1 00:00:00,881 --> 00:00:02,832 - Heisenberg uncertainty principle is a 2 00:00:02,832 --> 00:00:04,805 principle of quantum mechanics. 3 00:00:04,805 --> 00:00:06,686 And so if we take a particle, let's say we have 4 00:00:06,686 --> 00:00:11,686 a particle here of Mass M, moving with Velocity V, 5 00:00:11,748 --> 00:00:14,255 the momentum of that particle, the linear momentum 6 00:00:14,255 --> 00:00:16,809 is equal to the Mass times the Velocity. 7 00:00:16,809 --> 00:00:19,363 And according to the uncertainty principle, 8 00:00:19,363 --> 00:00:22,150 you can't know the position and momentum 9 00:00:22,150 --> 00:00:25,656 of that particle accurately, at the same time. 10 00:00:25,656 --> 00:00:28,593 So if you know the position, if you know where that particle 11 00:00:28,593 --> 00:00:32,168 is in space really well, you don't know the momentum, 12 00:00:32,168 --> 00:00:34,491 or you don't know the velocity of that particle, 13 00:00:34,491 --> 00:00:35,396 and vice versa. 14 00:00:35,396 --> 00:00:36,697 If you know the momentum really well, 15 00:00:36,697 --> 00:00:38,345 you don't know the position. 16 00:00:38,345 --> 00:00:40,574 So let's look at a mathematical description 17 00:00:40,574 --> 00:00:42,316 of the uncertainty principle. 18 00:00:42,316 --> 00:00:44,777 So the uncertainty in the position, 19 00:00:44,777 --> 00:00:47,424 so Delta X is the uncertainty in the position, 20 00:00:47,424 --> 00:00:49,931 times the uncertainty in the momentum, 21 00:00:49,931 --> 00:00:53,832 so Delta P is uncertainty in momentum, 22 00:00:53,832 --> 00:00:56,247 the product of these two must be greater than 23 00:00:56,247 --> 00:00:58,639 or equal to some constant. 24 00:00:58,639 --> 00:01:00,752 And that constant is Planck's Constant: 25 00:01:00,752 --> 00:01:03,747 h divided by four pi. 26 00:01:03,747 --> 00:01:08,066 So we have a constant divided by another constant. 27 00:01:08,066 --> 00:01:11,386 So this just gives us a number on the right side, 28 00:01:11,386 --> 00:01:12,872 and you might see something a little bit different 29 00:01:12,872 --> 00:01:13,986 in another textbook. 30 00:01:13,986 --> 00:01:15,356 It doesn't really matter that much, 31 00:01:15,356 --> 00:01:17,655 it just depends on how you define things. 32 00:01:17,655 --> 00:01:21,440 So the point is, the product of the two uncertainties 33 00:01:21,440 --> 00:01:24,806 must be greater than or equal to some number. 34 00:01:24,806 --> 00:01:27,337 So the uncertainties are inversely proportional 35 00:01:27,337 --> 00:01:31,308 to each other: if you increase one, you decrease the other. 36 00:01:31,308 --> 00:01:33,746 Let's go ahead and use some really simple numbers here, 37 00:01:33,746 --> 00:01:35,464 just so you can understand that point. 38 00:01:35,464 --> 00:01:39,318 So let's say, and this is just extremely simplified, 39 00:01:39,318 --> 00:01:40,828 so let's just see if we can understand that idea 40 00:01:40,828 --> 00:01:42,592 of inversely proportional. 41 00:01:42,592 --> 00:01:46,168 So if you have an uncertainty of two for the position, 42 00:01:46,168 --> 00:01:47,793 and let's say you had an uncertainty 43 00:01:47,793 --> 00:01:49,651 of two for the momentum. 