So let's say we do the following. Let's say we, uh, we have our B field. And this region of space has a B field that is everywhere pointing into the screen. What we just said is if we fire a particle, q, into this region and it's a positive charge it's going to feel a force and it's going to bend like that. Okay. Now the speed of that particle coming out over here is exactly equal to the speed of the particle when it went in. And that's because magnetic fields do no work. Can't change the kinetic energy of the particle, the kinetic energy just depends on the speed. And so if it goes in at v, it comes shooting back out at v. All right. How do we determine something about this radius, r, of curvature? Well, we talked about this last time and what we said was that r is just mv divided by qB. If I know the charge, I know the magnetic field, then I can calculate exactly what that radius is. And if I shoot particles into this thing with a known v, then in fact I can determine the mass of the particle. I can determine the mass by measuring that radius of curvature. Anybody know what this device is called? We have one of these here on campus. And it does exactly that, it shoots particles into this region of magnetic field and it measures the radius of curvature of their trajectory. And from that we determine the mass of the particle. This maybe is something that you've heard before. Anybody know what the term is? >>Mass spec. >>Mass spec, right. Mass spectrometer. That's what this device is. We have one over, uh, in the College of Sciences. It's, you know, a million dollar machine, very big, takes up an entire room shoots particles in, measures this curvature in the magnetic field. And therefore can tell you the mass of that particle. All right. Why is that important? Why do you want to measure the mass of something? Well, let's say we do the following experiment. Let's do our mass spec, but now we have two different objects of two different mass. Here's our region of magnetic field. One of those is going to come firing in and take a small radius of curvature. The other particle that comes in is going to take a much bigger radius of curvature. So now you have objects that are coming in that take two different trajectories. You put a detector there and you put a detector there and now whichever one fires you can determine which mass is which. Now if this is m1 and this is m2, then we can calculate exactly what those positions of the detectors need to be. r1 is going to be m1 times v divided by q times B. r2 is m2 times v divided by q times B. Let's take some real numbers from the mass spec here and let's see what these differences are. Right, if this is r1 and this is r2, what are those differences really? So, the q is one electron. Okay, that's the overall q of the particle coming in. Why? Because it was some atom that you knocked off one electron. And so it has a net charge of positive 1.6 times 10 to the minus 19 coulombs. The v of these particles coming in is 6.67 times 10 to the 5 meters per second. Okay, they come in very fast, right? This is part of why the thing is kind of expensive. The B is also a very big magnetic field 0.85 tesla. So this is why it's expensive, because it's hard to make big, strong magnetic fields. Let's tell you the two different masses and let's see if we can calculate the radius of curvature. So, mass number one is 19.93 times 10 to the minus 27 kilograms. Mass number two is 21.59 times 10 to the minus 27 kilograms. And now let's calculate r1 and r2. So r1 we said was m1 v divided by q times B. And we know all those numbers, right? Our m1 is this, 19.93. So somebody grab your calculator and punch this in and let's see what we get. v was 6.7 times ten to the five. q is one electron, which is 1.6 times ten to the minus nineteen coulombs. And B we said was 0.85 tesla. So punch in those numbers for r1 and tell me what you get. And let's do r2 next. For r2, everything's the same except for this one, 21.59 times 10 to the minus 27. We still have everything else the same. Okay? Anybody get a number for r1? >>0.0977. >>Like that? >>Yes. >>And SI units. That should be meters and what about the other one? >> [Inaudible] >>0.1058. >>Okay so this one is, uh, 9.77 centimeters. This one is 10.58 centimeters. So that tells you that your detectors need to be separated on the order of one centimeter. Okay? One centimeter is about, like that.That seems pretty reasonable, right? It seems like you could do that with real detectors. So why do you care about this stuff? Well mass one is not just some arbitrary mass. It is something very specific. Anybody know what that mass corresponds to? It is the mass of carbon-12. Anybody know what this mass is? It's the mass of carbon-13, right? Carbon-13 has an extra neutron on it and so it's heavier than carbon-12. And this is how you do stuff like carbon dating. You look at the ratio of carbon-12 to carbon-13 and this tells you how old something is. So mass spec is a way to date things. Right? How old is this chunk of material? Do carbon dating on it.