1

concept

## Mass Spectrometers

20m

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Hey, guys. So in this case, we're gonna talk about mass spectrometers, which are instruments used to measure mass. Now, this can be overwhelming at first because they're three different parts, and there are three different equations you can use. Um, but I will break it down, really? Simply for you. And hopefully, by the end of this video, agree with me that this is totally manageable. Let's check it out. All right, So, as I said, mass spec Trump mass spectrometers are instruments that measure mass of a known charge meaning that experimentally you would know your Q and be looking for em. Now, in a physics problem, you may actually be given the M and asked for a Q, right? Um, there are four steps to a mass spectrometer that you should know. I emerge the first two steps because they're pretty basic. So steps one and two are ionization and acceleration ionizing. Something means that you are adding or removing electrons so that it becomes either positively or negatively charged. And the reason you want to do this is because particles need to have charge on excess of elections or protons so that they actually fuel force eso that So you do ionization so that the particle the particles feel Ah, magnetic force and an electric force. If you if you don't have a charge, you don't feel those two forces. So right here you have something that's called Ayn Isar. So let's just draw that there and what it does. It's got some some particles chilling here, and somehow it magically strips them of electrons so that they become positively charged and then sort of shoots them in this direction so that these bunch of positive charges air hanging out over here. Okay, we're gonna do this with positive charges, but it could be with negative charges as well now, So that's ionization. We ionized them and then we throw them over here. Now they're going to get they're gonna go through acceleration. They're going to be accelerated through a potential difference, meaning you're gonna have a positive potential here in a negative potential here. Electric fields were created whenever you have a situation like this always going from high to low. So this is the direction of an electric field. Remember that positive charges fewer net force in the direction of the electric field. So these guys would be pushed this way by an electric force, which will result them results in them accelerating this way. By the way, the initial velocity here will be zero. Okay, I'm dropping a ton of information on you, but when we do an example, you see that this is pretty straightforward. Um, eso they're going to get over here with some sort of final velocity. Okay, so between here and here, they're actually going to have a constant velocity. Okay. Now, for this first part, the only equation need to know, um is you have one equation per part. Um, you remember that the work done on a charge as it moves through a potential difference is Q Delta V, where Delta is the potential difference between the two plates and that's typically given to you or you're asked to calculate it. Remember, Also, that work is also the change in kinetic energy. Okay, so because these two are both work, I could just say that one equals the other. Okay, so I can say that Q Delta V equals Delta K. Remember, Delta means change and Delta K is K final minus k initial, but this is almost always there. Probably always gonna be zero the initial velocity. So what you really end up with is the final kinetic energy, which is gonna be half M v Final Square. So this is the first equation that you have for this problem, and there's two more. Okay, now, if you don't want to remember all these letters, you could remember this part and sort of work your way there. So that's the first part. This thing, it's accelerated. It moves here with the constant speed, and now it's gonna go through what's called the velocity selector. So the second part is velocity selection through a velocity selector. And the idea is that you want a filter desired speeds. So let's talk about that. The only way to calculate the mass on a mass spectrometer is if you basically know everything else, and I'll show you this later. With the equations, you have to know everything else, meaning you have to know the velocity even to be able to calculate it. So what's gonna happen here is that these guys will have different masses. This is Mass one. This is mass to etcetera because they have different masses. They're gonna have different speeds here. And this is because of just basic F equals in May. Right? Acceleration is force over mass. So if you have different masses, you're gonna have different accelerations. Therefore, we're gonna have different speeds. But remember, we have to control the speeds. So what we're going to do is we're gonna make sure that all these charges run through this device so that we can get rid of the ones that are not the right speed. And the way you do this is by running them through an electric field again. Notice that this is going from positive to negative here. So there's an electric field that's pointing down. These are all positive charges. So when these charges air here, they're going to few a force this way. Force Electric. Okay. And they're going to get potentially deflected. But you want the right ones. You want the right ones to go straight through. Okay, so you want the You want the particles with the targets desired ideal speed to make it okay. You want them to make it all the way through the end and come out of the gate over here into this green area that we're gonna talk about. But if you have an election electric field here, they're gonna be pulled down. Which means we're gonna hit this wall. And that's bad news. Right? Slow ones. We're gonna hit it over here Fast one, we're gonna hit it over here. So what you do is you want to try to cancel that electric force with another force, and we're gonna try to cancel with the magnetic force. So over here, we're gonna try toe, have a magnetic force that cancels that electric force. So the next equation you can write is that f e equals F B. I think. Now let's expand this real quick Electric forces Q E and Magnetic Forces Q V b sign of data theano goal here between V and B is going to be 90. We'll talk about that. So