44 00:01:49,651 --> 00:01:52,112 Alright, so two times two is equal to four, 45 00:01:52,112 --> 00:01:55,479 so I won't even worry about greater than, 46 00:01:55,479 --> 00:01:56,733 I'll just put equal to here. 47 00:01:56,733 --> 00:01:59,914 So if two times two is equal to four. 48 00:01:59,914 --> 00:02:02,259 If I decrease the uncertainty of the position, 49 00:02:02,259 --> 00:02:03,977 so I decrease it to one, 50 00:02:03,977 --> 00:02:08,270 so the uncertainty in the momentum must increase to four, 51 00:02:08,270 --> 00:02:10,662 because one times four is equal to four. 52 00:02:10,663 --> 00:02:13,775 If I decrease the uncertainty in the position even more, 53 00:02:13,775 --> 00:02:17,450 so if I lower that to point five, I increase the uncertainty 54 00:02:17,450 --> 00:02:19,772 in the momentum, that must go up to eight. 55 00:02:19,772 --> 00:02:22,326 So point five times eight gives us four. 56 00:02:22,326 --> 00:02:24,462 And so, what I'm trying to show you here, 57 00:02:24,462 --> 00:02:28,200 is as you decrease the uncertainty in the position, 58 00:02:28,200 --> 00:02:31,730 you increase the uncertainty in the momentum. 59 00:02:31,730 --> 00:02:33,494 So another way of saying that is, 60 00:02:33,494 --> 00:02:37,279 the more accurately you know the position of a particle, 61 00:02:37,279 --> 00:02:40,808 the less accurately you know the momentum of that particle. 62 00:02:40,808 --> 00:02:44,013 And that's the idea of the uncertainty principle. 63 00:02:44,013 --> 00:02:46,868 And so let's apply this uncertainty principle 64 00:02:46,868 --> 00:02:49,655 to the Bohr model of the hydrogen atom. 65 00:02:49,655 --> 00:02:51,408 So let's look at a picture of the Bohr model 66 00:02:51,408 --> 00:02:52,819 of the hydrogen atom. 67 00:02:52,819 --> 00:02:55,280 Alright, we know our negatively charged electron 68 00:02:55,280 --> 00:02:58,600 orbits the nucleus, like a planet around the sun. 69 00:02:58,600 --> 00:03:01,503 And, let's say the electron is going this direction, 70 00:03:01,503 --> 00:03:05,256 so there is a velocity associated with that electron, 71 00:03:05,256 --> 00:03:08,030 so there is velocity going in that direction. 72 00:03:08,030 --> 00:03:10,221 Alright, the reason why the Bohr model is useful, 73 00:03:10,221 --> 00:03:12,218 is because it allows us to understand things like 74 00:03:12,218 --> 00:03:14,122 quantized energy levels. 75 00:03:14,122 --> 00:03:18,441 And we talked about the radius for the electron, 76 00:03:18,441 --> 00:03:21,042 so if there's a circle here, there's a radius 77 00:03:21,042 --> 00:03:23,154 for an electron in the ground state, 78 00:03:23,154 --> 00:03:26,103 this would be the radius of the first energy level, 79 00:03:26,103 --> 00:03:30,654 is equal to 5.3 times 10 to the negative 11 meters. 80 00:03:30,654 --> 00:03:33,626 So if we wanted to know the diameter of that circle, 81 00:03:33,626 --> 00:03:35,762 we could just multiply the radius by two. 82 00:03:35,762 --> 00:03:38,061 So two times that number would be equal 83 00:03:38,061 --> 00:03:43,061 to 1.06 times 10 to the negative 10 meters. 84 00:03:44,168 --> 00:03:47,186 And this is just a rough estimate of the size 85 00:03:47,186 --> 00:03:50,135 of the hydrogen atom using the Bohr model, 86 00:03:50,135 --> 00:03:52,550 with an electron in the ground state. 87 00:03:52,550 --> 00:03:55,499 Alright, we also did some calculations 88 00:03:55,499 --> 00:03:57,913 to figure out the velocity. 