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Find Mass-to-Charge Ratio in Spectrometer

Patrick Ford
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Hey, I saw some questions. We'll ask you to find the mass to charge ratio of particles going through a massive trauma. And that's what we're gonna do here. So let me show you eso Here's a mass spectrometers, velocity selector, electric field of magnitude 20. So remember, you get accelerated and then you go through a velocity selector V S that's going to have an electric field and we're telling you, hear that? That is a magnitude of 20 it says, when a certain charges accelerated to a constant 30. So it gets accelerated over here. It goes through the little hole and then it's now going to move here with a constant 30. It collides 40 m away from the velocity selector. What does that look like? Well, um, it means that it's gonna curve this way, and it's going to hit this wall here at a distance, D equals 40 m, Remember? Also, the distance is twice the radius because you have radius and radius, which means if the distance is 40 this means that the radius is 20. And the reason we want to change it to radius is because our other equations or that one other equation we're gonna need here is in terms of radius and not in terms of distance. I drew it down even though it could have gone up. We don't actually know. We're not being given enough information to figure out which way this is going, but it doesn't matter. I just picked one for the sake of illustration. Okay, this question. I want to find the master charge ratio. Okay, master charge ratio, which is M over Q. By the way, If I hadn't told you that we were looking for em over Q, you could just interpret that from the question the mass to charge ratio. You would do this and say, Hey, I'm looking for this, which means you're not looking for a mark. You you wanna leave? This is a big unit and then solve it. So how the heck are we gonna do that when we got these three equations and one of them hopefully will work for us. Okay, So r equals actually start with the first one just to keep it in order, so Q que Delta V equals half him the square. By the way, this is a potential difference, or voltage and this is a velocity. Two different things. Thea, the equation is that V velocity equals C over B, and the other equation is that r equals M V over Q be okay, and we're looking for the ratio em over. Q. Luckily, this is actually really straightforward because if you look here, you'll find one of these equations as an M and a Q, and it's right here. And not only do they have it, they're already sitting next to each other, which is awesome. So all you gotta do is move stuff around in such a way that the end of the queue stay Exactly. They are. So we're gonna move the V to the other side. So I'm gonna get BR over the Do I have B? Yep. 12 p. No, I don't have be, um, got excited there for a second. Do I have are ours 20. Do I have the velocity? The velocity is 30 so we don't have the We gotta get it. Can we get be? This equation here seems to be it seems like it's gonna work, so v equals e Overbey. Therefore be is e over. V E is 20 electric field strength and the velocity is 30. So be is 0.67. Okay, 0.67. Tesla's. So that's what's going to go over here. Points 67 Tesla. And if you do all of this, you're going to get that. That ratio is 0. 44. The units are kilograms per cool. Okay, so that's how you could do this. Um, the second you got stuck here because you didn't have to be you just go to a different equation and you get it right. That's for this one. Let's get going.