32,261 in fact, it's not an orbit. 287 00:13:32,261 --> 00:13:34,163 It's an orbital. 288 00:13:34,163 --> 00:13:39,034 And that's where we say orbital. 289 00:13:39,034 --> 00:13:39,935 That's why we stay it. 290 00:13:39,935 --> 00:13:42,438 OK, but-- we're listing quantum numbers. 291 00:13:42,438 --> 00:13:44,707 These are the quantum numbers. 292 00:13:44,707 --> 00:13:49,445 Oh, oh- I'm going all caps. 293 00:13:49,445 --> 00:13:52,581 Didn't even know I was going to do that. 294 00:13:52,581 --> 00:13:55,618 So we have n, which is called the principle-- 295 00:13:58,754 --> 00:14:04,660 principle quantum number. 296 00:14:04,660 --> 00:14:10,132 And this is going to be related to the main energy, kind 297 00:14:10,132 --> 00:14:12,301 of e, 1, 1, right? 298 00:14:12,301 --> 00:14:13,135 E, 2, 2. 299 00:14:13,135 --> 00:14:16,839 So this is going to be related to the main energy level. 300 00:14:16,839 --> 00:14:22,611 Main energy level, right? 301 00:14:22,611 --> 00:14:26,715 And it's also related to the radial distance. 302 00:14:26,715 --> 00:14:28,317 Radial distance. 303 00:14:31,620 --> 00:14:34,857 And sometimes we call this the shell. 304 00:14:34,857 --> 00:14:36,826 So sometimes the principal quantum number, 305 00:14:36,826 --> 00:14:38,794 this is the shell, right? 306 00:14:38,794 --> 00:14:42,031 It's the first shell, or the second shell. 307 00:14:42,031 --> 00:14:45,201 So we can call this the shell. 308 00:14:45,201 --> 00:14:47,536 Come back to that later. 309 00:14:47,536 --> 00:14:49,305 And you can see right there. 310 00:14:49,305 --> 00:14:51,907 OK, we'll talk about n equals 2 and 3 in a second. 311 00:14:51,907 --> 00:14:55,344 But you know-- oh, let's talk about it now. 312 00:14:55,344 --> 00:14:56,779 You can see right there-- 313 00:14:56,779 --> 00:15:03,352 it I go from n equals 1 to n equals 2, then I'm further out. 314 00:15:03,352 --> 00:15:05,020 Yeah, I still got non-0. 315 00:15:05,020 --> 00:15:07,923 Doesn't quite go to 0 like I just said there. 316 00:15:07,923 --> 00:15:10,593 But it's further out, it's shifted out, right? 317 00:15:10,593 --> 00:15:13,796 So with increasing n-- 318 00:15:13,796 --> 00:15:15,764 so another thing we can say about n 319 00:15:15,764 --> 00:15:34,750 is that with increasing n, you get higher energies and larger 320 00:15:34,750 --> 00:15:35,651 distances. 321 00:15:35,651 --> 00:15:38,520 larger r, a [? hole. ?] 322 00:15:38,520 --> 00:15:40,689 But you get something else. 323 00:15:40,689 --> 00:15:43,158 You get something else, and you can see it there. 324 00:15:43,158 --> 00:15:45,794 And I've been avoiding it, but I got to address it right now. 325 00:15:45,794 --> 00:15:49,732 Because those higher end functions go to 0. 326 00:15:49,732 --> 00:15:51,700 So they have nodes. 327 00:15:51,700 --> 00:15:55,571 With increasing n, you get more nodes. 328 00:15:55,571 --> 00:15:56,205 What's a node? 329 00:15:56,205 --> 00:15:58,941 A node is when it goes to 0. 330 00:15:58,941 --> 00:16:00,542 And there's more of them. 331 00:16:00,542 --> 00:16:02,811 Now that's also really important. 332 00:16:05,948 --> 00:16:13,822 So what that means is in Bohr, my orbit was r, e. 333 00:16:13,822 --> 00:16:16,659 Heisenberg said no way. 334 00:16:16,659 --> 00:16:17,660 Can't have them both. 335 00:16:17,660 --> 00:16:21,063 But I had a r, which was one value. 336 00:16:21,063 --> 00:16:22,831 And remember-- it could only then 337 00:16:22,831 --> 00:16:26,969 be the r of the next value, the next n. 338 00:16:26,969 --> 00:16:29,171 Now I'm basically saying the opposite. 339 00:16:29,171 --> 00:16:32,040 I'm saying, well actually, r can be anything. 340 00:16:32,040 --> 00:16:34,643 There's a probability cloud, so this electron 341 00:16:34,643 --> 00:16:41,517 could be anywhere with certain probability, except not here. 342 00:16:41,517 --> 00:16:43,285 In this one place. 343 00:16:43,285 --> 00:16:44,486 This node. 344 00:16:44,486 --> 00:16:45,354 It's 0. 345 00:16:45,354 --> 00:16:46,755 It's literally 0. 346 00:16:46,755 --> 00:16:49,491 The probability of finding the electron there is 0. 347 00:16:49,491 --> 00:16:50,726 It cannot exist there. 348 00:16:50,726 --> 00:16:52,962 But how bizarre is that? 349 00:16:52,962 --> 00:16:57,967 The electron can exist with probability out here, 350 00:16:57,967 --> 00:17:02,137 and probability in here, but it can't exist in between. 351 00:17:02,137 --> 00:17:05,340 It's the same electron. 352 00:17:05,340 --> 00:17:08,042 Try explaining how it goes back and forth. 353 00:17:08,042 --> 00:17:13,515 It skips over a zero probability part, r. 354 00:17:13,515 --> 00:17:14,016 Right? 355 00:17:14,016 --> 00:17:15,684 But these nodes are very important. 356 00:17:15,684 --> 00:17:18,186 And just to give you a sense of what this means, 357 00:17:18,186 --> 00:17:20,388 I found a very fancy animation, because I 358 00:17:20,388 --> 00:17:21,957 want to make sure you guys understand. 359 00:17:21,957 --> 00:17:23,625 So here's the electron. 360 00:17:23,625 --> 00:17:25,728 It's doing this, it's doing its waving thing. 361 00:17:25,728 --> 00:17:27,663 But look at what happens with the nodes. 362 00:17:27,663 --> 00:17:28,697 Uh uh. 363 00:17:28,697 --> 00:17:30,733 The probability there is always 0. 364 00:17:30,733 --> 00:17:31,700 You see that? 365 00:17:31,700 --> 00:17:32,968 Can't go-- no. 366 00:17:32,968 --> 00:17:35,170 Not gonna exist there. 367 00:17:35,170 --> 00:17:37,506 Right? 368 00:17:37,506 --> 00:17:39,074 That is super deep. 369 00:17:39,074 --> 00:17:43,379 Because there's no classical analog to these things. 370 00:17:43,379 --> 00:17:45,147 There's no classical analog. 371 00:17:45,147 --> 00:17:49,918 But this is what electrons do in an atom. 372 00:17:49,918 --> 00:17:51,887 Now, this is what the clouds look like-- 373 00:17:51,887 --> 00:17:53,822 a little better drawn than mine-- 374 00:17:53,822 --> 00:17:57,159 for n equals 1, n equals 2, and n equals 3. 375 00:17:57,159 --> 00:17:58,260 So again, you can see-- 376 00:17:58,260 --> 00:18:00,195 this is one electron. 377 00:18:00,195 --> 00:18:02,097 It's colored differently, just to contrast it, 378 00:18:02,097 --> 00:18:03,932 but this is one electron. 379 00:18:03,932 --> 00:18:04,433 Right? 