 Here you see a source that provides us with particles whose mass we want to investigate. Positively charged particles, negatively charged, or even neutral particles are shot out of this source. Nobody knows how heavy these particles are. And exactly therefore, you need a mass spectrometer to find out their mass. For a simple mass spectrometer, you first need a velocity selector. This consists of a plate capacitor whose plates are electrically charged. By charging the capacitor, an electric field is formed between the plates. Each time a particle enters this electric field, it experiences an electric force. This force deflects the particle either downwards or upwards, depending on how you have charged the plate capacitor. You can calculate the electric force acting on the particle with q times e. q is the charge of the particle and e is the electric field strength between the plates. You can control the field strength by changing the electric voltage u at the capacitor. In contrast to the electric field strength, you know the voltage because you set it yourself on the voltmeter. Therefore, you write e as u divided by a. a is the distance between the two plates. Next, you put the plate capacitor into an external magnetic field. So that the formula for mass does not become too complicated, we align it in such a way that its field lines are perpendicular to the direction of the particle's motion and perpendicular to the electric field lines of the plate capacitor. From your point of view, we allow the magnetic field lines to point out of the screen or into the screen. The strength of the magnetic field is described by the so-called magnetic flux density b. The larger b is, the stronger the magnetic field. If a charged particle enters the magnetic field, it experiences a magnetic force, in this case downward. It is also called Lorentz force and its direction can be determined with the so-called right hand rule. If the direction of motion of the particle and the direction of the magnetic field are perpendicular to each other, like here, then you can calculate the Lorentz force with q times v times b. Where v is the velocity of the particle. The knowledge of the velocity is important to determine the mass of the particle. The problem is, you don't know the velocity explicitly. But don't worry, if you now add an aperture to the right side of the capacitor, then you can determine the velocity yourself. With this aperture, you determine which particles are allowed to pass with a certain velocity and which are not. All other particles are stopped by the aperture. This experimental arrangement is called a Velocity Selector, or Wien Filter. A particle that has passed through the aperture must have traveled straight ahead through the electric and magnetic field present in the velocity selector. It was neither deflected by the electric force nor by the magnetic force, because otherwise the particles would not have made it through the aperture. The forces have acted on this particle with the same magnitude, but in opposite directions, which is why it didn't get on the wrong track. You express this balance of forces mathematically by equating the Lorentz force with the electric force. q times v times b is equal to q times u divided by a. To find out the velocity, you rearrange the equation for v. The charge q cancels. What remains is v equals u divided by a times b. So change the electric voltage and the strength of the magnetic field to set your desired velocity. Wonderful. You now have particles with known velocity landing behind the aperture. Now pay attention. This part is very crucial for a mass spectrometer. Behind the aperture there is also a magnetic field. To make the formula for the particle's mass easier at the end, we take the same magnetic field as inside the plate capacitor with the same strength and the same direction. So the particle flies out of the velocity selector into this magnetic field and experiences again a magnetic force, the Lorentz force, which deflects the particle into a circular path. After a short semicircular flight, it lands on a detector plate. On this plate, you can read how far the landing point of the particle is away from the aperture. In other words, you measure the diameter d of the circular path. The particle performs a circular motion because the Lorentz force is perpendicular to the direction of motion and thus acts as a centripetal force. So set the formulas for centripetal force and Lorentz force equal. q times v times b is equal to m times v squared divided by r. Now finally the mass m appears in your equations. It is part of the centripetal force formula, so rearrange the equation for mass. You can replace the velocity of the particles with the formula derived before. Replace it with u divided by a times b and the radius r is simply half of the diameter d. You can measure it at the detector plate. Now you have besides a built mass spectrometer also the corresponding formula to calculate the mass of a charged particle. m is equal to q times a times b squared times d divided by 2 times u. As you can see from the formula, to determine the mass of the particle, you must know the charge of the particle. Otherwise, you can only calculate the specific charge q over m. Furthermore, you obviously cannot determine the mass of uncharged particles, for example neutrons, because they do not experience Lorentz force in the magnetic field. Thus they do not perform a circular motion, but fly unaffected straight ahead. Well, then you cannot determine a circular diameter and the derived formula would make no sense. This formula also tells you some other useful facts about mass spectrometers. If you rearrange the formula for the diameter d, you will find that a heavy particle flies a larger semicircle than a light particle. A larger charge, on the other hand, will cause a smaller semicircle. So, that's it. Now you know how a mass spectrometer works. If you want to know more about it, feel free to visit my physics website when you visit denger.org. With this in mind, bye and see you next time.