15.1 Thomson Model

Okay, today's lesson, we're gonna look at starting our new unit, which is on nuclear physics. The first chapter that we're gonna look at is dealing with the atomic structure and different models that occurred over time to sort of explain how the atom and electrons are arranged. We're gonna go back to J.J. Thompson for the first model, but before we get to that, the early theory about atoms came from John Dalton. He basically thought that atoms were solid pieces of matter that couldn't be broken down any further, and we often call it a billion billiard ball model, thinking like an atom that's like a pool ball that it is what it is, it's the size and shape, whatever it is, and nothing can be changed. Obviously, that's no longer true. And then we have Katie Thompson, the sort of the first key guy to just show that it was actually quite a bit different. Most of his work dealt with cathode ray tubes, which remember is just a tube with a Charge plate separation is a key concept in which we attempt to move charged particles across it. Most of Thompson's experiments focused on electricity, magnetism, and related topics. Through these experiments, we gained knowledge about electrons and charges. Some other researchers also worked on cathode ray tubes, but for now, we will solely focus on the contributions of JJ Thompson. Thompson conducted three experiments that brought about significant changes. Firstly, he attempted to separate negative charges from positive charges using electric and magnetic fields. However, he couldn't achieve this separation because we now understand that in a cathode ray situation, all the charges are electrons. It is the movement of electrons between positive and negative plates. Since separation was unsuccessful, Thompson deduced that when charges transitioned from a positive to a negative plate, the charges must be negatives. It had to be an electron, so he said, "Well, in these situations, and it's only electrons that are moving, so obviously we can't separate them from any positives." He then tried to see if he could deflect them in an electric field, and he proved that that works. So he took the electric charges that were traveling in the cathode ray tube and he saw that they deflected towards the positive plate. Therefore, once again, they had to be electrons. The last experiment was, could he get them to be deflected in a magnetic field as well? And he did that and basically saw that the electric force and the magnetic force could be balanced. So this diagram is a little small, hard to see, but let's zoom in a little bit. It was a physics experiment involving the movement of electrons. The researcher heated up the electrons and then accelerated them by sending them through a charged plate. After the electrons passed through the charge plate, they were subjected to an electric field. The negative plates were located at the bottom, and the positive plates were at the top, causing the electrons to move upwards due to the electric force. Additionally, a magnetic field was present, directed into the page, resulting in a downward magnetic force if the left hand rule was used. The researcher adjusted the electric and magnetic fields accordingly. The concept was that if only the electric field was present, the electron would move towards the positive plate and curve upwards. Conversely, if only the magnetic field was present at the bottom, the electron would move downwards. If both fields were present, they would partially cancel each other out. By setting the fields just right, the electron could be manipulated to move in a specific direction. Straight across. And it's that process that he basically used to figure out what the velocity of the electrons are. So, he took the electric force formulas (we know electric force is EQ) and he took magnetic force qvb that we used in the previous units, and he basically made those two forces equal to each other. Because if the two forces are balanced, our electron would go straight across. So, we get QE equals QV be. The Q's cancel, you can rearrange it, solve it for velocity, and we get electric field divided by magnetic field. So, that was his first key result - being able to figure out the velocity of the electron if the two fields were balanced. We often call that the velocity selective formula because he selects the electric and magnetic field and balance them, so that he ends up getting a velocity. So, he knew that it was just the electrons and he could figure out what speed they were going at. So this first example is just saying calculate the velocity. We just use the equation: electric field divided by the magnetic field. This will give us a velocity in meters per second. Now, we get an answer of 2.09 x 10^7, so quite fast. We're dealing with electrons moving about a tenth of the speed of light. Pretty quick electrons being accelerated here. After that, he then said, "Well, what happens if we take the electric field off? We only have the magnetic field." And if we remember from a previous unit, our four electrons were traveling that way, and our magnetic force is downwards. We know the electron will then travel in a... circular path due to that magnetic force, always pulling it inwards. So, in that case, we can take our magnetic force, qvv, and make it equal to the circular force, V squared over R. We can rearrange and solve it for whatever we want. But, back in Thompson's time, he didn't know the charge of the electron and he didn't know the mass of the electron. So, what he basically did was solve for both. He just said, well, let's solve it for charge-to-mass ratio. We know the velocity we just calculated in the previous example, we know the field, and we can calculate the radius easy enough. So, we just need to figure out what the charge-to-mass ratio is, and you call that the charge-to-mass ratio. Let's do this example: So, charge-to-mass would be B over B R. The first thing we need to do is figure out that velocity. This electric Field over magnetic field, we get 1.86 to the power of 4/5 and 0.80 to the power of -4. If we calculate that, we get an answer of 3.2 to the power of 7 meters per second. Now, we can plug that into our charged mass formula. So, 3.2 to the power of 7, divided by magnetic field again, and the radius which they tell us is 0.325. If we do that calculation, we get a charge-to-mass ratio of 1.7 to the power of 11. And that would be coulombs per kilogram, okay. So that's the number based on those calculations. Now, it says, "Actually, let's compare this to the accepted value." So we know now that the charge of an electron is 1.6 times 10 to the power of -19, and we know the mass of an electron is 9.11 times 10 to the power of -31. If we actually divide those out, we get 1.76 times 10 to the power of 11. So you can see the numbers are pretty much the same. So, after Thompson figured out the whole charged mass thing and identifying that it's electrons moving in a cathode ray, that was a pretty big deal. So what Thompson then concluded was that the electrons have to be separate, and he wasn't sure sort of how they would be. Separated. So basically, what he thought is that they must be pretty small and they must be pretty densely charged to be able to hold the charge. So then, what he thought of is that the electrons enter just randomly inside of a positive fluid or a positive chunk of material. So, we often call it the plum pudding model or chocolate chip cookie model, or anything like that where you kind of see the negatives are just randomly scattered throughout the positive material. We know this is wrong, but he was sort of the first to sort of identify that negatives and positive charges are separate within the atom. And that's all.