11.5 Millikan's Oil Drop

Ok, today we're gonna do an application of charge plates, and we're gonna talk about this later on in later units, but it applies well to this part of the course now, so we'll talk about it now. We'll come back to it again later on with more details, but what happened in 1909? Robert Millikan came up with an experiment, and his goal was to try to figure out what the charge of an electron is. He actually found out quite a bit of information from his famous experiment. So, what he did basically was he took charge plates. He had two charged plates, and he drilled a hole in the top one. Then, what he did was he would spray fine drops of oil. So, he had like a kind of perfume bottle-type sprayer. Basically, what he would do is he'd spray oil in, and what he thought of as he said, "Well, we can charge these oil droplets." Just by friction and so on, he would get the droplets to gain a negative charge. So, what he did was he thought, "Well, if I can get these droplets to fall between the plates, I can actually create an electric field and a gravitational field." He just sort of sprayed a mist of droplets around the top plate, and then some of them, by chance, would fall through the hole. Okay, so then he'd get this electrically negative charged oil droplet in between the positive and negative plates. So, what he did then was he looked at if we had this negative plate and we got this negative charge on the bottom and positive on the top. We got this negatively charged oil droplet. We would know that gravity would pull him to the bottom, but if they were negatively charged, then they would repel upwards. So then, gravity's pulling... It down, but the electric force is pushing it up. So, then his logic was that while these two things actually should balance out, in this case, the oil droplet should have gravity going one way and the electric force going the other way. So, those two forces balance. Then the oil droplet would float, and that's exactly what Milliken did. He sprayed them randomly, and anytime he got a negative droplet to go inside the hole, he would adjust the voltage to try to see if he could get it to float. Because those two are equal, what we're really saying is that our electric force equals gravity. We know that the electric force is equal to $Q$ times the electric field, and gravity is equal to mass times gravity. We can change the electric field to voltage over distance, and that's it. So basically, what he tried to work with was mass times gravity times the distance between the plates, divided. By voltage, he could have these oil droplets. The idea was, could he figure out the charge on the droplet just by rearranging these formulas? So he did, but the hard part was how did he figure out the mass of the droplet? Right, with gravity we know, 9:21 the distance between the plates, he could measure the voltage he could change, so that was good. But the only problem is, he didn't know how to measure the mass of the droplets. So he spent a lot of time trying to figure it out. So, in when these things would float, he looked through a little telescope. And what he did is he had a CH line, so if he saw that an oil droplet was the size of the lines, he could calculate the radius and the diameter of the oil droplets. He could infer the volume and he used the density of the mineral oil. And he could then calculate the mass. So it was a pretty complicated way to measure the mass of the oil droplet but he got it to work. So from there, Pauly then had to do was use. That Q formula is used to calculate the charge on the oil droplet. The formula is mass (measured gravity times distance between the plates) divided by voltage. One interesting thing that was observed during this experiment is that every time it was conducted, the charge on the droplet was always a multiple of 1.6 to the power of negative nineteen. For example, if the droplet was small and the voltage was low, the charge would be 1.6 to the power of negative nineteen. If the droplet was larger or the voltage was higher, the charge would be a multiple of this value such as two electrons (3.2), four electrons (6.4), or even one hundred electrons (160). Through this process, the charge of the electron was determined. Once the charge was known, the formula was rearranged and solved. It was done by Robert A. Millikan, who is famous for coming up with the idea. The basic charge is 1.6 x 10^-19 coulombs, and using the formula he derived, he calculated the mass of the electron as 9.11 x 10^-31 kilograms. The formula is basically QV over gravity times distance. This is how he determined the mass of the electron, and the number he obtained is very close to the value we use today. Let's now do an example. It's a basic one. We have an oil droplet floating, and the question is how many electrons are on this oil droplet. There's an electric force pushing it up and gravity pulling it down, so we have QE equals mg, where Q is the charge, V is the voltage, E is the electric field, m is the mass, and g is the acceleration due to gravity. Remember, voltage is measured in volts and distance is measured in meters. So, the question is: what is our charge (q) in terms of mass (m), gravitational acceleration (g), and distance between the plates (d)? To find the charge, we can use the equation q = mgd / V. Let's plug in the values: m = mass,g = gravitational acceleration,d = distance between the plates,V = voltage. In this case, we have a mass of 0.095 grams, which is equivalent to 0.000095 kilograms. The distance between the plates is 0.0095 meters. The voltage is 340 volts. So, we can calculate the charge as follows: q = (0.000095 kg) * (9.8 m/s^2) * (0.0095 m) / 340 V. Simplifying this expression, we get: q = 9.05 x 10^-8 coulombs. Now, let's consider an oil droplet with a charge is 9.25. We know that each electron has a charge of 1.6 x 10^-19 coulombs. To determine the number of electrons, we can divide the charge by the charge of a single electron: Number of electrons = 9.25 / (1.6 x 10^-19). So, the number of electrons is approximately: 5.78 x 10^18 electrons. Those out and we're done. The question is, 9 divided by 1.6. We get an answer of 5.6. It doesn't make sense to have part of an electron, so we round it to the nearest whole number. In this case, we'd say 6 electrons. The oil droplet has 6 electrons on it to be able to float in that sort of charged plate situation. Okay, so they're pretty easy questions. There's one on the review sheet that I gave you that talks about floating the oil droplets. All you have to do is balance your electric force with gravity. That's all for today.