89 00:03:57,913 --> 00:04:01,210 So the velocity of an electron in the ground state 90 00:04:01,210 --> 00:04:03,695 of a hydrogen atom using the Bohr model, 91 00:04:03,695 --> 00:04:04,786 we calculated that to be 92 00:04:04,786 --> 00:04:08,171 2.2 times 10 to the six meters per second. 93 00:04:08,171 --> 00:04:10,144 And since we know the mass of an electron, 94 00:04:10,144 --> 00:04:12,606 we can actually calculate the linear momentum. 95 00:04:12,606 --> 00:04:14,463 So the linear momentum P is equal 96 00:04:14,463 --> 00:04:16,668 to the mass times the velocity. 97 00:04:16,668 --> 00:04:21,668 Let's say we knew the velocity with a 10% uncertainty 98 00:04:21,846 --> 00:04:23,426 associated with that number. 99 00:04:23,426 --> 00:04:26,073 So a 10% uncertainty. 100 00:04:26,073 --> 00:04:30,577 If we convert that to a decimal, we just divide 10 by 100, 101 00:04:30,577 --> 00:04:34,362 so we get 10% is equal to point one. 102 00:04:34,362 --> 00:04:35,778 So we have point one here. 103 00:04:35,778 --> 00:04:38,355 If I want to know the uncertainty of the momentum 104 00:04:38,355 --> 00:04:40,793 of that electron, so the uncertainty 105 00:04:40,793 --> 00:04:43,394 in the momentum of that particle, 106 00:04:43,394 --> 00:04:45,995 momentum is equal to mass times velocity. 107 00:04:45,995 --> 00:04:50,360 If there's a 10% uncertainty associated with the velocity, 108 00:04:50,360 --> 00:04:52,658 we need to multiply this by point one. 109 00:04:52,658 --> 00:04:54,586 So let's go ahead and do that. 110 00:04:54,586 --> 00:04:58,092 So we would have the mass of the electron 111 00:04:58,092 --> 00:05:02,689 is 9.11 times 10 to the negative 31st. 112 00:05:02,689 --> 00:05:04,918 The velocity of the electron is 113 00:05:04,918 --> 00:05:08,122 2.2 times 10 to the sixth, and we know that 114 00:05:08,122 --> 00:05:10,839 with 10% uncertainty, so we need to multiply 115 00:05:10,839 --> 00:05:12,929 all of that by point one. 116 00:05:12,929 --> 00:05:14,740 So let's go ahead and do that. 117 00:05:14,740 --> 00:05:17,395 We're gonna multiply all those things together. 118 00:05:17,395 --> 00:05:18,812 So we take the mass of an electron, 119 00:05:18,812 --> 00:05:23,812 9.11 times 10 to the negative 31st 120 00:05:23,897 --> 00:05:26,056 and we multiply that by the velocity, 121 00:05:26,056 --> 00:05:29,980 2.2 times 10 to the sixth, 122 00:05:29,980 --> 00:05:32,581 and we know there's a 10% uncertainty 123 00:05:32,581 --> 00:05:34,229 associated with the velocity, 124 00:05:34,229 --> 00:05:36,853 so we get an uncertainty in the momentum 125 00:05:36,853 --> 00:05:40,893 2.0 times 10 to the negative 25. 126 00:05:40,893 --> 00:05:43,075 So the uncertainty in the momentum is 127 00:05:43,075 --> 00:05:47,673 2.0 times 10 to the negative 25. 128 00:05:47,673 --> 00:05:48,718 And the units would be, 129 00:05:48,718 --> 00:05:51,469 this is the mass in kilograms, and the velocity 130 00:05:51,469 --> 00:05:53,327 was in meters over seconds, 131 00:05:53,327 --> 00:05:55,927 so kilograms times meters per second. 132 00:05:55,927 --> 00:05:59,968 Alright, so this is the uncertainty associated 133 00:05:59,968 --> 00:06:02,150 with the momentum of our electrons. 