1. The mass 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 magnetie 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 the relative abundances of the isotopes. Nuckei lrwo isopes often schenai In this problem we will determine the separation of 1#C and 4C on the detector plate. As you can see, the masses of these isotopes How fast is a 1C ion going when it enters the are very nearly M11 = 12m, and M4 = 14 me. respectively, where m, = 1.67x107 kg is the mass of a proton. magnetic field? Answer in terms of Va, mp, and e. (For simplicity, assume that the ions emerging from the ionizing chamber are at rest.) Because these isotopes are the same as far as b) Draw a force diagram for a #C ion when it is their charged constituents, their chemical properties are for all practical purposes identical. So we cannot separate these isotopes from one another via chemical procedures. traveling inside the magnetic field in a circular path with the speed caleulated in part (m). (Neglect gravity.) c) Use Newton's Second Law Fme = ma to A mass spectrometer uses a magnetic field to separate the isotopes as follows. determine the radius of the 1#C 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 magnetic field. detector ple accelerator separator ionizing chamber e) What is the separation of the ions on the detector plate? Answer in terms of Vo, Bo, m, and e. Đ If we want the separation to be at least 1 em, and the magnetie 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 Be = 0.1 T), where will the 12C ions strike the detector plate? •