380 00:18:04,433 --> 00:18:04,933 And 381 00:18:04,933 --> 00:18:07,469 These are plus and minus of this, right? 382 00:18:07,469 --> 00:18:09,371 So it'd be like a wavy wave, and you're just 383 00:18:09,371 --> 00:18:11,940 showing plus and minus with the yellow and blue. 384 00:18:11,940 --> 00:18:14,610 But that note in between is where it can never be. 385 00:18:14,610 --> 00:18:15,744 But it's one electron. 386 00:18:15,744 --> 00:18:17,279 It's not many, it's one. 387 00:18:17,279 --> 00:18:20,682 And this is its probability distribution. 388 00:18:20,682 --> 00:18:22,851 Now I want to make one really important point, which 389 00:18:22,851 --> 00:18:24,686 is that-- 390 00:18:24,686 --> 00:18:26,321 look at what I'm plotting here. 391 00:18:26,321 --> 00:18:29,458 Maybe something-- that's size squared, right? 392 00:18:29,458 --> 00:18:34,029 So it's only the square of the wave function 393 00:18:34,029 --> 00:18:38,767 that we can relate any physical meaning to. 394 00:18:38,767 --> 00:18:41,336 The physical meaning I just related to you 395 00:18:41,336 --> 00:18:44,073 is the probability of being somewhere. 396 00:18:44,073 --> 00:18:46,542 That's what size squared gives us-- the probability 397 00:18:46,542 --> 00:18:48,210 of being somewhere. 398 00:18:48,210 --> 00:18:49,945 But ask your teacher-- 399 00:18:49,945 --> 00:18:53,015 not me, your quantum teacher. 400 00:18:53,015 --> 00:18:55,050 Ask what psi means. 401 00:18:55,050 --> 00:18:56,385 And they're going to have a-- 402 00:18:56,385 --> 00:18:58,954 it's going to be an interesting class. 403 00:18:58,954 --> 00:18:59,788 Force the issue. 404 00:18:59,788 --> 00:19:03,725 Don't let them go until they answer. 405 00:19:03,725 --> 00:19:05,127 We still don't know. 406 00:19:05,127 --> 00:19:07,162 We still don't know what the actual wave 407 00:19:07,162 --> 00:19:09,765 function means physically. 408 00:19:09,765 --> 00:19:11,733 We cannot attribute a physical meaning to it, 409 00:19:11,733 --> 00:19:14,002 only to its square. 410 00:19:14,002 --> 00:19:16,138 So we go about our business for the last 100 years 411 00:19:16,138 --> 00:19:18,340 squaring it and saying, OK, well it describes nature. 412 00:19:18,340 --> 00:19:18,907 That's great. 413 00:19:18,907 --> 00:19:23,712 But no one, still, knows what it means without the square. 414 00:19:23,712 --> 00:19:24,913 I find that incredible. 415 00:19:24,913 --> 00:19:28,584 And it led Bohr to say all sorts of really cool things. 416 00:19:28,584 --> 00:19:31,653 He said, "We must be clear that when it comes to atoms, 417 00:19:31,653 --> 00:19:36,225 language can be used only as in poetry. 418 00:19:36,225 --> 00:19:38,760 The poet, too, is not nearly so concerned 419 00:19:38,760 --> 00:19:41,797 with describing facts as with creating images 420 00:19:41,797 --> 00:19:44,299 and establishing mental connections." 421 00:19:44,299 --> 00:19:45,801 That's Bohr like deep in it, trying 422 00:19:45,801 --> 00:19:48,570 to figure out what psi means. 423 00:19:48,570 --> 00:19:49,872 He's like, I don't know. 424 00:19:49,872 --> 00:19:52,741 It's poetry. 425 00:19:52,741 --> 00:19:55,010 OK, that's cool. 426 00:19:55,010 --> 00:19:56,879 That's cool. 427 00:19:56,879 --> 00:19:58,547 V squared means something, v doesn't. 428 00:19:58,547 --> 00:19:59,615 Really? 429 00:19:59,615 --> 00:20:00,549 No. 430 00:20:00,549 --> 00:20:02,951 Classically, we've got nothing. 431 00:20:02,951 --> 00:20:03,785 Right? 432 00:20:03,785 --> 00:20:04,887 Quantum mechanics. 433 00:20:04,887 --> 00:20:06,388 Oh, it's a beautiful thing. 434 00:20:06,388 --> 00:20:07,289 Why does this matter? 435 00:20:07,289 --> 00:20:09,324 I'm going to give you a brief "why this matters." 436 00:20:09,324 --> 00:20:12,561 And we've been talking about the quantum nature of things, 437 00:20:12,561 --> 00:20:13,328 right? 438 00:20:13,328 --> 00:20:14,830 Quantum is this. 439 00:20:14,830 --> 00:20:16,532 Quantum are these differences. 440 00:20:16,532 --> 00:20:17,933 It's this probability. 441 00:20:17,933 --> 00:20:20,669 It's quantization of energies. 442 00:20:20,669 --> 00:20:22,371 What does that mean, right? 443 00:20:22,371 --> 00:20:25,774 Well, last time I told you that by electrons 444 00:20:25,774 --> 00:20:28,243 being quantum, and having wave-like character-- 445 00:20:28,243 --> 00:20:30,445 we're able to use them to see things, 446 00:20:30,445 --> 00:20:32,814 and it started the nanotechnology revolution 447 00:20:32,814 --> 00:20:34,116 about 30 years ago. 448 00:20:34,116 --> 00:20:36,251 And today I want to give you an example of that 449 00:20:36,251 --> 00:20:38,954 in my "why this matters." 450 00:20:38,954 --> 00:20:42,691 And it has to do with quantum domination, which should be 451 00:20:42,691 --> 00:20:46,495 the title of a movie or a book. 452 00:20:46,495 --> 00:20:49,064 And here's the example-- take a piece of bulk material. 453 00:20:49,064 --> 00:20:50,999 Take a piece of silicon, OK? 454 00:20:50,999 --> 00:20:52,668 And if you look at the silicon, it's 455 00:20:52,668 --> 00:20:54,303 kind of boring to look at optically. 456 00:20:54,303 --> 00:20:55,704 It's not very interesting. 457 00:20:55,704 --> 00:20:57,406 You know, don't tell that to your iPhone, 458 00:20:57,406 --> 00:21:00,943 which has a lot of it in there, but it's boring. 459 00:21:00,943 --> 00:21:04,613 But now, take out your little nano ice cream scooper, 460 00:21:04,613 --> 00:21:05,514 which you all have. 461 00:21:05,514 --> 00:21:07,482 And you take a little tiny piece of it. 462 00:21:07,482 --> 00:21:10,052 We call that a quantum dot. 463 00:21:10,052 --> 00:21:10,752 Why? 464 00:21:10,752 --> 00:21:13,322 We call it a quantum dot because it kind of looks 465 00:21:13,322 --> 00:21:15,958 like a dot-- its smallish. 466 00:21:15,958 --> 00:21:18,560 But we call it that because quantum mechanics 467 00:21:18,560 --> 00:21:20,362 takes over the properties. 468 00:21:20,362 --> 00:21:23,732 Here's an example-- shine light on this thing, 469 00:21:23,732 --> 00:21:25,834 or have it glow, and all of a sudden instead 470 00:21:25,834 --> 00:21:29,805 of being boring it can be any color you want. 471 00:21:29,805 --> 00:21:30,572 Why? 472 00:21:30,572 --> 00:21:32,307 Because if I shine light-- and here is 473 00:21:32,307 --> 00:21:36,011 a very sophisticated picture of a laser, which you can tell 474 00:21:36,011 --> 00:21:38,447 I had trouble making transparent. 