1 00:00:01,558 --> 00:00:02,400 - [Voiceover] I'm sure that most of you 2 00:00:02,400 --> 00:00:04,366 know the famous story of Isaac Newton 3 00:00:04,366 --> 00:00:05,866 where he took a narrow beam of light 4 00:00:05,866 --> 00:00:08,566 and he put that narrow beam of light through a prism 5 00:00:08,566 --> 00:00:10,401 and the prism separated the white light 6 00:00:10,401 --> 00:00:12,633 into all the different colors of the rainbow. 7 00:00:12,633 --> 00:00:13,833 And so if you did this experiment, 8 00:00:13,833 --> 00:00:16,274 you might see something like this rectangle up here 9 00:00:16,274 --> 00:00:18,866 so all of these different colors of the rainbow 10 00:00:18,866 --> 00:00:22,733 and I'm gonna call this a continuous spectrum. 11 00:00:22,733 --> 00:00:24,333 It's continuous because you see all 12 00:00:24,333 --> 00:00:26,333 these colors right next to each other. 13 00:00:26,333 --> 00:00:28,100 So they kind of blend together. 14 00:00:28,100 --> 00:00:30,033 So that's a continuous spectrum 15 00:00:30,033 --> 00:00:32,232 If you did this similar thing with hydrogen, 16 00:00:32,232 --> 00:00:34,766 you don't see a continuous spectrum. 17 00:00:34,766 --> 00:00:36,500 So, if you passed a current through 18 00:00:36,500 --> 00:00:38,933 a tube containing hydrogen gas, 19 00:00:38,933 --> 00:00:41,100 the electrons in the hydrogen atoms 20 00:00:41,100 --> 00:00:43,133 are going to absorb energy 21 00:00:43,133 --> 00:00:46,033 and jump up to a higher energy level. 22 00:00:46,033 --> 00:00:49,000 When those electrons fall down to a lower energy level 23 00:00:49,000 --> 00:00:51,466 they emit light and so we talked 24 00:00:51,466 --> 00:00:53,165 about this in the last video. 25 00:00:53,165 --> 00:00:55,209 This is the concept of emission. 26 00:00:55,209 --> 00:00:57,912 If you use something like a prism or a defraction 27 00:00:57,912 --> 00:01:00,653 grading to separate out the light, 28 00:01:00,653 --> 00:01:02,789 for hydrogen, you don't get a continuous spectrum. 29 00:01:02,789 --> 00:01:05,366 You'd see these four lines of color. 30 00:01:05,366 --> 00:01:09,847 So, since you see lines, we call this a line spectrum. 31 00:01:09,847 --> 00:01:13,099 So this is the line spectrum for hydrogen. 32 00:01:13,099 --> 00:01:16,488 So you see one red line and it turns out that 33 00:01:16,488 --> 00:01:18,985 that red line has a wave length. 34 00:01:18,985 --> 00:01:23,443 That red light has a wave length of 656 nanometers. 35 00:01:23,443 --> 00:01:25,869 You'll also see a blue green line 36 00:01:25,869 --> 00:01:29,665 and so this has a wave length of 486 nanometers. 37 00:01:29,665 --> 00:01:32,706 A blue line, 434 nanometers, 38 00:01:32,706 --> 00:01:35,945 and a violet line at 410 nanometers. 39 00:01:35,945 --> 00:01:40,021 And so this emission spectrum is unique to hydrogen 40 00:01:40,021 --> 00:01:42,691 and so this is one way to identify elements. 41 00:01:42,691 --> 00:01:45,175 And so this is a pretty important thing. 42 00:01:45,175 --> 00:01:48,043 And since line spectrum are unique, 43 00:01:48,043 --> 00:01:49,772 this is pretty important to explain 44 00:01:49,772 --> 00:01:52,291 where those wavelengths come from. 45 00:01:52,291 --> 00:01:54,730 And we can do that by using the equation 46 00:01:54,730 --> 00:01:56,424 we derived in the previous video. 47 00:01:56,424 --> 00:02:00,116 So I call this equation the Balmer Rydberg equation. 