this is just gonna go away, okay? I can cancel accuse, and I end up with this relationship here, which is that I can simplify or not simplify. I can make this more standard looking by moving to be around. So it's gonna look like this. This is the second equation that you can use or that you will need to use in a lot of these questions. V equals E over. Be Okay, So let's talk about the direction of this thing. So I have a positive charge, someone to use the right hand rule, write with my right hand, and I want the force to be up. How do we get the force to be up? Well, my palm has to be going up because this is force. So it's something like this, right? Something like this or something like this. Well, it's actually be this orientation because I want my velocity to be going to the right if you look in the diagram, right. So velocity to the right force up means that my hand is going away from me and into the page, right? Don't just look at the video. Do this yourself away from you into the page. So that means that to accomplish this cancelation of forces, my magnetic field needs to be into the page here. Okay, so that's the direction. Now, if you look at this equation, this equation ties E b and V. And the idea is that this on Lee is going to cancel the charges that are going to have the target speed, Because if you have a different speed if you look at FB FB equals Q V B. If you have the wrong speed, you're gonna have the wrong force. That isn't going to exactly cancel E. So what you're gonna end up doing is you're gonna either hit over here hit over here, right? So this is sort of a filter and Onley the forces. Only the particles with the right speed will make it over here. Okay, now we're gonna get to the last part when you get here. The way that these devices are built is that not only their electric and magnetic fields here, um, inside of the velocity selector. There's also the same exact magnetic field out here into the deflection area. Okay, now, what's gonna happen that's a little bit different. Here is when you come out of the gate here, right, you still have the magnetic force because you still have a magnetic fields, but you no longer have electric force. So I want you to write it and then scratch it out. You no longer have electric force because there's no longer an electric fields right you only have that between the parallel plates. So what happens is you are now going to move in a struck Euller, um, path like this. And that's a terrible semicircle. That's pretty good. So remember, if you're going into if you have, if you are charged moving into a constant magnetic field, you have circular motion, okay? And this circular motion is going to have a radius R. And you may remember our circular motion equation, which is the third equation we're going to use, Which is that our equals M V over Q B. We talked about this in the previous video. You have to memorize that equation, not just for those simpler problems, but also because you're gonna need it here. Okay, One last thing that I wanna mention about equations is that sometimes you were given or asked for, not the radius, but this distance Here. Okay, this this and I'm gonna try it over here, and hopefully you see that this distance is just one radius. Two radius. Okay, so I'm gonna erase this so that it's not very messy. Hopefully you believe me distance is true. Are that's another one. It's not really an equation. It's just sort of like an accessory that you may need to use. Cool. So if you know the velocity because you've filtered Onley the good particles with the right velocity on do you know the magnetic field? Because you control the device so you can adjust the magnetic fields. And you know the charge. You know the charge because you know how much charge you gave these things over here on the iron Isar? Um, and you and you can you can measure the distance, right? You like, take a picture of this and you see Oh, crap, They're all hitting over here Now I can measure D and from d. I confined are right now, you know, all three, all four variables. Which means you're able to solve for mass. Now, if you want, you can rewrite this and say, you know, mass equals Q B R over V so that it's a more straightforward equation. But now you gotta remember two equations. I don't think it's worth it. I wouldn't really do this. I would just leave it, um, as the standard rotation equation. Circular motion equation. Cool. All right, so there's a lot of a lot of crap, but let's solve a problem here. And I think you'll see that it's not that bad. This is quite a long problem, because I wanna hit a ah lot of different things. So here on, by the way, a lot of the text here just describing how mass spectrometer work. So you get familiar with language. Ah, charge of two. So charge positive to see positive means we're gonna use the right hand rule, not the left. Uh, it's accelerated to an ex accelerating the positive X axis, which is to the rights. So we have a positive charge. So if you want to draw, you don't have to draw. But I'm just gonna draw here. You got your little cues. By the way, there's so you got you here and you are gonna have a little negative there, right? Um, it gets accelerated through a potential difference. Delta Wien Potential difference here. Delta v. Delta V is not given to us. And if you look a question D were being asked for What is Delta V? So that's coming way. Wanna know what that is? Later it then passes through horizontal plates so he gets accelerated here and then he goes here with the constant speed. And then here's accelerated. It's gonna pass through horizontal plates right here. Horizontal plates that have an electric field, three Newtons per Coolum. So electric fields over here E equals three. That points up, by the way, if it points up, it means that you have positive here. Negative here, always high to low. It has a magnetic fields, magnetic fields b equals for Tesla that also exists between the plates. So inside of here, there's a magnetic field and a lot of direction yet so let's not draw that. And remember, here you have sort of the deflection zone because this guy will go straight through here, right? It's gonna go straight through here, and it's going to deflect either this way or that way. We don't know yet, so let's not right that yet on, by the way, the same magnetic