475 00:21:38,447 --> 00:21:41,750 And so you shine a laser on this piece-- 476 00:21:41,750 --> 00:21:46,288 we know already, light excites charge in an atom. 477 00:21:46,288 --> 00:21:47,623 It does the same in solids. 478 00:21:47,623 --> 00:21:50,726 So here's my piece of silicon, and what that does 479 00:21:50,726 --> 00:21:53,862 is it sends an electron up in energy levels. 480 00:21:53,862 --> 00:21:55,631 But the electron is up in an energy level, 481 00:21:55,631 --> 00:21:57,432 and it left behind a hole. 482 00:21:57,432 --> 00:21:59,334 Which is something we'll talk about later when 483 00:21:59,334 --> 00:22:01,236 we talk about semiconductors. 484 00:22:01,236 --> 00:22:04,072 A hole is just a positive charge. 485 00:22:04,072 --> 00:22:06,875 And it turns out that that electron and that hole 486 00:22:06,875 --> 00:22:11,313 are attracted to each other, but not-- they can't get too close. 487 00:22:11,313 --> 00:22:13,882 But they want to kind of hang out at a certain distance. 488 00:22:13,882 --> 00:22:14,383 Where? 489 00:22:14,383 --> 00:22:15,584 How far? 490 00:22:15,584 --> 00:22:18,153 Yeah-- quantum mechanics. 491 00:22:18,153 --> 00:22:21,123 N 2, 3, 4 tells us. 492 00:22:21,123 --> 00:22:24,626 It tells us how far, right? 493 00:22:24,626 --> 00:22:25,594 They want to hang out-- 494 00:22:25,594 --> 00:22:28,063 and now all of a sudden, I've nano-scooped them out, 495 00:22:28,063 --> 00:22:29,231 and I've made a quantum dot. 496 00:22:29,231 --> 00:22:31,099 But if I try to do the same thing there, 497 00:22:31,099 --> 00:22:33,001 that's how far they wanted to be. 498 00:22:33,001 --> 00:22:33,935 And they can't be. 499 00:22:33,935 --> 00:22:36,972 They literally ran out of real estate. 500 00:22:36,972 --> 00:22:38,940 They ran out of atoms. 501 00:22:38,940 --> 00:22:41,743 They cannot be out here, because there's no stuff out here. 502 00:22:41,743 --> 00:22:43,745 So they get squeezed. 503 00:22:43,745 --> 00:22:46,415 I am squeezing these quantum mechanical objects, 504 00:22:46,415 --> 00:22:48,116 this electron and this hole. 505 00:22:48,116 --> 00:22:52,487 And by squeezing them, I'm changing the way 506 00:22:52,487 --> 00:22:53,855 they interact with light. 507 00:22:53,855 --> 00:22:57,659 I'm changing the color, right? 508 00:22:57,659 --> 00:22:58,560 Oh. 509 00:22:58,560 --> 00:23:01,163 It's all stuff we've learned that explains 510 00:23:01,163 --> 00:23:03,765 something revolutionary. 511 00:23:03,765 --> 00:23:07,102 By the way, if you buy a QLED TV, is it as good as OLED? 512 00:23:07,102 --> 00:23:08,036 No. 513 00:23:08,036 --> 00:23:09,805 But is it better than LED? 514 00:23:09,805 --> 00:23:10,939 Yeah, a little bit. 515 00:23:10,939 --> 00:23:12,040 That's what they-- QLED-- 516 00:23:12,040 --> 00:23:14,142 quantum is quantum dots. 517 00:23:14,142 --> 00:23:17,913 They have coated the LED emitters with quantum dots 518 00:23:17,913 --> 00:23:20,349 to give you better color. 519 00:23:20,349 --> 00:23:24,386 Now what this means, why this matters, 520 00:23:24,386 --> 00:23:27,089 is nothing less than the periodic table itself. 521 00:23:27,089 --> 00:23:29,658 Because I think I showed you this-- 522 00:23:29,658 --> 00:23:31,893 we're living in these different ages, which I love. 523 00:23:31,893 --> 00:23:33,995 We have the periodic table that has-- 524 00:23:33,995 --> 00:23:36,498 the ability to work with it is what's brought us 525 00:23:36,498 --> 00:23:39,634 to the age of materials design. 526 00:23:39,634 --> 00:23:44,706 But see, now I've literally just told you that by changing 527 00:23:44,706 --> 00:23:47,042 the size-- nothing more than the size-- 528 00:23:47,042 --> 00:23:50,045 I can tune a property because of quantum mechanics. 529 00:23:50,045 --> 00:23:52,748 Because I'm changing its quantum mechanical interactions. 530 00:23:52,748 --> 00:23:56,218 It would be like saying, I can take a piece of this table-- 531 00:23:56,218 --> 00:23:57,686 I can break a piece of this table, 532 00:23:57,686 --> 00:24:00,088 and it's now going to be red. 533 00:24:00,088 --> 00:24:03,425 That's exactly what we're doing, but at a very tiny size. 534 00:24:03,425 --> 00:24:06,795 That is as if we are taking this periodic table 535 00:24:06,795 --> 00:24:09,798 and giving it a whole other dimension. 536 00:24:09,798 --> 00:24:14,236 Every element can do more things than we thought possible 537 00:24:14,236 --> 00:24:17,372 because we can tune these properties related 538 00:24:17,372 --> 00:24:19,408 to quantum mechanics. 539 00:24:19,408 --> 00:24:20,876 So that's a big deal. 540 00:24:20,876 --> 00:24:22,477 That's a very big deal. 541 00:24:22,477 --> 00:24:22,978 OK. 542 00:24:22,978 --> 00:24:26,848 Now back to our solution to the Schrodinger equation. 543 00:24:26,848 --> 00:24:29,151 For an electron in an atom. 544 00:24:29,151 --> 00:24:36,458 Because now we move on and we solve for the next one, 545 00:24:36,458 --> 00:24:37,492 which is-- 546 00:24:37,492 --> 00:24:39,494 OK, so we did r. 547 00:24:39,494 --> 00:24:42,030 Now we're going to do theta. 548 00:24:42,030 --> 00:24:44,299 And what happens with theta is, you 549 00:24:44,299 --> 00:24:48,737 get another quantization of that variable. 550 00:24:48,737 --> 00:24:50,639 And that's the second quantum number. 551 00:24:50,639 --> 00:24:51,907 So we're going to put it here. 552 00:24:51,907 --> 00:24:56,244 N-- I'll number them so we don't lose track. 553 00:24:56,244 --> 00:24:59,548 Who knows how many they'll be? 554 00:24:59,548 --> 00:25:01,082 OK. 555 00:25:01,082 --> 00:25:03,418 Not three. 556 00:25:03,418 --> 00:25:07,322 OK, so the second one is l. 557 00:25:07,322 --> 00:25:12,093 And it's the angular quantum number. 558 00:25:15,163 --> 00:25:23,271 And it has also quantization 0, 1, 2, 3. 559 00:25:23,271 --> 00:25:23,772 OK? 560 00:25:23,772 --> 00:25:26,641 So l can be-- 561 00:25:26,641 --> 00:25:29,077 Oh, I need to put that up there. 562 00:25:29,077 --> 00:25:31,246 I meant to put that right here. 563 00:25:31,246 --> 00:25:35,383 This is just like what we learned for Bohr, right? 564 00:25:38,753 --> 00:25:46,761 And l can be 0, 1, 2, all the way up to l minus 1. 