134 00:06:02,150 --> 00:06:06,817 Let's plug it in to our uncertainty principle here: 135 00:06:06,817 --> 00:06:10,463 we had the uncertainty in the position of the electron, 136 00:06:10,463 --> 00:06:13,644 times the uncertainty in the momentum of the electron 137 00:06:13,644 --> 00:06:15,640 must be greater than or equal to 138 00:06:15,640 --> 00:06:19,379 Planck's Constant divided by four pi. 139 00:06:19,379 --> 00:06:22,235 So we can take that uncertainty in the momentum 140 00:06:22,235 --> 00:06:24,858 and we can plug it in here. 141 00:06:24,858 --> 00:06:27,180 So now we have the uncertainty in the position 142 00:06:27,180 --> 00:06:30,524 of the electron in the ground state of the hydrogen atom 143 00:06:30,524 --> 00:06:34,819 times 2.0 times 10 to the negative 25. 144 00:06:34,819 --> 00:06:37,977 This product must be greater than or equal to, 145 00:06:37,977 --> 00:06:42,977 Planck's Constant is 6.626 times 10 to the negative 34. 146 00:06:43,851 --> 00:06:48,851 Alright, divide that by four pi. 147 00:06:48,861 --> 00:06:52,100 So we could solve for the uncertainty in the position. 148 00:06:52,100 --> 00:06:56,140 So, Delta X must be greater than or equal to, 149 00:06:56,140 --> 00:06:58,927 let's go ahead and do that math. 150 00:06:58,927 --> 00:07:00,250 So we have Planck's Constant, 151 00:07:00,250 --> 00:07:05,250 6.626 times 10 to the negative 34, 152 00:07:06,763 --> 00:07:11,763 we divide that by 4, we need to divide that also by pi, 153 00:07:13,706 --> 00:07:15,958 and then we need to divide by the 154 00:07:15,958 --> 00:07:17,746 uncertainty in the momentum. 155 00:07:17,746 --> 00:07:20,509 So we also need to divide by the uncertainty in momentum, 156 00:07:20,509 --> 00:07:25,509 that's 2.0 times 10 to the negative 25, 157 00:07:25,524 --> 00:07:30,524 and that gives us 2.6 times 10 to the negative 10. 158 00:07:30,632 --> 00:07:33,994 So the uncertainty in the position must be greater than 159 00:07:33,994 --> 00:07:38,994 or equal to 2.6 times 10 to the negative 10 160 00:07:39,776 --> 00:07:41,378 and if you worked our your units, 161 00:07:41,378 --> 00:07:43,514 you would get meters for this. 162 00:07:43,514 --> 00:07:46,068 So the uncertainty in the position must be 163 00:07:46,068 --> 00:07:46,950 greater than or equal to 164 00:07:46,950 --> 00:07:49,458 2.6 times 10 to the negative 10 meters. 165 00:07:49,458 --> 00:07:53,219 Let's go back up here to the picture of the hydrogen atom. 166 00:07:53,219 --> 00:07:55,774 2.6 times 10 to the negative 10 meters, 167 00:07:55,774 --> 00:08:00,464 that's greater than the diameter of our hydrogen atom, 168 00:08:00,464 --> 00:08:04,597 so the uncertainty would be greater than this diameter. 169 00:08:04,597 --> 00:08:07,406 So the uncertainty in the position would be greater than 170 00:08:07,406 --> 00:08:10,309 the diameter of the hydrogen atom, using the Bohr model. 171 00:08:10,309 --> 00:08:12,097 So the Bohr model is wrong. 172 00:08:12,097 --> 00:08:15,603 It's telling us we know the electron is orbiting the nucleus 173 00:08:15,603 --> 00:08:18,737 at a certain radius, and it's moving at a certain velocity. 174 00:08:18,737 --> 00:08:21,523 The uncertainty principle says this isn't true. 175 00:08:21,523 --> 00:08:24,054 If we know the velocity fairly accurately, 176 00:08:24,054 --> 00:08:27,050 we don't know the position of the electron, 177 00:08:27,050 --> 00:08:28,257 the position of the electron is greater than 178 00:08:28,257 --> 00:08:30,440 the diameter, according to the Bohr model. 179 00:08:30,440 --> 00:08:34,445 So this just one reason why the Bohr model is wrong. 