48 00:02:00,116 --> 00:02:02,403 And you can see that one over lamda, 49 00:02:02,403 --> 00:02:05,804 lamda is the wavelength of light that's emitted, 50 00:02:05,804 --> 00:02:09,345 is equal to R, which is the Rydberg constant, 51 00:02:09,345 --> 00:02:13,106 times one over I squared, where I is talking 52 00:02:13,106 --> 00:02:15,870 about the lower energy level, 53 00:02:15,870 --> 00:02:18,471 minus one over J squared, where J is 54 00:02:18,471 --> 00:02:20,920 referring to the higher energy level. 55 00:02:20,920 --> 00:02:23,091 For example, let's say we were considering 56 00:02:23,091 --> 00:02:25,459 an excited electron that's falling 57 00:02:25,459 --> 00:02:28,640 from a higher energy level n is equal to three. 58 00:02:28,640 --> 00:02:29,511 So let me write this here. 59 00:02:29,511 --> 00:02:30,753 So we have an electron that's falling 60 00:02:30,753 --> 00:02:32,634 from n is equal to three down to 61 00:02:32,634 --> 00:02:35,920 a lower energy level, n is equal to two. 62 00:02:35,920 --> 00:02:37,905 All right, so it's going to emit light 63 00:02:37,905 --> 00:02:40,181 when it undergoes that transition. 64 00:02:40,181 --> 00:02:44,325 So let's look at a visual representation of this. 65 00:02:44,325 --> 00:02:45,462 Now let's see if we can calculate 66 00:02:45,462 --> 00:02:48,005 the wavelength of light that's emitted. 67 00:02:48,005 --> 00:02:49,723 All right, so if an electron is falling 68 00:02:49,723 --> 00:02:52,835 from n is equal to three to n is equal to two, 69 00:02:52,835 --> 00:02:54,252 I'm gonna go ahead and draw an electron here. 70 00:02:54,252 --> 00:02:55,912 So an electron is falling from n is equal 71 00:02:55,912 --> 00:02:59,221 to three energy level down to n is equal to two, 72 00:02:59,221 --> 00:03:02,345 and the difference in those two energy levels 73 00:03:02,345 --> 00:03:04,027 are that difference in energy is equal 74 00:03:04,027 --> 00:03:05,885 to the energy of the photon. 75 00:03:05,885 --> 00:03:07,405 And so that's how we calculated the 76 00:03:07,405 --> 00:03:10,599 Balmer Rydberg equation in the previous video. 77 00:03:10,599 --> 00:03:11,901 All right, let's go ahead and calculate 78 00:03:11,901 --> 00:03:13,989 the wavelength of light that's emitted 79 00:03:13,989 --> 00:03:15,603 when the electron falls from the third 80 00:03:15,603 --> 00:03:17,239 energy level to the second. 81 00:03:17,239 --> 00:03:20,037 So, we have one over lamda is equal 82 00:03:20,037 --> 00:03:23,137 to the Rydberg constant, as we saw in the 83 00:03:23,137 --> 00:03:26,260 previous video, is one point zero nine seven 84 00:03:26,260 --> 00:03:27,862 times ten to the seventh. 85 00:03:27,862 --> 00:03:31,043 The units would be one over meter, all right? 86 00:03:31,043 --> 00:03:32,807 One over I squared. 87 00:03:32,807 --> 00:03:37,255 So, I refers to the lower energy level, all right? 88 00:03:37,255 --> 00:03:41,097 So the lower energy level is when n is equal to two. 89 00:03:41,097 --> 00:03:46,097 So we plug in one over two squared. 90 00:03:46,275 --> 00:03:48,457 And then, from that, we're going to 91 00:03:48,457 --> 00:03:51,000 subtract one over the higher energy level. 92 00:03:51,000 --> 00:03:52,893 That's n is equal to three, right? 93 00:03:52,893 --> 00:03:55,133 So this would be one over three squared. 94 00:03:55,133 --> 00:03:59,743 So one over two squared minus one over three squared. 