565 00:25:46,761 --> 00:25:48,830 OK? 566 00:25:48,830 --> 00:25:52,534 I'm going too fast, that's n minus 1. 567 00:25:52,534 --> 00:25:55,136 L goes from 0 to n minus 1. 568 00:25:57,939 --> 00:26:01,877 OK, so what that means right away-- 569 00:26:01,877 --> 00:26:03,879 what you can see-- if it only goes to n minus 1, 570 00:26:03,879 --> 00:26:10,986 then for example for n equals 1 then l equals 0. 571 00:26:10,986 --> 00:26:12,554 That's it. 572 00:26:12,554 --> 00:26:14,089 There's no other options. 573 00:26:14,089 --> 00:26:16,091 It stops, right? 574 00:26:16,091 --> 00:26:17,626 And we have a name for this. 575 00:26:17,626 --> 00:26:19,427 We call this s, the s orbital. 576 00:26:23,198 --> 00:26:31,473 And for n equals 2, l can be 0, or l can be 1. 577 00:26:31,473 --> 00:26:34,109 And this one is called-- 578 00:26:34,109 --> 00:26:36,211 this one is the p orbital. 579 00:26:36,211 --> 00:26:42,384 This is the p orbital, OK? 580 00:26:42,384 --> 00:26:43,184 Those have names. 581 00:26:43,184 --> 00:26:45,353 And so on and so on. 582 00:26:45,353 --> 00:26:48,456 d, f-- 583 00:26:48,456 --> 00:26:53,261 This is old notation that we cannot get rid of. 584 00:26:53,261 --> 00:26:55,063 This is called spectroscopic notation, 585 00:26:55,063 --> 00:26:56,865 because it comes from spectroscopists. 586 00:26:56,865 --> 00:27:00,435 And remember, I told you-- never make a spectroscopist angry. 587 00:27:00,435 --> 00:27:01,970 Don't do it. 588 00:27:01,970 --> 00:27:03,138 Don't do it. 589 00:27:03,138 --> 00:27:05,340 And so we use their notation still. 590 00:27:05,340 --> 00:27:06,741 s was sharp. 591 00:27:06,741 --> 00:27:08,577 Spherically symmetric. 592 00:27:08,577 --> 00:27:10,045 p was principle, because it sort of 593 00:27:10,045 --> 00:27:12,414 dominated in some experiments. d was more diffuse. 594 00:27:12,414 --> 00:27:15,050 f fundamental, because it looked kind of like the hydrogen atom 595 00:27:15,050 --> 00:27:16,518 sometimes. 596 00:27:16,518 --> 00:27:19,054 These shouldn't be the names, but they are because they still 597 00:27:19,054 --> 00:27:20,422 stay with us. 598 00:27:20,422 --> 00:27:23,458 Spectroscopic notation-- s, p, d, f. 599 00:27:23,458 --> 00:27:26,494 What they really do is just correspond-- 600 00:27:26,494 --> 00:27:27,929 that looks like "porbital." 601 00:27:30,565 --> 00:27:32,567 Let's put a little more space there. 602 00:27:32,567 --> 00:27:34,336 P orbital. 603 00:27:34,336 --> 00:27:35,170 Right? 604 00:27:35,170 --> 00:27:38,340 Because what they really mean is nothing more 605 00:27:38,340 --> 00:27:40,976 than a quantum number for the second quantum number, which 606 00:27:40,976 --> 00:27:43,445 is the angular quantum number. 607 00:27:43,445 --> 00:27:46,881 These are also sometimes called subshells, right? 608 00:27:46,881 --> 00:27:50,819 Because they're underneath the shell. 609 00:27:50,819 --> 00:27:53,088 And as you can see from this picture, 610 00:27:53,088 --> 00:27:58,059 it describes the angular shape. 611 00:27:58,059 --> 00:28:01,963 The angular shape of the orbital. 612 00:28:01,963 --> 00:28:03,164 The shape, right? 613 00:28:03,164 --> 00:28:04,099 So it gives us a shape. 614 00:28:08,069 --> 00:28:16,678 Now-- if we think about it, and we think about that p orbital, 615 00:28:16,678 --> 00:28:19,648 that has a different shape than the [INAUDIBLE].. 616 00:28:19,648 --> 00:28:22,450 Then you think, well, this could be aligned 617 00:28:22,450 --> 00:28:24,819 in different directions, right? 618 00:28:24,819 --> 00:28:26,588 So if I think about that p orbital-- well, 619 00:28:26,588 --> 00:28:29,057 I could align it in three different ways. 620 00:28:29,057 --> 00:28:33,461 It could go along this axis, this axis, or that one, right? 621 00:28:33,461 --> 00:28:36,564 And so those are p orbitals in hydrogen 622 00:28:36,564 --> 00:28:39,367 that have three possible orientations, 623 00:28:39,367 --> 00:28:43,371 and that automatically gets us to another quantum number. 624 00:28:43,371 --> 00:28:46,441 In fact, it's the last one, and it makes sense 625 00:28:46,441 --> 00:28:49,611 just physically-- that's phi, right? 626 00:28:49,611 --> 00:28:52,213 So the last one-- 627 00:28:52,213 --> 00:28:53,915 or is it the last one-- 628 00:28:53,915 --> 00:28:54,949 is m. 629 00:28:54,949 --> 00:29:02,457 And we call it m sub l, which is the magnetic quantum number. 630 00:29:05,260 --> 00:29:11,800 And this one can have quantization equal to minus l, 631 00:29:11,800 --> 00:29:12,300 right? 632 00:29:12,300 --> 00:29:15,937 All the way up to plus l. 633 00:29:15,937 --> 00:29:22,977 So the number of orientations that the orbital can have-- 634 00:29:22,977 --> 00:29:31,986 if I'm a-- n equals 2, l equals 1, 635 00:29:31,986 --> 00:29:38,326 then m sub l equals minus 1, 0, 1. 636 00:29:38,326 --> 00:29:40,261 Three orientations. 637 00:29:40,261 --> 00:29:40,762 Right? 638 00:29:40,762 --> 00:29:44,499 It's got three orientations-- three possible magnetic quantum 639 00:29:44,499 --> 00:29:44,999 numbers. 640 00:29:44,999 --> 00:29:46,835 Why is it called the magnetic quantum number? 641 00:29:46,835 --> 00:29:50,972 Because those are the experiments. 642 00:29:50,972 --> 00:29:53,975 We're done using magnetization-- 643 00:29:53,975 --> 00:29:58,246 magnetic fields-- to discover these 644 00:29:58,246 --> 00:30:00,548 orientations, to sort through it. 645 00:30:00,548 --> 00:30:02,317 To see it. 646 00:30:02,317 --> 00:30:03,017 OK. 647 00:30:03,017 --> 00:30:04,953 So if I had l equals-- 648 00:30:04,953 --> 00:30:10,291 all right, so if I had, for example l equals 2. 649 00:30:10,291 --> 00:30:13,495 Then m sub l would have five values. 650 00:30:13,495 --> 00:30:16,030 Five possible values, right? 651 00:30:18,733 --> 00:30:20,902 I should put a plus there, just to be sure we 652 00:30:20,902 --> 00:30:22,637 keep track of minus and plus. 653 00:30:22,637 --> 00:30:25,473 These are quantum numbers. 654 00:30:25,473 --> 00:30:27,075 That means they're integers, right? 655 00:30:27,075 --> 00:30:32,947 But they can have these ranges and these rules, and again-- 656 00:30:32,947 --> 00:30:35,350 you may think, why did this come out like this? 657 00:30:35,350 --> 00:30:39,354 Well, it comes out from solving this equation-- 658 00:30:39,354 --> 00:30:41,723 separation of variables-- 659 00:30:41,723 --> 00:30:42,824 with that potential. 