180 00:08:34,445 --> 00:08:36,303 But again, we keep the Bohr model around 181 00:08:36,303 --> 00:08:38,462 because it is useful as a simple model 182 00:08:38,462 --> 00:08:40,597 when you're just starting to get into chemistry. 183 00:08:40,597 --> 00:08:44,313 But this concept of the uncertainty principle goes 184 00:08:44,313 --> 00:08:46,635 against our natural intuitions. 185 00:08:46,635 --> 00:08:48,841 So our every day life doesn't really give us 186 00:08:48,841 --> 00:08:51,697 any experience with the uncertainty principle. 187 00:08:51,697 --> 00:08:53,995 For example, if we had a particle, 188 00:08:53,995 --> 00:08:55,783 let's make it a much bigger particle here, 189 00:08:55,783 --> 00:08:58,036 so a much bigger particle than an electron, 190 00:08:58,036 --> 00:09:00,334 so something that we can actually see in our real life, 191 00:09:00,334 --> 00:09:03,028 and so this has a much bigger mass, 192 00:09:03,028 --> 00:09:04,839 and moving with some velocity, 193 00:09:04,839 --> 00:09:07,718 logic tells us we can figure out pretty accurately 194 00:09:07,718 --> 00:09:09,831 where the position of that object is, 195 00:09:09,831 --> 00:09:11,479 and we can probably, pretty accurately, 196 00:09:11,479 --> 00:09:14,475 figure out the velocity, and so we know the momentum. 197 00:09:14,475 --> 00:09:16,773 And, that's true. 198 00:09:16,773 --> 00:09:19,374 We do know these things fairly accurately. 199 00:09:19,374 --> 00:09:21,255 But if you did a calculation using 200 00:09:21,255 --> 00:09:24,494 the uncertainty principle, so if you plugged in some 201 00:09:24,494 --> 00:09:26,700 different numbers, like if you increased the mass, 202 00:09:26,700 --> 00:09:29,265 so instead of 9.11 times 10 to the negative 31st, 203 00:09:29,265 --> 00:09:31,471 let's say you're using nine kilograms, 204 00:09:31,471 --> 00:09:34,420 and you plugged in some velocity here, 205 00:09:34,420 --> 00:09:37,114 and you solved for the uncertainty in the position, 206 00:09:37,114 --> 00:09:38,692 you're gonna get an uncertainty in the position 207 00:09:38,692 --> 00:09:40,341 that's extremely small. 208 00:09:40,341 --> 00:09:42,616 So you don't really notice those things 209 00:09:42,616 --> 00:09:44,613 on a macroscopic scale. 210 00:09:44,613 --> 00:09:47,771 You only notice them when you think about the atomic scale. 211 00:09:47,771 --> 00:09:50,627 And so that's why this isn't really an intuitive concept. 212 00:09:50,627 --> 00:09:52,299 Same idea with quantum mechanics: 213 00:09:52,299 --> 00:09:53,419 quantum mechanics is something 214 00:09:53,419 --> 00:09:56,507 that makes absolutely no sense when you first encounter it. 215 00:09:56,507 --> 00:09:58,574 You have no experience with quantum mechanics 216 00:09:58,574 --> 00:10:00,780 in your daily life, it just doesn't make any sense. 217 00:10:00,780 --> 00:10:02,359 You don't see these sorts of things. 218 00:10:02,359 --> 00:10:05,006 So this is just showing you an application 219 00:10:05,006 --> 00:10:07,002 at an atomic scale. 220 00:10:07,002 --> 00:10:09,557 Again, this is the uncertainty principle. 221 00:10:09,557 --> 00:10:11,832 We'll get more into quantum mechanics, 222 00:10:11,832 --> 00:10:13,434 and how quantum mechanics affects 223 00:10:13,434 --> 00:00:00,000 electrons and atoms in the next few videos.