95 00:03:59,743 --> 00:04:00,451 Let's go ahead and get out 96 00:04:00,451 --> 00:04:03,574 the calculator and let's do that math. 97 00:04:03,574 --> 00:04:06,407 So one over two squared, that's one fourth, 98 00:04:06,407 --> 00:04:11,260 so that's point two five, minus one over 99 00:04:11,260 --> 00:04:13,083 three squared, so that's one over nine. 100 00:04:13,083 --> 00:04:15,903 So, one fourth minus one ninth gives us 101 00:04:15,903 --> 00:04:18,880 point one three eight repeating. 102 00:04:18,880 --> 00:04:20,337 And if we multiply that number by the 103 00:04:20,338 --> 00:04:23,658 Rydberg constant, right, that's one point 104 00:04:23,658 --> 00:04:28,658 zero nine seven times ten to the seventh, 105 00:04:30,090 --> 00:04:34,977 we get one five two three six one one. 106 00:04:34,977 --> 00:04:36,290 So let me go ahead and write that down. 107 00:04:36,290 --> 00:04:40,655 So now we have one over lamda is equal to 108 00:04:40,655 --> 00:04:45,655 one five two three six one one. 109 00:04:45,730 --> 00:04:48,154 So to solve for lamda, all we need to 110 00:04:48,154 --> 00:04:50,975 do is take one over that number. 111 00:04:50,975 --> 00:04:53,773 So one over that number gives us 112 00:04:53,773 --> 00:04:57,709 six point five six times ten to the negative seven 113 00:04:57,709 --> 00:04:59,369 and that would now be in meters. 114 00:04:59,369 --> 00:05:04,233 So we have lamda is equal to six point five 115 00:05:04,233 --> 00:05:09,233 six times ten to the negative seventh meters. 116 00:05:09,434 --> 00:05:11,872 So let's convert that into, let's go like this, 117 00:05:11,872 --> 00:05:15,485 let's go 656, that's the same thing 118 00:05:15,485 --> 00:05:19,164 as 656 times ten to the negative ninth meters. 119 00:05:19,164 --> 00:05:22,240 And so that's 656 nanometers. 120 00:05:22,240 --> 00:05:27,104 656 nanometers, and that should sound familiar to you. 121 00:05:27,104 --> 00:05:28,383 All right, so let's go back up here 122 00:05:28,383 --> 00:05:32,817 and see where we've seen 656 nanometers before. 123 00:05:32,817 --> 00:05:35,580 656 nanometers is the wavelength 124 00:05:35,580 --> 00:05:38,343 of this red line right here. 125 00:05:38,343 --> 00:05:42,418 So, that red line represents the light 126 00:05:42,418 --> 00:05:44,741 that's emitted when an electron falls 127 00:05:44,741 --> 00:05:48,269 from the third energy level down to the second energy level. 128 00:05:48,269 --> 00:05:50,150 So let's go back down to here 129 00:05:50,150 --> 00:05:52,031 and let's go ahead and show that. 130 00:05:52,031 --> 00:05:54,365 So we can say that a photon, right, 131 00:05:54,365 --> 00:05:57,348 a photon of red light is given off 132 00:05:57,348 --> 00:05:59,089 as the electron falls from the third 133 00:05:59,089 --> 00:06:01,667 energy level to the second energy level. 134 00:06:01,667 --> 00:06:03,571 So that explains the red line in the 135 00:06:03,571 --> 00:06:05,347 line spectrum of hydrogen. 136 00:06:05,347 --> 00:06:08,388 So how can we explain these other lines that we see, right? 137 00:06:08,388 --> 00:06:10,375 So we have these other lines over here, right? 138 00:06:10,375 --> 00:06:11,918 We have this blue green one, 139 00:06:11,918 --> 00:06:14,600 this blue one, and this violet one. 140 00:06:14,600 --> 00:06:16,632 So if you do the math, you can use the 141 00:06:16,632 --> 00:06:19,499 Balmer Rydberg equation or you can do this 142 00:06:19,499 --> 00:06:21,229 and you can plug in some more numbers 143 00:06:21,229 --> 00:06:23,539 and you can calculate those values. 