660 00:30:42,824 --> 00:30:44,793 That's it, right? 661 00:30:44,793 --> 00:30:45,293 That's it. 662 00:30:45,293 --> 00:30:49,931 You get these allowed values of these three variables, quantum 663 00:30:49,931 --> 00:30:50,698 numbers. 664 00:30:50,698 --> 00:30:51,499 OK? 665 00:30:51,499 --> 00:30:51,966 All right. 666 00:30:56,137 --> 00:30:57,205 Now-- and there's the d. 667 00:30:57,205 --> 00:30:59,140 These are called d-- 668 00:30:59,140 --> 00:31:03,211 So if n equals 2-- 669 00:31:03,211 --> 00:31:03,711 OK. 670 00:31:03,711 --> 00:31:07,148 So did I mess up here? 671 00:31:07,148 --> 00:31:12,320 No, I didn't, because n would have to be 3 here, right? 672 00:31:12,320 --> 00:31:13,988 For l to be 2. 673 00:31:13,988 --> 00:31:17,158 Because l can't be equal to n, because I wrote it there 674 00:31:17,158 --> 00:31:21,296 as the list of allowed quantum numbers that l can have. 675 00:31:21,296 --> 00:31:24,699 And there it is for the d orbitals. 676 00:31:24,699 --> 00:31:26,901 And so there's five d orbitals. 677 00:31:26,901 --> 00:31:27,702 Five d orbitals. 678 00:31:27,702 --> 00:31:31,906 And you can do f on your own, and it's an extremely fun thing 679 00:31:31,906 --> 00:31:33,141 to do at night. 680 00:31:33,141 --> 00:31:34,475 Late at night. 681 00:31:34,475 --> 00:31:38,613 Now, this gives you the orbitals. 682 00:31:38,613 --> 00:31:39,647 You get them all. 683 00:31:39,647 --> 00:31:41,216 These are the orbitals. 684 00:31:41,216 --> 00:31:43,885 These are the beautiful, beautiful orbitals 685 00:31:43,885 --> 00:31:46,554 that we have from quantum mechanics 686 00:31:46,554 --> 00:31:48,756 describing an electron in an atom. 687 00:31:48,756 --> 00:31:55,196 Which tells you everything about where that electron can be, 688 00:31:55,196 --> 00:31:59,834 how it behaves, what its energies are, 689 00:31:59,834 --> 00:32:03,338 and therefore literally why atoms are what they are. 690 00:32:03,338 --> 00:32:05,240 That's what it tells us, right? 691 00:32:05,240 --> 00:32:09,978 Because the next thing we need to do is fill up our atoms. 692 00:32:09,978 --> 00:32:13,648 And know how electrons fill atoms using these quantum 693 00:32:13,648 --> 00:32:15,049 numbers. 694 00:32:15,049 --> 00:32:16,684 And then relate that to chemistry, 695 00:32:16,684 --> 00:32:19,254 and to the differences between one atom and another, 696 00:32:19,254 --> 00:32:21,689 and explaining why atoms are different. 697 00:32:21,689 --> 00:32:24,559 Remember, that was our goal. 698 00:32:24,559 --> 00:32:26,227 We needed to go quantum to answer that. 699 00:32:29,264 --> 00:32:32,367 So we're getting closer, but we're still not there. 700 00:32:32,367 --> 00:32:36,738 And one of the reasons is there is a fourth quantum number. 701 00:32:36,738 --> 00:32:38,239 And this came out of experiments-- 702 00:32:38,239 --> 00:32:40,041 I thought that I would just show you 703 00:32:40,041 --> 00:32:45,914 a very quick video, because it's easier to see this in action. 704 00:32:45,914 --> 00:32:47,649 And so these are experiments that 705 00:32:47,649 --> 00:32:51,185 were done by Stern and Gerlach that 706 00:32:51,185 --> 00:32:53,855 showed something very peculiar about atoms 707 00:32:53,855 --> 00:32:55,223 and their electrons. 708 00:32:55,223 --> 00:32:57,625 OK, so here I'm just going to play it. 709 00:32:57,625 --> 00:32:58,927 It's got a really nice-- 710 00:32:58,927 --> 00:32:59,661 oh, that's loud. 711 00:33:02,597 --> 00:33:03,665 Yeah? 712 00:33:03,665 --> 00:33:04,432 I don't mind that. 713 00:33:04,432 --> 00:33:04,933 That's good. 714 00:33:04,933 --> 00:33:06,401 So you can read the text here. 715 00:33:06,401 --> 00:33:07,635 OK, so they've got a magnet. 716 00:33:07,635 --> 00:33:10,038 A very strong magnet, right? 717 00:33:10,038 --> 00:33:11,506 Magnetic fields. 718 00:33:11,506 --> 00:33:13,708 And they're going to shoot a classical magnet. 719 00:33:13,708 --> 00:33:14,842 There's a classical magnet. 720 00:33:14,842 --> 00:33:17,845 And you see it's going to react to the magnetic field, 721 00:33:17,845 --> 00:33:20,615 and be pushed up. 722 00:33:20,615 --> 00:33:22,850 That magnetic could've been oriented differently. 723 00:33:22,850 --> 00:33:23,785 Like sideways, right? 724 00:33:23,785 --> 00:33:25,653 In which case it doesn't feel this. 725 00:33:25,653 --> 00:33:27,121 And you could throw a bunch of them 726 00:33:27,121 --> 00:33:30,491 randomly, with random orientations, 727 00:33:30,491 --> 00:33:32,226 and that's what you would see. 728 00:33:32,226 --> 00:33:33,962 [JAZZY MUSIC] 729 00:33:33,962 --> 00:33:35,263 It's good music, too. 730 00:33:35,263 --> 00:33:36,397 But now-- watch this. 731 00:33:36,397 --> 00:33:37,966 I love the animation here. 732 00:33:37,966 --> 00:33:40,201 Look at this. 733 00:33:40,201 --> 00:33:43,638 And the bass, right? 734 00:33:43,638 --> 00:33:46,374 Those are what happens to atoms with electrons. 735 00:33:46,374 --> 00:33:48,376 You'd shoot them through a high field, 736 00:33:48,376 --> 00:33:51,145 and you don't get anything. 737 00:33:51,145 --> 00:33:52,680 You get two things. 738 00:33:52,680 --> 00:33:54,148 Only two. 739 00:33:54,148 --> 00:33:56,951 [JAZZY MUSIC] 740 00:34:07,795 --> 00:34:10,098 I'm just playing it because I really want to groove out 741 00:34:10,098 --> 00:34:13,534 and I'm debating-- 742 00:34:13,534 --> 00:34:15,103 OK. 743 00:34:15,103 --> 00:34:17,237 All done. 744 00:34:17,237 --> 00:34:19,040 I was debating how embarrassing it would be 745 00:34:19,040 --> 00:34:20,541 if I just started grooving out. 746 00:34:23,844 --> 00:34:27,047 So this was Sterin and Gerlach, who discovered, essentially, 747 00:34:27,047 --> 00:34:31,953 a fourth quantum number that can have only two values. 748 00:34:31,953 --> 00:34:35,223 So they showed that this thing that the atoms were doing 749 00:34:35,223 --> 00:34:37,225 was because of the electrons. 750 00:34:37,225 --> 00:34:40,128 And that the only way you could explain 751 00:34:40,128 --> 00:34:42,964 what these electrons were doing is if there 752 00:34:42,964 --> 00:34:45,099 was this thing called spin. 753 00:34:45,099 --> 00:34:47,034 And if you really need to think classically-- 754 00:34:47,034 --> 00:34:50,438 and it's dangerous to do so, because then you'd 755 00:34:50,438 --> 00:34:53,074 forget that I could be all the way over there, right? 