field for is also going to exist in this deflection zone over here. Okay, that's what it says here. This magnetic field also exists outside of the plates and causes the charge that deflects in the circular arc of radius five centimeters. So this means that the radius of this deflection is going to be 0. meters. Okay. All right. Question What must? But what must the direction of the magnetic fields be? So the direction of the magnetic field. You will always determine that by looking here. Okay, so you have a positive charge, which means the electric force will be up because the electric force for positive charge goes in the direction of the electric field. The backwards if you have a negative charge. Therefore you want your magnetic charge to be going down. That's the step. Now, we're gonna use the right hand rule to determine the direction that the magnetic field has toe have so that you actually get forced down. So forced down means palm down. And it could be this, but actually, my charge is supposed to be, um, going to the right. So you end up with something like this, Okay? Actually, that's bad, because now my palm is up. So you actually do this. Okay, So you're fingers were pointing towards your face. Your thumb is to the right. Please do this. Now. My force is down, which is what we want. What this means That my fingers were coming at my face, which means they're popping out of the page into me. Which means that this is a direction of out of the page, which is given by a dots. So the direction of magnetic fields is little dots everywhere, right? The little dots everywhere. Lots of little dots. So it's going to look like this. So what is the direction? The direction is out of the page and we got the first part done sketch the deflection that the charge will experience. There's two options here, and it's either going to be like this or like this, right? Uh, and that will depend on the direction of the force. So the direction of the magnetic force, the magnetic force will be the same out here, and because this is being pulled down, it's goingto arc down. Okay, so that's the sketch. We got the sketch done. Uh, they could have asked. Is this gonna are up or down? It's our king down. Okay. And then now we want to calculate the mass of the charge. Right. So now we're actually gonna start calculating stuff. How do we do this? Well, we have three equations you can think of it. It's sort of a menu on. I'm gonna write them here. One is Q. Delta V equals the change in kinetic energy. Or you can write Que Delta V equals of final kinetic energy. Right square. That's Equation one. The second equation is V equals and we wrote this up there. The equals e b you ever be. And the third equation is the radius one M V over Cuba. Be So that's it. Those are the three equations. That's all you gotta play with now. This is just an algebra problem, and I'm gonna get out of the way. So we're looking for Mass. Where do you see Mass? There's mass here and there's mass here. So let's see. Do I know Delta V? I don't know. Delta V Do I know the velocity? We don't know the velocity either, and I know Q So this equation is kind of ugly. I have two unknowns and I'm looking for em. I have three unknowns. That's terrible. What about this equation? Do I know V? I don't know, V, but I know que I know. Be right. I know. CUC used to I know BBS for And I know our because the radius is five centimeters. So I know this as well, so the situation is still not totally ready. But at least here I have three unknowns, which is bad news. And here I only have two. So this equation is not as bad. But before I can find em, I'm gonna have to find V. Well, there's a V here and there's a V here, right? And this is just problem solving skills, this equation. We already said it was bad. So let's try to get the V from here. Do I know E and B? And I do. So the first thing we're gonna do is actually do V equals E Overbey and is three Bs four. So the answer is gonna be 75 meters per second for this part. Now I got V. That's good news, so we can find em. So I'm gonna rearrange this equation. M is going to be Q b R over V please. It is. Carefully move this stuff around carefully and cue is to B is four are is 0. points, five in all of that, divided by V. V s 75 okay. And if you do all of this, if you do all of this, you get that. The answer is points. 53 kilograms. Okay, 0.53 kg. That is the mass. So we're done with part. See, now we're just down to part D, which is finding Delta V, Delta V shows up in this equation on Lee. So that's what we're gonna go for. Okay, we're running out of space here, but we're gonna right. The Delta V equals M v. Final square, divided by cute. Okay, the mass is points 53. The velocity square is 0.75 square, and the charge we know is too right here. So if you plug all of this in you get 0.0 75 volts. That's the potential difference that this thing must have been accelerated through. Okay, so this was a long video, and this was a long example, but I wanted to move slowly through explaining the spectrometer. Eso you understand? All the characteristics, all the properties. And I wanted to do a long example where we talked about a bunch of different things and I wanted to move through that slowly as well But hopefully you're seeing that all you gotta do, no matter what the questions were asked of you is just use a combination of these three things as well as think about directions with the right hand rule. Cool. That's it for this one. Let's get going.

2

Problem

A negative charge in a spectrometer is accelerated in the negative x-axis. It is later deflected and collides some distance ABOVE velocity selector. What are the orientations of the electric and magnetic fields, respectively, inside the selector?

A

up and out of the page

B

up and into the page

C

down and out of the page

D

down and into the page

3

Problem

A 2 kg, −3 C charge is accelerated through a potential difference of 4 V. The velocity selector has an electric field of magnitude 5 N/C. How far from the velocity selector will the charge collide against the spectrometer "wall"?

A

0.117 m

B

0.267 m

C

1.60 m

D

3.20 m

E

6.69 m

F

38.4 m

4

example

## Find Mass-to-Charge Ratio in Spectrometer

4m

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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.