144 00:06:23,539 --> 00:06:26,072 So those are electrons falling from 145 00:06:26,072 --> 00:06:29,413 higher energy levels down to the second energy level. 146 00:06:29,413 --> 00:06:32,827 So let's go ahead and draw them on our diagram, here. 147 00:06:32,827 --> 00:06:34,789 So, let's say an electron fell from the 148 00:06:34,789 --> 00:06:38,307 fourth energy level down to the second. 149 00:06:38,307 --> 00:06:39,723 All right, so that energy difference, 150 00:06:39,723 --> 00:06:41,627 if you do the calculation, that turns 151 00:06:41,627 --> 00:06:45,923 out to be the blue green line in your line spectrum. 152 00:06:45,923 --> 00:06:48,592 So, I'll represent the light emitted like that. 153 00:06:48,592 --> 00:06:51,390 And if an electron fell from the fifth energy 154 00:06:51,390 --> 00:06:53,945 level down to the second energy level, 155 00:06:53,945 --> 00:06:56,104 that corresponds to the blue line 156 00:06:56,104 --> 00:06:58,170 that you see on the line spectrum. 157 00:06:58,170 --> 00:07:01,166 And then, finally, the violet line must be 158 00:07:01,166 --> 00:07:04,289 the transition from the sixth energy level 159 00:07:04,289 --> 00:07:08,409 down to the second, so let's go ahead and draw that in. 160 00:07:08,409 --> 00:07:13,122 And so now we have a way of explaining 161 00:07:13,122 --> 00:07:16,711 this line spectrum of hydrogen that we can observe. 162 00:07:16,711 --> 00:07:18,882 And since we calculated this Balmer Rydberg 163 00:07:18,882 --> 00:07:21,389 equation using the Bohr equation, 164 00:07:21,389 --> 00:07:23,247 using the Bohr model, I should say, 165 00:07:23,247 --> 00:07:25,767 the Bohr model is what allowed us to do this. 166 00:07:25,767 --> 00:07:27,890 So the Bohr model explains these different 167 00:07:27,890 --> 00:07:29,841 energy levels that we see. 168 00:07:29,841 --> 00:07:32,848 So when you look at the line spectrum of hydrogen, 169 00:07:32,848 --> 00:07:35,484 it's kind of like you're seeing energy levels. 170 00:07:35,484 --> 00:07:36,981 At least that's how I like to think about it 171 00:07:36,981 --> 00:07:38,688 'cause you're, it's the only real way 172 00:07:38,688 --> 00:07:41,045 you can see the difference of energy. 173 00:07:41,045 --> 00:07:43,448 All right, so energy is quantized. 174 00:07:43,448 --> 00:07:45,630 We call this the Balmer series. 175 00:07:45,630 --> 00:07:50,630 So this is called the Balmer series for hydrogen. 176 00:07:52,886 --> 00:07:54,895 But there are different transitions that you could do. 177 00:07:54,895 --> 00:07:58,157 For example, let's think about an electron 178 00:07:58,157 --> 00:08:01,919 going from the second energy level to the first. 179 00:08:01,919 --> 00:08:04,804 All right, so let's get some more room here 180 00:08:04,804 --> 00:08:07,879 If I drew a line here, again, not drawn to scale. 181 00:08:07,879 --> 00:08:09,621 Think about an electron going from the 182 00:08:09,621 --> 00:08:12,256 second energy level down to the first. 183 00:08:12,256 --> 00:08:14,857 So from n is equal to two to n is equal to one. 184 00:08:14,857 --> 00:08:17,120 Let's use our equation and let's 185 00:08:17,120 --> 00:08:19,419 calculate that wavelength next. 186 00:08:19,419 --> 00:08:21,973 So this would be one over lamda 187 00:08:21,973 --> 00:08:24,818 is equal to the Rydberg constant, one 188 00:08:24,818 --> 00:08:28,753 point zero nine seven times ten to the seventh, 189 00:08:28,753 --> 00:08:31,237 that's one over meters, and then we're 190 00:08:31,237 --> 00:08:33,928 going from the second energy level to the first, 191 00:08:33,928 --> 00:08:36,764 so this would be one over the lower energy level squared 192 00:08:36,764 --> 00:08:40,398 so n is equal to one squared minus 193 00:08:40,398 --> 00:08:43,417 one over two squared. 