756 00:34:53,074 --> 00:34:54,108 Right now. 757 00:34:54,108 --> 00:34:55,943 But if you really need to think classically, 758 00:34:55,943 --> 00:34:57,645 you can think of a charge spinning. 759 00:34:57,645 --> 00:35:00,481 It could be spinning this way or that way. 760 00:35:00,481 --> 00:35:03,284 In a way, it helps our classical needs. 761 00:35:03,284 --> 00:35:05,453 But it's so not what's happening. 762 00:35:05,453 --> 00:35:09,757 But it does help our classical desires, right? 763 00:35:09,757 --> 00:35:11,993 And that would give you the two fields. 764 00:35:11,993 --> 00:35:12,960 Right? 765 00:35:12,960 --> 00:35:16,097 But I would advise you just to think about spin as simply 766 00:35:16,097 --> 00:35:18,800 a fourth quantum number. 767 00:35:18,800 --> 00:35:22,303 And so we call that one number 4. 768 00:35:22,303 --> 00:35:24,105 Not from that equation. 769 00:35:24,105 --> 00:35:26,674 Separate from those experiments. 770 00:35:26,674 --> 00:35:31,379 And that is-- we call that the spin M sub 771 00:35:31,379 --> 00:35:35,283 s is the spin quantum number. 772 00:35:35,283 --> 00:35:39,187 And it's the fourth one in our series. 773 00:35:39,187 --> 00:35:41,355 The fourth quantum number. 774 00:35:41,355 --> 00:35:43,191 And it has only two values-- 775 00:35:43,191 --> 00:35:46,160 up or down. 776 00:35:46,160 --> 00:35:51,699 Or if you like, you could write it as plus 1/2 or minus 1/2. 777 00:35:51,699 --> 00:35:55,903 Or you could write it as up or down arrows. 778 00:35:55,903 --> 00:36:00,808 So many ways to distinguish two things that are opposite. 779 00:36:00,808 --> 00:36:02,143 Spin up, spin down. 780 00:36:02,143 --> 00:36:04,445 Two values that this can have. 781 00:36:07,982 --> 00:36:08,950 So we're not ready yet. 782 00:36:08,950 --> 00:36:09,851 We're still not ready. 783 00:36:09,851 --> 00:36:15,256 We're so close, but we're still not there, right? 784 00:36:15,256 --> 00:36:17,525 Because we still don't know, well-- can't I just--? 785 00:36:17,525 --> 00:36:18,059 How do I--? 786 00:36:18,059 --> 00:36:22,396 What are the rules here going to be? 787 00:36:22,396 --> 00:36:24,632 For populating atoms. 788 00:36:24,632 --> 00:36:28,236 And this is where Pauli said something very important, 789 00:36:28,236 --> 00:36:33,341 and made this incredibly important statement. 790 00:36:33,341 --> 00:36:36,511 Which is that-- no particles in the same system-- 791 00:36:36,511 --> 00:36:40,815 read that as, no electrons in the same atom-- 792 00:36:40,815 --> 00:36:44,051 can have the same quantum numbers. 793 00:36:44,051 --> 00:36:47,655 No electrons in the same atom can have the same quantum 794 00:36:47,655 --> 00:36:48,723 numbers. 795 00:36:48,723 --> 00:36:51,792 And that immediately tells you-- 796 00:36:51,792 --> 00:36:55,263 again, this has to do with the nature of quantum mechanics-- 797 00:36:55,263 --> 00:37:01,068 what that immediately tells you is that two electrons-- 798 00:37:01,068 --> 00:37:04,338 ho-ho, this is big! 799 00:37:04,338 --> 00:37:08,209 Two electrons-- I'm gonna write, two electrons, and watch this-- 800 00:37:08,209 --> 00:37:09,477 I'm going all caps-- 801 00:37:09,477 --> 00:37:16,817 only two electrons can occupy an orbital. 802 00:37:20,955 --> 00:37:21,489 An orbital. 803 00:37:25,860 --> 00:37:27,929 Or- bi- tal. 804 00:37:30,565 --> 00:37:35,503 That called the Pauli exclusion principle. 805 00:37:35,503 --> 00:37:36,003 OK. 806 00:37:39,240 --> 00:37:41,142 So we're going to use all of this information 807 00:37:41,142 --> 00:37:45,513 to fill stuff up, but I don't want to do that yet. 808 00:37:45,513 --> 00:37:48,282 On Wednesday, we're filling up the table, 809 00:37:48,282 --> 00:37:49,650 and we're making our first solid. 810 00:37:49,650 --> 00:37:51,419 I figure it's our three week anniversary. 811 00:37:51,419 --> 00:37:53,955 I know you've all been looking forward to it. 812 00:37:53,955 --> 00:37:55,456 I've been thinking about it a lot. 813 00:37:55,456 --> 00:37:59,460 And I think-- that makes me want to throw t-shirts. 814 00:37:59,460 --> 00:38:00,494 [STUDENTS CHEERING] 815 00:38:00,494 --> 00:38:03,264 I got to do this. 816 00:38:03,264 --> 00:38:04,599 All right, all right. 817 00:38:04,599 --> 00:38:05,766 I got to go-- 818 00:38:05,766 --> 00:38:06,467 I know. 819 00:38:06,467 --> 00:38:07,935 I got to go backwards here. 820 00:38:10,538 --> 00:38:12,106 OK, OK, hold on, hold on. 821 00:38:14,709 --> 00:38:16,344 I'm missing there and there, I know. 822 00:38:16,344 --> 00:38:17,845 I got to work on my arm. 823 00:38:17,845 --> 00:38:18,713 Yeah. 824 00:38:18,713 --> 00:38:19,747 Show you love over there. 825 00:38:19,747 --> 00:38:21,515 OK, all right. 826 00:38:21,515 --> 00:38:25,519 I'll have more on Wednesday, and the reason is-- 827 00:38:25,519 --> 00:38:27,488 we're making our first solid. 828 00:38:27,488 --> 00:38:29,123 I almost wanted to leave it a surprise, 829 00:38:29,123 --> 00:38:31,392 but I couldn't help myself. 830 00:38:31,392 --> 00:38:32,860 It's extremely exciting. 831 00:38:32,860 --> 00:38:35,329 This is, after all, solid-state chemistry, 832 00:38:35,329 --> 00:38:37,398 and Wednesday we're making a solid. 833 00:38:37,398 --> 00:38:37,898 Literally. 834 00:38:37,898 --> 00:38:40,968 We are not only making a bond, but we're making a solid, 835 00:38:40,968 --> 00:38:42,003 and talking about solids. 836 00:38:42,003 --> 00:38:43,771 So that's going to be very exciting. 837 00:38:43,771 --> 00:38:46,440 And we're going to start by filling elements. 838 00:38:46,440 --> 00:38:50,778 But before we do that, I want to explain something 839 00:38:50,778 --> 00:38:54,382 very important, which is-- 840 00:38:54,382 --> 00:38:56,951 what's happening with energy? 841 00:38:56,951 --> 00:38:57,518 Right? 842 00:38:57,518 --> 00:39:01,088 We did just see something dramatic. 843 00:39:01,088 --> 00:39:04,358 As you go from Bohr to quantum, something very dramatic 844 00:39:04,358 --> 00:39:09,063 happens with where, right? 845 00:39:09,063 --> 00:39:11,632 And we know something else very dramatic 846 00:39:11,632 --> 00:39:15,036 happens, which is right here. 847 00:39:15,036 --> 00:39:18,439 You know, that's Bohr over there- n equals 1, [INAUDIBLE].. 