WEBVTT 00:00:00.000 --> 00:00:02.840 This is College Physics Answers with Shaun Dychko. 00:00:03.462 --> 00:00:05.977 A lithium-bromide molecule 00:00:05.970 --> 00:00:09.634 oscillates with a frequency of 1.7 times 10 to the 13 hertz 00:00:09.908 --> 00:00:11.645 and our questions are - 00:00:11.640 --> 00:00:15.554 what is the energy difference between oscillator states? 00:00:15.980 --> 00:00:21.211 And then given that the oscillator has an energy of 1 electron volt in part (b), 00:00:21.291 --> 00:00:23.405 figure out which state that must be, 00:00:23.400 --> 00:00:25.794 what is the number, n, in other words? 00:00:27.420 --> 00:00:32.377 So we are told by equation [29.3] 00:00:32.605 --> 00:00:34.765 that the difference in 00:00:35.040 --> 00:00:38.365 consecutive energy states is Planck's constant 00:00:38.360 --> 00:00:40.937 times the frequency of the oscillation. 00:00:41.531 --> 00:00:45.737 So that's 4.14 times 10 to the minus 15 electron volt seconds 00:00:45.730 --> 00:00:48.320 times 1.7 times 10 to the 13 hertz, 00:00:48.320 --> 00:00:50.457 which gives an energy difference between 00:00:50.450 --> 00:00:54.297 states of 0.070 electron volts. 00:00:54.685 --> 00:00:57.885 And we chose this value for Planck's constant because we wanted 00:00:57.880 --> 00:00:59.988 to have our answer in electron volt units. 00:01:01.931 --> 00:01:04.731 Now in part (b), we have to figure out, what is 00:01:04.730 --> 00:01:07.417 n in this formula, this is [29.1]. 00:01:07.771 --> 00:01:10.845 And we'll solve it for n by first multiplying 00:01:10.840 --> 00:01:13.302 through by hf into the brackets 00:01:13.300 --> 00:01:17.988 and so we have nhf plus one-half times hf 00:01:17.980 --> 00:01:19.771 equals the energy 00:01:19.770 --> 00:01:23.200 and we'll switch the sides around to have the unknown—n—on the left. 00:01:24.365 --> 00:01:28.411 Then subtract hf over 2 from both sides 00:01:29.542 --> 00:01:31.234 and you get this line here 00:01:31.462 --> 00:01:35.988 and then divide both sides by Planck's constant times frequency 00:01:39.268 --> 00:01:40.902 and you end up with this line here. 00:01:41.080 --> 00:01:46.537 These hf's cancel there leaving hf in the denominator below energy. 00:01:46.948 --> 00:01:51.097 So the nth state is energy 00:01:51.090 --> 00:01:53.977 divided by Planck's constant times frequency minus a half. 00:01:54.205 --> 00:01:55.428 So that's 1 electron volt 00:01:55.420 --> 00:01:58.377 divided by Planck's constant, using electron volt units, 00:01:58.914 --> 00:02:02.685 in order to match with the electron volt units in the numerator. 00:02:03.165 --> 00:02:06.228 And multiply by the frequency 00:02:06.220 --> 00:02:11.154 minus a half gives us 13.7 and the closest whole number to that is 14; 00:02:11.150 --> 00:02:14.102 n has to be a whole number, which is to say it can be 1 00:02:14.100 --> 00:02:17.222 0, 1, 2, 3, and so on.