The masa spectrometer. In a sample of ordinary carbon, most of the carbon atoms consist of six electrons bound to a nucleus of six protons and six neutrons. But a small fraction of the carbon atoms in the sample will be alightly heavier, consisting of six electrons, six protons, and eight neutrons. electrons). When the ions emerge from the ionizing chamber, they are accelerated through a potential difference Vo, at which point they enter a uniform magnetic field Bo as shown. The magnetic field deflects the ions into a circular path, and they eventually collide with a detector plate. The reason this whole scheme works is that ions of different isotopes will end up in different places on the detector plate. This allows identification of abundances of the isotopes. Nucli fer iwo isopes of carbon (schemai) the relative In this problem we will determine the separation of C and 14C on the detactor plate. As you can see, the massea of these isotopes are very nearly M12 = 12m, and M14 = 14 mp. respectively, where m, = 1.67x107 lkg is the mass of a proton. a) How fast ia a 1C ion going when it enters the magnetic field? Answer in terms of Vo, mp, and e. (For simplicity, assume that the ions umerging from the ionizing chamber are at rest.) Because these isotopes are the same as far as their charged constituents, their chemical properties are for all practical purposes identical. So we cannot separate these isotopen from one another via chemical proceduros. b) Draw a force diagram for a 1C ion when it is traveling inside the magnetic field in a circular path with the speed caleulated in part (a). (Neglect gravity.) A mass spectrometer uses a magnetic field to separate the isotopos as follows. c) Use Newton's Second Law Fnm - ma to determine the radius of the 1C ion's circular path. Answer in terms of Vo, Bo, mp, and e. d) Looking at your answer for part (c), write down an expression for the radius of a 14C ion's circular path within the magnetie field. detector plte accelerator separator ionizing chamber e) What is the soparation of the ions on the detector plate? Answer in terms of Vo, Bo, mp, and e. ) If we want the separation to be at least 1 cm, and the magnetice field we are using is 0.1 Tesla, then how large is the acoelerator voltage Vo going to have to be? In the ionizing chamber, an electric discharge runs through the atoms in the carbon gas, causing them to become singly ionized (which means that they have lost one of their outer g) With the voltage set at this level (and with Bo = 0.1 T), where will the 12C ions strike the detector plate? •