848 00:39:18,439 --> 00:39:23,077 Bohr is 1, 2, 3, right? 849 00:39:23,077 --> 00:39:26,414 Now it's like-- oh no, wait, it's 1 and with 1s. 850 00:39:26,414 --> 00:39:29,550 2-- I can put two electrons in there, thanks to Pauli. 851 00:39:29,550 --> 00:39:31,852 I know I can put two, because I have all the quantum 852 00:39:31,852 --> 00:39:34,021 numbers in here the same except spin, which 853 00:39:34,021 --> 00:39:36,457 could be up or down, right? 854 00:39:36,457 --> 00:39:40,728 N equals 1, l equals 0, m sub l equals 0, spin is up or down. 855 00:39:40,728 --> 00:39:41,562 Two electrons. 856 00:39:41,562 --> 00:39:45,032 But look, I'm now here at n equals 2, 857 00:39:45,032 --> 00:39:47,034 going from the Bohr model to quantum. 858 00:39:47,034 --> 00:39:52,106 I've got this and I've got three p orbitals. 859 00:39:52,106 --> 00:39:54,642 So now all of a sudden I've got eight electrons 860 00:39:54,642 --> 00:39:57,445 that can go into that quantum number. 861 00:39:57,445 --> 00:40:01,916 That's very different than Bohr, right? 862 00:40:01,916 --> 00:40:05,119 And that's called degeneracy, because you're taking something 863 00:40:05,119 --> 00:40:07,388 and you're saying, there are multiple variations 864 00:40:07,388 --> 00:40:09,256 that have the same n. 865 00:40:09,256 --> 00:40:10,991 But there's something else that I 866 00:40:10,991 --> 00:40:14,528 want to explain right now that is can be understood very 867 00:40:14,528 --> 00:40:16,564 physically and intuitively. 868 00:40:16,564 --> 00:40:19,333 And that is that the motivation-- one 869 00:40:19,333 --> 00:40:21,702 of the big motivations of this was that we 870 00:40:21,702 --> 00:40:24,372 needed more than one electron. 871 00:40:24,372 --> 00:40:28,109 Our atoms are not all hydrogen and ionized atoms. 872 00:40:28,109 --> 00:40:31,011 They are just neutral atoms going up above hydrogen. 873 00:40:31,011 --> 00:40:34,882 So what happens when we go multi electron? 874 00:40:34,882 --> 00:40:36,984 And there's two effects that I want to explain. 875 00:40:36,984 --> 00:40:39,153 Here's what happens to this picture. 876 00:40:39,153 --> 00:40:40,855 Those are the one electron levels, right? 877 00:40:40,855 --> 00:40:42,656 There's Bohr over there. 878 00:40:42,656 --> 00:40:46,360 This is what you really get in terms of energy. 879 00:40:46,360 --> 00:40:46,861 Right? 880 00:40:46,861 --> 00:40:48,763 This is energy along the vertical axis. 881 00:40:48,763 --> 00:40:52,233 And there's two reasons, two very important reasons, 882 00:40:52,233 --> 00:40:54,068 why these are so different. 883 00:40:54,068 --> 00:40:56,103 One is called shielding, and the other 884 00:40:56,103 --> 00:40:57,338 is called orbital penetration. 885 00:40:57,338 --> 00:40:59,206 And I want to talk about both of them 886 00:40:59,206 --> 00:41:03,511 in the last seven minutes of class. 887 00:41:03,511 --> 00:41:05,012 I'm going over here. 888 00:41:08,983 --> 00:41:11,652 All right, so let's talk about-- 889 00:41:11,652 --> 00:41:12,720 let's do shielding first. 890 00:41:15,723 --> 00:41:19,927 Shielding is something that you can kind of 891 00:41:19,927 --> 00:41:23,497 get a very good sense for it if you just look at what's 892 00:41:23,497 --> 00:41:25,132 happening in these atoms. 893 00:41:28,102 --> 00:41:35,576 So in shielding-- let's take an example. 894 00:41:35,576 --> 00:41:40,314 I'm going to give you an atom with 15 protons and 15 895 00:41:40,314 --> 00:41:41,749 electrons. 896 00:41:41,749 --> 00:41:43,918 What atom is it? 897 00:41:43,918 --> 00:41:46,253 Anybody know? 898 00:41:46,253 --> 00:41:47,421 Phosphorus. 899 00:41:47,421 --> 00:41:50,458 OK, so I'm going to take an example of the phosphorus atom, 900 00:41:50,458 --> 00:41:53,027 OK? 901 00:41:53,027 --> 00:41:59,733 And I've got 15 positive charges in the nucleus. 902 00:41:59,733 --> 00:42:00,868 15. 903 00:42:00,868 --> 00:42:03,437 Right? 904 00:42:03,437 --> 00:42:05,873 Now, 15 protons. 905 00:42:05,873 --> 00:42:09,510 Now I've got my levels, and it gets 906 00:42:09,510 --> 00:42:14,381 very difficult to draw levels as probability distributions. 907 00:42:14,381 --> 00:42:16,484 So I'm going to draw them as rings, even though we 908 00:42:16,484 --> 00:42:17,918 know they're not, right? 909 00:42:17,918 --> 00:42:18,986 These are my orbitals. 910 00:42:18,986 --> 00:42:23,290 But I've got like an electron here, OK, an electron there. 911 00:42:23,290 --> 00:42:23,791 All right. 912 00:42:23,791 --> 00:42:27,795 So I've got two electrons in the n equals 1-- 913 00:42:27,795 --> 00:42:29,763 n equals 1 orbital. 914 00:42:29,763 --> 00:42:34,201 So that's the 1s orbital, right there on the bottom. 915 00:42:34,201 --> 00:42:36,103 But if I go out-- 916 00:42:36,103 --> 00:42:39,940 OK, so I'm going to go out now. 917 00:42:39,940 --> 00:42:42,776 To n equals 2. 918 00:42:42,776 --> 00:42:50,451 Well, now I've got 1, 2, 3, 4, and-- 919 00:42:50,451 --> 00:42:52,753 oh boy-- put one here. 920 00:42:52,753 --> 00:42:57,191 5, 6, 7, 8. 921 00:42:57,191 --> 00:43:01,595 Because here-- remember, I've got l equals 0 and l equals 1, 922 00:43:01,595 --> 00:43:04,765 and as we just said, because n sub s can be up or down, 923 00:43:04,765 --> 00:43:07,334 I've got eight electrons here. 924 00:43:07,334 --> 00:43:10,437 So here, I've got n equals 1, here I've got n equals 2. 925 00:43:10,437 --> 00:43:11,772 That's eight electrons. 926 00:43:11,772 --> 00:43:13,440 And then out here-- 927 00:43:13,440 --> 00:43:16,310 oh, now it gets really interesting-- because for n 928 00:43:16,310 --> 00:43:18,946 equals 3, how many electrons do I have left? 929 00:43:18,946 --> 00:43:23,717 1, 2, 3, 4, 5. 930 00:43:23,717 --> 00:43:25,819 And you can already see what's happening. 931 00:43:25,819 --> 00:43:27,855 So remember, Rutherford told us this. 932 00:43:27,855 --> 00:43:31,158 All this charge is in a tiny little point here. 933 00:43:31,158 --> 00:43:36,063 You wouldn't even see it if we were drawing this to scale. 934 00:43:36,063 --> 00:43:39,433 But what are these electrons seeing? 935 00:43:39,433 --> 00:43:40,734 What are the electrons seeing? 936 00:43:40,734 --> 00:43:43,537 Well, these inner two electrons are just 937 00:43:43,537 --> 00:43:45,339 seeing this huge amount of charge. 