WEBVTT 00:00:00.000 --> 00:00:02.840 This is College Physics Answers with Shaun Dychko. 00:00:03.070 --> 00:00:05.840 The charge to mass ratio for an electron 00:00:05.840 --> 00:00:10.220 1.76 times 10 to the 11 coulombs for every kilogram 00:00:10.560 --> 00:00:16.570 and for protons, it's 9.58 times 10 to the 7 coulombs for every kilogram. 00:00:16.570 --> 00:00:19.870 So you need fewer charges of protons 00:00:19.870 --> 00:00:23.970 to make up a kilogram because protons are more massive 00:00:23.970 --> 00:00:26.410 so you need fewer of the protons. 00:00:28.130 --> 00:00:31.010 So the charge on each is the same 00:00:31.010 --> 00:00:35.080 so we'll say q subscript p for proton and q subscript e for electron; 00:00:35.080 --> 00:00:36.180 we'll just call it q 00:00:36.180 --> 00:00:38.780 because the elementary charge is the same for each. 00:00:39.570 --> 00:00:42.400 Now we want to find out what the mass ratio is 00:00:42.400 --> 00:00:44.990 of the proton versus the electron 00:00:44.990 --> 00:00:48.010 and using these charge to mass ratios. 00:00:48.510 --> 00:00:50.220 So ultimately what we want is 00:00:50.220 --> 00:00:53.180 the mass of the proton divided by mass of the electron 00:00:53.180 --> 00:00:55.810 that's the mass ratio of the two particles. 00:00:56.610 --> 00:01:00.770 So we'll rewrite this charge to mass ratio for the proton 00:01:00.770 --> 00:01:03.400 as mass of the proton divided by 00:01:03.400 --> 00:01:06.270 charge of the proton; we are taking the reciprocal of this in other words 00:01:06.270 --> 00:01:12.240 because this is really a fraction— 9.58 times 10 to the 7 coulombs 00:01:12.240 --> 00:01:14.450 for every 1 kilogram— 00:01:14.720 --> 00:01:16.570 and we can take the reciprocal of it 00:01:16.570 --> 00:01:19.220 and instead write it as 1 kilogram 00:01:19.220 --> 00:01:23.040 for every 9.58 times 10 to the 7 coulombs. 00:01:23.960 --> 00:01:25.550 So that's what we are doing here. 00:01:25.550 --> 00:01:29.790 We are taking the reciprocal of the charge to mass ratio of the proton 00:01:29.790 --> 00:01:33.070 and then substituted the q in place of q p 00:01:33.070 --> 00:01:36.170 because the elementary charge is the same for a proton and an electron. 00:01:36.560 --> 00:01:39.200 And then we are multiplying by 00:01:39.200 --> 00:01:42.250 the charge to mass ratio for the electron 00:01:42.250 --> 00:01:47.300 and noticing that the charges cancel leaving us with the mass ratio. 00:01:48.510 --> 00:01:51.700 So we can fill in each of these fractions; 00:01:51.700 --> 00:01:56.830 here's the first, the reciprocal of the charge to mass ratio for the proton 00:01:57.120 --> 00:02:00.830 and then here's the charge to mass ratio for the electron 00:02:00.830 --> 00:02:04.260 and this works out to 1840 00:02:04.260 --> 00:02:09.820 and so the proton is 1840 times as massive as the electron.