194 00:08:43,417 --> 00:08:45,518 All right, so let's get some more room, 195 00:08:45,518 --> 00:08:46,992 get out the calculator here. 196 00:08:46,992 --> 00:08:50,695 So, one over one squared is just one, 197 00:08:50,695 --> 00:08:54,318 minus one fourth, so that's point seven five 198 00:08:54,318 --> 00:08:58,241 and so if we take point seven five of the Rydberg constant, 199 00:08:58,241 --> 00:08:59,112 let's go ahead and do that. 200 00:08:59,112 --> 00:09:04,112 So one point zero nine seven times ten 201 00:09:04,423 --> 00:09:07,343 to the seventh is our Rydberg constant. 202 00:09:07,343 --> 00:09:10,756 Then multiply that by point seven five, right? 203 00:09:10,756 --> 00:09:13,671 So three fourths, then we should get that number there. 204 00:09:13,671 --> 00:09:17,827 So that's eight two two seven five zero zero. 205 00:09:17,827 --> 00:09:18,814 So let's write that down. 206 00:09:18,814 --> 00:09:21,693 One over the wavelength is equal to 207 00:09:21,693 --> 00:09:26,693 eight two two seven five zero. 208 00:09:26,704 --> 00:09:28,357 So to solve for that wavelength, 209 00:09:28,357 --> 00:09:31,109 just take one divided by that number 210 00:09:31,109 --> 00:09:33,443 and that gives you one point two one 211 00:09:33,443 --> 00:09:36,624 times ten to the negative seven and that'd be in meters. 212 00:09:36,624 --> 00:09:40,699 So the wavelength here is equal to one point, 213 00:09:40,699 --> 00:09:42,024 let me see what that was again. 214 00:09:42,024 --> 00:09:44,067 One point two one five. 215 00:09:44,067 --> 00:09:48,268 One point two one five times ten 216 00:09:48,268 --> 00:09:50,625 to the negative seventh meters. 217 00:09:50,625 --> 00:09:53,121 And so if you move this over two, right, 218 00:09:53,121 --> 00:09:56,708 that's 122 nanometers. 219 00:09:56,708 --> 00:10:00,644 So this is 122 nanometers, but this 220 00:10:00,644 --> 00:10:02,768 is not a wavelength that we can see. 221 00:10:02,768 --> 00:10:06,960 So 122 nanometers, right, that falls into 222 00:10:06,960 --> 00:10:10,384 the UV region, the ultraviolet region, 223 00:10:10,384 --> 00:10:11,499 so we can't see that. 224 00:10:11,499 --> 00:10:14,816 We can see the ones in the visible spectrum only. 225 00:10:14,816 --> 00:10:18,603 And so this will represent a line in a different series 226 00:10:18,603 --> 00:10:21,577 and you can use the Balmer Rydberg equation 227 00:10:21,577 --> 00:10:23,363 to calculate all the other possible 228 00:10:23,363 --> 00:10:25,337 transitions for hydrogen and 229 00:10:25,337 --> 00:10:27,056 that's beyond the scope of this video. 230 00:10:27,056 --> 00:10:28,994 So, here, I just wanted to show you that 231 00:10:28,994 --> 00:10:31,514 the emission spectrum of hydrogen 232 00:10:31,514 --> 00:10:35,635 can be explained using the Balmer Rydberg equation 233 00:10:35,635 --> 00:10:39,478 which we derived using the Bohr model of the hydrogen atom. 234 00:10:39,478 --> 00:10:41,160 So even thought the Bohr model of the hydrogen 235 00:10:41,160 --> 00:10:45,317 atom is not reality, it does allow us to figure 236 00:10:45,317 --> 00:00:00,000 some things out and to realize that energy is quantized.