938 00:43:45,339 --> 00:43:47,474 They are happy. 939 00:43:47,474 --> 00:43:49,376 Low energy. 940 00:43:49,376 --> 00:43:50,044 Right? 941 00:43:50,044 --> 00:43:51,712 The lower your energy, the happier. 942 00:43:51,712 --> 00:43:53,647 You're in a lower energy, ground state. 943 00:43:53,647 --> 00:43:57,851 Remember-- more lower energy, more happiness. 944 00:43:57,851 --> 00:43:59,153 More bound. 945 00:43:59,153 --> 00:44:00,654 Right? 946 00:44:00,654 --> 00:44:05,793 So those electrons down there are enjoying. 947 00:44:05,793 --> 00:44:07,861 But these out here-- 948 00:44:07,861 --> 00:44:08,429 you see? 949 00:44:08,429 --> 00:44:10,731 These electrons. 950 00:44:10,731 --> 00:44:12,766 Those electrons in here-- 951 00:44:12,766 --> 00:44:17,805 these shield the outer electrons, these shield 952 00:44:17,805 --> 00:44:23,744 outer electrons by two electrons. 953 00:44:23,744 --> 00:44:24,411 Right? 954 00:44:24,411 --> 00:44:27,481 Because they're kind of in the way. 955 00:44:27,481 --> 00:44:30,117 It's like you've got this negative charge that's 956 00:44:30,117 --> 00:44:33,053 in between me and the positive charge, right? 957 00:44:33,053 --> 00:44:35,456 And so if I'm out here at n equals 2, 958 00:44:35,456 --> 00:44:42,162 I don't see 15 positive charges there anymore. 959 00:44:42,162 --> 00:44:44,865 I see 13-- ish. 960 00:44:44,865 --> 00:44:46,900 That's shielding. 961 00:44:46,900 --> 00:44:48,369 But now this one-- 962 00:44:48,369 --> 00:44:53,307 this has the 2s and the 2p electrons. 963 00:44:53,307 --> 00:44:55,976 It's got eight electrons there, and those 964 00:44:55,976 --> 00:44:58,779 are shielding another eight. 965 00:44:58,779 --> 00:45:03,651 Those are shielding another eight protons. 966 00:45:07,388 --> 00:45:09,623 To things outside of them, right? 967 00:45:09,623 --> 00:45:11,225 Shielding doesn't work going in. 968 00:45:11,225 --> 00:45:17,965 If I'm this electron and I look out, all I see are repulsive-- 969 00:45:17,965 --> 00:45:19,967 I see repulsiveness. 970 00:45:19,967 --> 00:45:20,601 In a good way-- 971 00:45:20,601 --> 00:45:21,869 I'm sure they're friends. 972 00:45:21,869 --> 00:45:26,206 But two negative charges, right? 973 00:45:26,206 --> 00:45:27,841 So I'm only looking in. 974 00:45:27,841 --> 00:45:30,444 Looking in, shielded. 975 00:45:30,444 --> 00:45:32,980 Looking in, shielded. 976 00:45:32,980 --> 00:45:36,316 So these ones have sort of an effective-- 977 00:45:36,316 --> 00:45:38,118 z effective. 978 00:45:38,118 --> 00:45:41,789 You know, that could be something like five. 979 00:45:41,789 --> 00:45:44,258 This is not the z of the atom, but it's 980 00:45:44,258 --> 00:45:46,760 sort of like those very outer electrons don't 981 00:45:46,760 --> 00:45:49,063 see the whole proton cloud. 982 00:45:49,063 --> 00:45:49,830 They get shielded. 983 00:45:49,830 --> 00:45:52,599 And that's a very important part of what 984 00:45:52,599 --> 00:45:56,103 happens to orbitals when you put a lot of electrons in them. 985 00:45:56,103 --> 00:45:58,505 And there's one more thing that happens, 986 00:45:58,505 --> 00:46:03,343 and it goes back to this plot that I showed you before, 987 00:46:03,343 --> 00:46:08,449 which is that the orbitals themselves 988 00:46:08,449 --> 00:46:14,555 are very different than just like a straight line from Bohr. 989 00:46:14,555 --> 00:46:17,091 They have these shapes to them, right? 990 00:46:17,091 --> 00:46:25,532 So the second thing that happens is that if I have that same s-- 991 00:46:25,532 --> 00:46:28,836 this is s, so this would now be the 1s. 992 00:46:28,836 --> 00:46:30,003 And now I'm going to put-- 993 00:46:30,003 --> 00:46:33,507 remember that 2s looked like this. 994 00:46:33,507 --> 00:46:34,742 And it had the node there. 995 00:46:34,742 --> 00:46:35,342 Remember that? 996 00:46:35,342 --> 00:46:36,944 Ho-ho. 997 00:46:36,944 --> 00:46:39,580 That was 2s. 998 00:46:39,580 --> 00:46:44,184 But now we're going to put the 2p there. 999 00:46:44,184 --> 00:46:47,488 May not be drawn to scale. 1000 00:46:47,488 --> 00:46:49,089 OK, here's the 2p. 1001 00:46:53,093 --> 00:46:56,096 Something very, very interesting is happening here. 1002 00:46:56,096 --> 00:46:58,932 And again, it has to do with what electrons are seeing. 1003 00:46:58,932 --> 00:47:02,269 Because the 2s electron has a probability-- 1004 00:47:02,269 --> 00:47:05,239 remember, this is the probability normalized, 1005 00:47:05,239 --> 00:47:08,642 so we put in r-squared there, right? 1006 00:47:08,642 --> 00:47:11,945 That probability-- all that means is if I integrate over 1007 00:47:11,945 --> 00:47:13,080 everything, it's 1. 1008 00:47:13,080 --> 00:47:14,548 It's got to be somewhere. 1009 00:47:14,548 --> 00:47:19,686 But look, the 2s electron can be really deep inside the shells. 1010 00:47:19,686 --> 00:47:22,689 It can be in there. 1011 00:47:22,689 --> 00:47:26,493 Literally-- look, it's even inside the 1s. 1012 00:47:26,493 --> 00:47:31,799 So it gets some of that 15-proton action, right? 1013 00:47:31,799 --> 00:47:35,102 Orbital penetration leads to massive changes. 1014 00:47:35,102 --> 00:47:37,404 Orbital penetration is what this is called, 1015 00:47:37,404 --> 00:47:40,741 and it allows some of the-- 1016 00:47:40,741 --> 00:47:42,810 but the p doesn't have that. 1017 00:47:42,810 --> 00:47:44,378 It goes in a little, but the p doesn't 1018 00:47:44,378 --> 00:47:46,180 have that peak, all the way in there, 1019 00:47:46,180 --> 00:47:48,182 where it can see all that positive charge. 1020 00:47:48,182 --> 00:47:52,886 And that is why these two things are different. 1021 00:47:52,886 --> 00:47:53,554 You see? 1022 00:47:53,554 --> 00:47:57,558 Because the 2s now, can be closer sometimes 1023 00:47:57,558 --> 00:48:00,127 to those 15 protons, right? 1024 00:48:00,127 --> 00:48:03,330 And so it lowers the energy, making it happier. 1025 00:48:03,330 --> 00:48:05,532 It finds a lower happy place. 1026 00:48:05,532 --> 00:48:06,033 OK? 1027 00:48:06,033 --> 00:48:11,772 So we're going to use this, and on Wednesday, we're 1028 00:48:11,772 --> 00:48:14,308 going to take these things and we're going to fill them up, 1029 00:48:14,308 --> 00:48:16,877 and we're going to make our first solid. 1030 00:48:16,877 --> 00:48:19,813 Have a very good rest of your day.