1. Leo decided he needed to build a cyclotron for his lab like we discussed in class and he tried to follow the diagram in the lecture slides for the patent issued to E. O. Lawrence in 1932, for which he got the Nobel prize in physics. Remember it works by constructing two D-shaped electrodes on which are put a potential difference, and inside of which charged particles such as ionized atoms are inserted. A simplified graphic is shown in the inset figure on the left. Below is a top view Magnetic field perpendicular of his final cyclotron. The way it works is to electrodes that first, in the figure labeled 1 below, a positively charged particle (an ion) is electrodes inserted at point A, and then it is accelerated from the lower electrode to the upper one by the potential difference AV into the space inside the upper electrode. Then the magnetic field exerts a force on the particle and causes it to describe an arc of a circle, until it gets to point B, shown in Figure 2, below. D shaped D shaped D shaped electrode electrode electrode 1 3 +V B B +V +V C A D D shaped D shaped D shaped electrode electrode electrodeAt just the right time, the potentials on the electrodes are reversed so the lower plate is positive and upper one is negative and the particle is accelerated in the gap between them, gaining more energy, finally entering the space inside the lower electrode. Inside the lower electrode the magnetic field (still going into the paper in the figure) causes the particle to again follow a half circle (in the direction shown by the arrow in the figure labelled 2, until it gets to point C shown in the figure labelled 3. There, the particle again gains energy going between the two electrodes, on which the potential has been reversed again at just the right time. Now the magnetic field again causes the particle to follow a half circle until it gts to point D, where it is allowed to exit the electrode and be used in an experiment. For his first experiment, he inserted a singly ionized ( i.e. lacking one electron) carbon atom (12 atomic mass units, amu), and put a potential difference on the electrodes of 500 V. He set the magnetic field value to be 5.5 x 10 T = 55 gauss. Note 1 amu = 1.660540199E-27 kg a) What was the energy of the ion in eV at the end of its path at point D? b) What was the velocity of the ion at point D? c) What was the radius of the final half circle from point C to point D? d) If instead of singly ionized carbon (12 amu) he wanted to run another experiment with singly ionized oxygen atoms (16 amu) how could he adjust the potential difference and the magnetic field strength to keep the radius of the final half circle the same